[
  {
    "name": "simulated_learning",
    "input": {
      "x": [
        [
          1,
          1.83,
          56.39
        ],
        [
          1,
          2.49,
          61.62
        ],
        [
          1,
          1.52,
          34.88
        ],
        [
          1,
          4.85,
          78.07
        ],
        [
          1,
          2.6,
          66.36
        ],
        [
          1,
          9.7,
          81.6
        ],
        [
          1,
          10.7,
          75.03
        ],
        [
          1,
          10.83,
          80.27
        ],
        [
          1,
          8.16,
          81.41
        ],
        [
          1,
          4.2,
          59.63
        ],
        [
          1,
          11.8,
          84.54
        ],
        [
          1,
          7.45,
          71.37
        ],
        [
          1,
          11.99,
          86.19
        ],
        [
          1,
          2.59,
          50.28
        ],
        [
          1,
          1.92,
          45.47
        ],
        [
          1,
          10.05,
          83.86
        ],
        [
          1,
          3.83,
          50.96
        ],
        [
          1,
          2.02,
          28.23
        ],
        [
          1,
          10.73,
          83.28
        ],
        [
          1,
          1.58,
          50.61
        ],
        [
          1,
          6.63,
          65.27
        ],
        [
          1,
          4.48,
          58.04
        ],
        [
          1,
          2.67,
          58.73
        ],
        [
          1,
          8.37,
          75.27
        ],
        [
          1,
          4.04,
          64.07
        ],
        [
          1,
          9.04,
          72.06
        ],
        [
          1,
          7.51,
          70.66
        ],
        [
          1,
          9.3,
          88.99
        ],
        [
          1,
          3.19,
          48.59
        ],
        [
          1,
          1.3,
          39.56
        ],
        [
          1,
          6.15,
          70.58
        ],
        [
          1,
          9.61,
          87.11
        ],
        [
          1,
          10.8,
          71.4
        ],
        [
          1,
          10.65,
          74.56
        ],
        [
          1,
          1.48,
          49.19
        ],
        [
          1,
          4.19,
          48.81
        ],
        [
          1,
          1.76,
          48.94
        ],
        [
          1,
          9.84,
          70.92
        ],
        [
          1,
          5.65,
          79.16
        ],
        [
          1,
          11.71,
          93.65
        ],
        [
          1,
          10.41,
          87.76
        ],
        [
          1,
          4.5,
          74.61
        ],
        [
          1,
          8.76,
          58.68
        ],
        [
          1,
          3.39,
          42.27
        ],
        [
          1,
          8.26,
          66.12
        ],
        [
          1,
          5.08,
          73.77
        ],
        [
          1,
          10.19,
          72.85
        ],
        [
          1,
          11.97,
          79.13
        ],
        [
          1,
          11.61,
          84.14
        ],
        [
          1,
          4.79,
          64.25
        ],
        [
          1,
          9.25,
          69.29
        ],
        [
          1,
          4.78,
          58.54
        ],
        [
          1,
          2.39,
          48.95
        ],
        [
          1,
          4.81,
          52.58
        ],
        [
          1,
          2.59,
          52.99
        ],
        [
          1,
          7.56,
          69.2
        ],
        [
          1,
          4.29,
          69.75
        ],
        [
          1,
          7.59,
          77.72
        ],
        [
          1,
          8.39,
          79.59
        ],
        [
          1,
          10.55,
          84.76
        ],
        [
          1,
          6.6,
          59.23
        ],
        [
          1,
          9.8,
          83.91
        ],
        [
          1,
          9.78,
          72.62
        ],
        [
          1,
          10.13,
          68.86
        ],
        [
          1,
          10.02,
          75.17
        ],
        [
          1,
          6.1,
          59.55
        ],
        [
          1,
          1.16,
          55.02
        ],
        [
          1,
          10.95,
          95
        ],
        [
          1,
          5.15,
          60.94
        ],
        [
          1,
          8.94,
          60.52
        ],
        [
          1,
          2.31,
          53.74
        ],
        [
          1,
          7.65,
          72.07
        ],
        [
          1,
          10.6,
          74.89
        ],
        [
          1,
          8.62,
          70.42
        ],
        [
          1,
          6.94,
          70.08
        ],
        [
          1,
          4.16,
          51.82
        ],
        [
          1,
          8.52,
          75.87
        ],
        [
          1,
          8.26,
          80.1
        ],
        [
          1,
          7.84,
          77.18
        ],
        [
          1,
          10,
          81.56
        ],
        [
          1,
          6.41,
          61.14
        ],
        [
          1,
          8.08,
          74.06
        ],
        [
          1,
          7.53,
          69.84
        ],
        [
          1,
          9.37,
          71.92
        ],
        [
          1,
          2.5,
          37.32
        ],
        [
          1,
          7.21,
          78.28
        ],
        [
          1,
          2.53,
          53.38
        ],
        [
          1,
          4.98,
          73.13
        ],
        [
          1,
          7.35,
          68.11
        ],
        [
          1,
          5.76,
          60.89
        ],
        [
          1,
          1.25,
          54.01
        ],
        [
          1,
          7.52,
          64.25
        ],
        [
          1,
          1.36,
          40.08
        ],
        [
          1,
          4.68,
          59.68
        ],
        [
          1,
          8.02,
          58.34
        ],
        [
          1,
          6.32,
          56.81
        ],
        [
          1,
          11.98,
          61.9
        ],
        [
          1,
          10.74,
          74.75
        ],
        [
          1,
          7.83,
          66.12
        ],
        [
          1,
          1.76,
          52.3
        ],
        [
          1,
          11.29,
          86.01
        ],
        [
          1,
          8.06,
          56.46
        ],
        [
          1,
          8.97,
          61.82
        ],
        [
          1,
          10.91,
          72.69
        ],
        [
          1,
          1.09,
          31.47
        ],
        [
          1,
          2.99,
          48.2
        ],
        [
          1,
          4.13,
          62.12
        ],
        [
          1,
          2.41,
          66.31
        ],
        [
          1,
          5.97,
          46.22
        ],
        [
          1,
          9.03,
          73.07
        ],
        [
          1,
          9.21,
          79.32
        ],
        [
          1,
          3.14,
          52.42
        ],
        [
          1,
          2.2,
          47.49
        ],
        [
          1,
          1.26,
          38.22
        ],
        [
          1,
          7.2,
          60.45
        ],
        [
          1,
          4.14,
          69.24
        ],
        [
          1,
          6.85,
          59.9
        ],
        [
          1,
          4.83,
          69.45
        ],
        [
          1,
          10.62,
          81.19
        ],
        [
          1,
          11.35,
          67.69
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -1.2516486480529185,
        0.150439105575555,
        -5.373685964953288e-05
      ],
      "covariance": [
        [
          0.49574638391729187,
          0.020751441172230427,
          -0.009352824838575694
        ],
        [
          0.020751441172230427,
          0.0037880870822965484,
          -0.0007035561934037832
        ],
        [
          -0.009352824838575694,
          -0.0007035561934037832,
          0.00021294603715964886
        ]
      ],
      "std_errors": [
        0.7040925961244671,
        0.061547437658253074,
        0.014592670665770843
      ],
      "z_statistics": [
        -1.7776761962025467,
        2.444278938318762,
        -0.003682455451802954
      ],
      "p_values": [
        0.07545705137037936,
        0.014514199888096579,
        0.9970618322896567
      ],
      "conf_int": [
        [
          -2.6316447782381793,
          0.12834748213234248
        ],
        [
          0.029808344424654784,
          0.2710698667264552
        ],
        [
          -0.02865484580281451,
          0.028547372083515443
        ]
      ],
      "fitted": [
        0.16369728683961227,
        0.18933038818409664,
        0.15271567556997936,
        0.2993696865928525,
        0.19377390833499755,
        0.5805207057409745,
        0.6383372675957584,
        0.6455349587980368,
        0.4886555054551864,
        0.26663939132988723,
        0.6981161020520543,
        0.44641959043335383,
        0.7079770925927505,
        0.1935980965120653,
        0.1672100596849044,
        0.6009311428144859,
        0.24882076499986835,
        0.1712394555325807,
        0.6398611765958502,
        0.15465415405090063,
        0.3983019408398941,
        0.2806875121435193,
        0.1967929977876973,
        0.5013890712031029,
        0.25871321230414646,
        0.5415933171655215,
        0.4500052781304514,
        0.5567178775432332,
        0.21935926846335219,
        0.14498130585086313,
        0.3706089738859609,
        0.575106473600061,
        0.6440318687983023,
        0.6355244749444353,
        0.15111990808030362,
        0.2663362230969559,
        0.1612078902038669,
        0.5889563467113352,
        0.3424001358803528,
        0.6932068230365533,
        0.6216079181006213,
        0.2814018885668942,
        0.525134520440419,
        0.2284589474004137,
        0.4949835458648132,
        0.3115780898754522,
        0.6092677731904086,
        0.7070734613352531,
        0.6880844481092385,
        0.2964985421470724,
        0.5541643220804043,
        0.2960845142891703,
        0.18546582444516074,
        0.2977571942164481,
        0.1935581244086657,
        0.45301497085536463,
        0.2709265877104149,
        0.4546219623706678,
        0.5024967763561548,
        0.6296510097362015,
        0.39668640003435296,
        0.5863421368557351,
        0.5854061284195601,
        0.6058809249526564,
        0.5993680783962796,
        0.36799432501603735,
        0.14004974148389915,
        0.6519367391835172,
        0.3155561101060854,
        0.5358662467698234,
        0.1821975465350638,
        0.45832188659406153,
        0.6326881732339106,
        0.5164924772875306,
        0.41630040013426695,
        0.2648033149567762,
        0.5103775186331073,
        0.49468386908598055,
        0.4695689430599854,
        0.5980719168938007,
        0.38567119033308456,
        0.48401450319483946,
        0.45121384152931543,
        0.5612349564972694,
        0.1900922647530744,
        0.43203749248177853,
        0.1910846732128424,
        0.3062908574672974,
        0.4405475051422215,
        0.34886318994904597,
        0.14309836633456882,
        0.45073714554799116,
        0.14704183424488532,
        0.29088516935554587,
        0.4807537075791541,
        0.38059202335964437,
        0.7079087066258082,
        0.6405953213534987,
        0.4692069504793542,
        0.16116374644732562,
        0.6708230344404013,
        0.4831921753169088,
        0.5376313456688957,
        0.6501538495922274,
        0.1379973344092275,
        0.21057554170154166,
        0.26314703451773547,
        0.18602132746686525,
        0.36091619910285044,
        0.5409748322169149,
        0.5515716455127256,
        0.21708179868340585,
        0.17794248609566501,
        0.14363055834735977,
        0.4318227451678413,
        0.2635132866172604,
        0.4112387469925449,
        0.2984860463431296,
        0.6336935092340839,
        0.6744367363167406
      ],
      "residuals": [
        -0.16369728683961227,
        -0.18933038818409664,
        0.8472843244300207,
        -0.2993696865928525,
        0.8062260916650025,
        0.4194792942590255,
        0.3616627324042416,
        0.3544650412019632,
        0.5113444945448136,
        -0.26663939132988723,
        0.3018838979479457,
        -0.44641959043335383,
        -0.7079770925927505,
        -0.1935980965120653,
        -0.1672100596849044,
        -0.6009311428144859,
        -0.24882076499986835,
        -0.1712394555325807,
        0.3601388234041498,
        -0.15465415405090063,
        0.6016980591601059,
        -0.2806875121435193,
        -0.1967929977876973,
        -0.5013890712031029,
        -0.25871321230414646,
        -0.5415933171655215,
        0.5499947218695487,
        0.4432821224567668,
        -0.21935926846335219,
        -0.14498130585086313,
        0.6293910261140391,
        -0.575106473600061,
        0.3559681312016977,
        0.3644755250555647,
        -0.15111990808030362,
        -0.2663362230969559,
        -0.1612078902038669,
        -0.5889563467113352,
        -0.3424001358803528,
        -0.6932068230365533,
        0.3783920818993787,
        -0.2814018885668942,
        -0.525134520440419,
        -0.2284589474004137,
        -0.4949835458648132,
        -0.3115780898754522,
        0.3907322268095914,
        0.29292653866474694,
        0.3119155518907615,
        -0.2964985421470724,
        -0.5541643220804043,
        -0.2960845142891703,
        -0.18546582444516074,
        0.7022428057835519,
        -0.1935581244086657,
        0.5469850291446354,
        -0.2709265877104149,
        -0.4546219623706678,
        -0.5024967763561548,
        -0.6296510097362015,
        -0.39668640003435296,
        -0.5863421368557351,
        -0.5854061284195601,
        -0.6058809249526564,
        0.4006319216037204,
        0.6320056749839627,
        -0.14004974148389915,
        0.34806326081648276,
        0.6844438898939146,
        -0.5358662467698234,
        0.8178024534649362,
        -0.45832188659406153,
        0.3673118267660894,
        -0.5164924772875306,
        0.583699599865733,
        -0.2648033149567762,
        -0.5103775186331073,
        0.5053161309140195,
        -0.4695689430599854,
        0.4019280831061993,
        -0.38567119033308456,
        0.5159854968051605,
        0.5487861584706846,
        -0.5612349564972694,
        -0.1900922647530744,
        -0.43203749248177853,
        -0.1910846732128424,
        0.6937091425327027,
        -0.4405475051422215,
        -0.34886318994904597,
        -0.14309836633456882,
        -0.45073714554799116,
        -0.14704183424488532,
        0.7091148306444541,
        -0.4807537075791541,
        0.6194079766403556,
        0.2920912933741918,
        0.3594046786465013,
        0.5307930495206459,
        0.8388362535526743,
        0.32917696555959874,
        0.5168078246830912,
        0.4623686543311043,
        -0.6501538495922274,
        -0.1379973344092275,
        0.7894244582984583,
        -0.26314703451773547,
        -0.18602132746686525,
        -0.36091619910285044,
        0.4590251677830851,
        0.44842835448727436,
        0.7829182013165942,
        -0.17794248609566501,
        -0.14363055834735977,
        0.5681772548321586,
        0.7364867133827395,
        -0.4112387469925449,
        -0.2984860463431296,
        0.36630649076591615,
        0.3255632636832594
      ],
      "log_likelihood": -72.92760485518879,
      "deviance": 145.85520971037755,
      "null_deviance": 162.2990865129829,
      "aic": 151.85520971037758,
      "df_residual": 117
    },
    "statsmodels": {
      "coefficients": [
        -1.2516486481792626,
        0.1504391055607626,
        -5.373685641417176e-05
      ],
      "covariance": [
        [
          0.49574638406524896,
          0.02075144116500321,
          -0.009352824839753835
        ],
        [
          0.02075144116500321,
          0.003788087079757051,
          -0.0007035561930192478
        ],
        [
          -0.009352824839753835,
          -0.0007035561930192478,
          0.0002129460371313448
        ]
      ],
      "std_errors": [
        0.7040925962295363,
        0.061547437637622666,
        0.01459267066480104
      ],
      "z_statistics": [
        -1.7776761961167127,
        2.444278938897731,
        -0.0036824552303363054
      ],
      "p_values": [
        0.07545705138448477,
        0.014514199864802301,
        0.9970618324663604
      ],
      "conf_int": [
        [
          -2.6316447785704558,
          0.12834748221193082
        ],
        [
          0.029808344450297175,
          0.271069866671228
        ],
        [
          -0.028654845797678376,
          0.028547372084850035
        ]
      ],
      "fitted": [
        0.16369728684678098,
        0.18933038819389492,
        0.15271567556148974,
        0.29936968661178276,
        0.19377390834870112,
        0.5805207057386981,
        0.6383372675800679,
        0.6455349587880485,
        0.48865550546170267,
        0.2666393913313501,
        0.6981161020425085,
        0.44641959043112417,
        0.7079770925842168,
        0.1935980965115211,
        0.16721005968299318,
        0.600931142813061,
        0.2488207649941231,
        0.17123945551608338,
        0.6398611765900035,
        0.15465415405423777,
        0.3983019408347825,
        0.2806875121418902,
        0.19679299779439918,
        0.5013890712004576,
        0.25871321231100025,
        0.5415933171548375,
        0.45000527812695856,
        0.5567178775527114,
        0.21935926845852632,
        0.14498130584685592,
        0.3706089738901295,
        0.5751064736052854,
        0.6440318687777703,
        0.6355244749284101,
        0.1511199080828602,
        0.2663362230869711,
        0.16120789020532417,
        0.5889563466948231,
        0.3424001358973226,
        0.6932068230377574,
        0.621607918101991,
        0.2814018885832532,
        0.5251345204141113,
        0.22845894738839467,
        0.49498354585100796,
        0.31157808988859914,
        0.6092677731745224,
        0.7070734613189533,
        0.6880844481000907,
        0.2964985421507632,
        0.5541643220649909,
        0.296084514286525,
        0.1854658244442713,
        0.29775719420696056,
        0.1935581244105281,
        0.4530149708497042,
        0.27092658772229306,
        0.4546219623757546,
        0.5024967763589673,
        0.6296510097331139,
        0.3966864000218848,
        0.5863421368558012,
        0.5854061284055044,
        0.605880924932106,
        0.5993680783841582,
        0.36799432500702495,
        0.14004974149158134,
        0.6519367391905547,
        0.31555611010417917,
        0.5358662467448775,
        0.18219754653859455,
        0.4583218865915486,
        0.6326881732185247,
        0.5164924772771586,
        0.4163004001333816,
        0.2648033149501544,
        0.5103775186303521,
        0.4946838690902181,
        0.4695689430629245,
        0.5980719168897807,
        0.3856711903241531,
        0.4840145031923457,
        0.45121384152465377,
        0.5612349564845507,
        0.19009226474151586,
        0.43203749248974616,
        0.1910846732152754,
        0.30629085748013873,
        0.4405475051364192,
        0.34886318994366416,
        0.143098366341325,
        0.45073714553622857,
        0.1470418342410228,
        0.2908851693546936,
        0.4807537075567484,
        0.38059202334591874,
        0.7079087065903333,
        0.640595321337282,
        0.469206950468119,
        0.16116374645144022,
        0.6708230344349466,
        0.4831921752918366,
        0.5376313456454542,
        0.6501538495727657,
        0.13799733440026785,
        0.2105755416973188,
        0.2631470345221558,
        0.18602132748093858,
        0.3609161990784679,
        0.5409748322075846,
        0.5515716455103704,
        0.2170817986824672,
        0.17794248609430002,
        0.1436305583425299,
        0.43182274515318964,
        0.26351328662915924,
        0.411238746979367,
        0.29848604635246256,
        0.6336935092262711,
        0.6744367362896428
      ],
      "residuals": [
        -0.16369728684678098,
        -0.18933038819389492,
        0.8472843244385102,
        -0.29936968661178276,
        0.8062260916512989,
        0.4194792942613019,
        0.3616627324199321,
        0.35446504121195155,
        0.5113444945382973,
        -0.2666393913313501,
        0.3018838979574915,
        -0.44641959043112417,
        -0.7079770925842168,
        -0.1935980965115211,
        -0.16721005968299318,
        -0.600931142813061,
        -0.2488207649941231,
        -0.17123945551608338,
        0.3601388234099965,
        -0.15465415405423777,
        0.6016980591652175,
        -0.2806875121418902,
        -0.19679299779439918,
        -0.5013890712004576,
        -0.25871321231100025,
        -0.5415933171548375,
        0.5499947218730414,
        0.4432821224472886,
        -0.21935926845852632,
        -0.14498130584685592,
        0.6293910261098705,
        -0.5751064736052854,
        0.3559681312222297,
        0.36447552507158987,
        -0.1511199080828602,
        -0.2663362230869711,
        -0.16120789020532417,
        -0.5889563466948231,
        -0.3424001358973226,
        -0.6932068230377574,
        0.378392081898009,
        -0.2814018885832532,
        -0.5251345204141113,
        -0.22845894738839467,
        -0.49498354585100796,
        -0.31157808988859914,
        0.3907322268254776,
        0.2929265386810467,
        0.31191555189990927,
        -0.2964985421507632,
        -0.5541643220649909,
        -0.296084514286525,
        -0.1854658244442713,
        0.7022428057930394,
        -0.1935581244105281,
        0.5469850291502958,
        -0.27092658772229306,
        -0.4546219623757546,
        -0.5024967763589673,
        -0.6296510097331139,
        -0.3966864000218848,
        -0.5863421368558012,
        -0.5854061284055044,
        -0.605880924932106,
        0.4006319216158418,
        0.632005674992975,
        -0.14004974149158134,
        0.3480632608094453,
        0.6844438898958208,
        -0.5358662467448775,
        0.8178024534614055,
        -0.4583218865915486,
        0.36731182678147534,
        -0.5164924772771586,
        0.5836995998666183,
        -0.2648033149501544,
        -0.5103775186303521,
        0.5053161309097819,
        -0.4695689430629245,
        0.4019280831102193,
        -0.3856711903241531,
        0.5159854968076543,
        0.5487861584753462,
        -0.5612349564845507,
        -0.19009226474151586,
        -0.43203749248974616,
        -0.1910846732152754,
        0.6937091425198613,
        -0.4405475051364192,
        -0.34886318994366416,
        -0.143098366341325,
        -0.45073714553622857,
        -0.1470418342410228,
        0.7091148306453063,
        -0.4807537075567484,
        0.6194079766540812,
        0.29209129340966666,
        0.35940467866271797,
        0.530793049531881,
        0.8388362535485598,
        0.3291769655650534,
        0.5168078247081633,
        0.46236865435454577,
        -0.6501538495727657,
        -0.13799733440026785,
        0.7894244583026813,
        -0.2631470345221558,
        -0.18602132748093858,
        -0.3609161990784679,
        0.4590251677924154,
        0.4484283544896296,
        0.7829182013175329,
        -0.17794248609430002,
        -0.1436305583425299,
        0.5681772548468104,
        0.7364867133708408,
        -0.411238746979367,
        -0.29848604635246256,
        0.3663064907737289,
        0.32556326371035715
      ],
      "log_likelihood": -72.92760485518878,
      "deviance": 145.85520971037755,
      "null_deviance": 162.29908651298285,
      "aic": 151.85520971037755,
      "df_residual": 117
    },
    "phit": {
      "coefficients": [
        -1.2516486482422335,
        0.15043910556634585,
        -5.373685624978972e-05
      ],
      "covariance": [
        [
          0.4957463840845633,
          0.02075144116512848,
          -0.009352824840031953
        ],
        [
          0.02075144116512848,
          0.0037880870798565566,
          -0.0007035561930330633
        ],
        [
          -0.009352824840031955,
          -0.0007035561930330633,
          0.00021294603713682139
        ]
      ],
      "std_errors": [
        0.7040925962432522,
        0.06154743763843103,
        0.014592670664988688
      ],
      "z_statistics": [
        -1.7776761961715188,
        2.4442789389563426,
        -0.003682455219024254
      ],
      "p_values": [
        0.0754570513719971,
        0.014514199861824251,
        0.997061832475386
      ],
      "conf_int": [
        [
          -2.631644778660309,
          0.12834748217584235
        ],
        [
          0.029808344454296087,
          0.2710698666783956
        ],
        [
          -0.028654845797881773,
          0.028547372085382196
        ]
      ],
      "fitted": [
        0.1636972868502152,
        0.18933038820063852,
        0.1527156755629273,
        0.2993696866037732,
        0.1937739083562546,
        0.5805207057404959,
        0.6383372675834791,
        0.6455349587920266,
        0.48865550546009606,
        0.26663939132158543,
        0.6981161020483693,
        0.4464195904273117,
        0.7079770925904467,
        0.19359809651831625,
        0.1672100596863615,
        0.6009311428157352,
        0.2488207649835963,
        0.17123945551917413,
        0.6398611765939799,
        0.15465415405648733,
        0.3983019408289072,
        0.280687512132313,
        0.19679299780201578,
        0.5013890711989154,
        0.25871321230133226,
        0.5415933171545785,
        0.450005278123228,
        0.5567178775541258,
        0.21935926846899378,
        0.14498130584774588,
        0.3706089738836954,
        0.5751064736072462,
        0.6440318687811485,
        0.6355244749316964,
        0.15111990808470202,
        0.26633622307660965,
        0.1612078902081856,
        0.5889563466962338,
        0.3424001358905578,
        0.6932068230440098,
        0.621607918105633,
        0.2814018885746211,
        0.5251345204123534,
        0.22845894740002826,
        0.49498354584862087,
        0.3115780898806504,
        0.6092677731767865,
        0.7070734613247545,
        0.688084448105638,
        0.2964985421418871,
        0.5541643220650164,
        0.29608451427731086,
        0.1854658244499494,
        0.2977571941974413,
        0.19355812441744163,
        0.45301497084598574,
        0.2709265877131672,
        0.45462196237265584,
        0.5024967763577528,
        0.6296510097368401,
        0.3966864000155687,
        0.5863421368579587,
        0.5854061284068963,
        0.6058809249339943,
        0.5993680783862183,
        0.3679943249998172,
        0.14004974148796917,
        0.6519367391956492,
        0.31555611009557616,
        0.5358662467436426,
        0.18219754654407513,
        0.4583218865882111,
        0.6326881732217348,
        0.5164924772758563,
        0.41630040012842584,
        0.26480331493993037,
        0.5103775186291838,
        0.4946838690887478,
        0.46956894306033453,
        0.5980719168922057,
        0.3856711903176011,
        0.48401450319008,
        0.45121384152091265,
        0.5612349564850106,
        0.1900922647472625,
        0.4320374924858747,
        0.1910846732218779,
        0.30629085747201634,
        0.44054750513218316,
        0.3488631899359682,
        0.1430983663378256,
        0.4507371455321022,
        0.14704183424212272,
        0.29088516934542763,
        0.4807537075533203,
        0.3805920233389301,
        0.7079087065951732,
        0.6405953213407523,
        0.46920695046478383,
        0.16116374645443357,
        0.670823034440085,
        0.48319217528837344,
        0.5376313456443712,
        0.650153849576429,
        0.13799733439569392,
        0.21057554170641682,
        0.26314703451246235,
        0.18602132748746053,
        0.36091619907021477,
        0.5409748322073693,
        0.5515716455109598,
        0.2170817986927641,
        0.17794248609898863,
        0.1436305583384624,
        0.43182274514814445,
        0.26351328661985934,
        0.41123874697357876,
        0.2984860463439334,
        0.6336935092299101,
        0.6744367362937942
      ],
      "residuals": [
        -0.1636972868502152,
        -0.18933038820063852,
        0.8472843244370727,
        -0.2993696866037732,
        0.8062260916437454,
        0.41947929425950414,
        0.3616627324165209,
        0.3544650412079734,
        0.5113444945399039,
        -0.26663939132158543,
        0.30188389795163073,
        -0.4464195904273117,
        -0.7079770925904467,
        -0.19359809651831625,
        -0.1672100596863615,
        -0.6009311428157352,
        -0.2488207649835963,
        -0.17123945551917413,
        0.3601388234060201,
        -0.15465415405648733,
        0.6016980591710928,
        -0.280687512132313,
        -0.19679299780201578,
        -0.5013890711989154,
        -0.25871321230133226,
        -0.5415933171545785,
        0.549994721876772,
        0.44328212244587417,
        -0.21935926846899378,
        -0.14498130584774588,
        0.6293910261163046,
        -0.5751064736072462,
        0.3559681312188515,
        0.3644755250683036,
        -0.15111990808470202,
        -0.26633622307660965,
        -0.1612078902081856,
        -0.5889563466962338,
        -0.3424001358905578,
        -0.6932068230440098,
        0.378392081894367,
        -0.2814018885746211,
        -0.5251345204123534,
        -0.22845894740002826,
        -0.49498354584862087,
        -0.3115780898806504,
        0.3907322268232135,
        0.29292653867524554,
        0.31191555189436204,
        -0.2964985421418871,
        -0.5541643220650164,
        -0.29608451427731086,
        -0.1854658244499494,
        0.7022428058025587,
        -0.19355812441744163,
        0.5469850291540143,
        -0.2709265877131672,
        -0.45462196237265584,
        -0.5024967763577528,
        -0.6296510097368401,
        -0.3966864000155687,
        -0.5863421368579587,
        -0.5854061284068963,
        -0.6058809249339943,
        0.4006319216137817,
        0.6320056750001828,
        -0.14004974148796917,
        0.3480632608043508,
        0.6844438899044238,
        -0.5358662467436426,
        0.8178024534559248,
        -0.4583218865882111,
        0.36731182677826524,
        -0.5164924772758563,
        0.5836995998715742,
        -0.26480331493993037,
        -0.5103775186291838,
        0.5053161309112522,
        -0.46956894306033453,
        0.40192808310779427,
        -0.3856711903176011,
        0.51598549680992,
        0.5487861584790874,
        -0.5612349564850106,
        -0.1900922647472625,
        -0.4320374924858747,
        -0.1910846732218779,
        0.6937091425279837,
        -0.44054750513218316,
        -0.3488631899359682,
        -0.1430983663378256,
        -0.4507371455321022,
        -0.14704183424212272,
        0.7091148306545724,
        -0.4807537075533203,
        0.6194079766610698,
        0.29209129340482676,
        0.35940467865924774,
        0.5307930495352162,
        0.8388362535455665,
        0.32917696555991505,
        0.5168078247116266,
        0.4623686543556288,
        -0.650153849576429,
        -0.13799733439569392,
        0.7894244582935832,
        -0.26314703451246235,
        -0.18602132748746053,
        -0.36091619907021477,
        0.4590251677926307,
        0.44842835448904017,
        0.7829182013072359,
        -0.17794248609898863,
        -0.1436305583384624,
        0.5681772548518556,
        0.7364867133801407,
        -0.41123874697357876,
        -0.2984860463439334,
        0.3663064907700899,
        0.3255632637062058
      ],
      "log_likelihood": -72.92760485505298,
      "deviance": 145.85520971010595,
      "null_deviance": 162.2990865129829,
      "aic": 151.85520971010595,
      "df_residual": 117,
      "iterations": 9,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 1.263440463361576e-10,
        "phit": 1.8931500811447677e-10
      },
      "covariance": {
        "statsmodels": 1.479570910234429e-10,
        "phit": 1.6727141893824182e-10
      },
      "std_errors": {
        "statsmodels": 1.0506928660447556e-10,
        "phit": 1.187850928729972e-10
      },
      "z_statistics": {
        "statsmodels": 5.789688728441433e-10,
        "phit": 6.375806549385743e-10
      },
      "p_values": {
        "statsmodels": 1.7670365171085223e-10,
        "phit": 1.857293208118449e-10
      },
      "conf_int": {
        "statsmodels": 3.3227642859401385e-10,
        "phit": 4.221298866013967e-10
      },
      "fitted": {
        "statsmodels": 3.5474845283545164e-11,
        "phit": 3.263567194267125e-11
      },
      "residuals": {
        "statsmodels": 3.5474845283545164e-11,
        "phit": 3.263567194267125e-11
      },
      "log_likelihood": {
        "statsmodels": 1.4210854715202004e-14,
        "phit": 1.3581313851318555e-10
      },
      "deviance": {
        "statsmodels": 0.0,
        "phit": 2.715978553169407e-10
      },
      "null_deviance": {
        "statsmodels": 5.684341886080802e-14,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 2.842170943040401e-14,
        "phit": 2.716262770263711e-10
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "simple",
    "input": {
      "x": [
        [
          1,
          1.83
        ],
        [
          1,
          2.49
        ],
        [
          1,
          1.52
        ],
        [
          1,
          4.85
        ],
        [
          1,
          2.6
        ],
        [
          1,
          9.7
        ],
        [
          1,
          10.7
        ],
        [
          1,
          10.83
        ],
        [
          1,
          8.16
        ],
        [
          1,
          4.2
        ],
        [
          1,
          11.8
        ],
        [
          1,
          7.45
        ],
        [
          1,
          11.99
        ],
        [
          1,
          2.59
        ],
        [
          1,
          1.92
        ],
        [
          1,
          10.05
        ],
        [
          1,
          3.83
        ],
        [
          1,
          2.02
        ],
        [
          1,
          10.73
        ],
        [
          1,
          1.58
        ],
        [
          1,
          6.63
        ],
        [
          1,
          4.48
        ],
        [
          1,
          2.67
        ],
        [
          1,
          8.37
        ],
        [
          1,
          4.04
        ],
        [
          1,
          9.04
        ],
        [
          1,
          7.51
        ],
        [
          1,
          9.3
        ],
        [
          1,
          3.19
        ],
        [
          1,
          1.3
        ],
        [
          1,
          6.15
        ],
        [
          1,
          9.61
        ],
        [
          1,
          10.8
        ],
        [
          1,
          10.65
        ],
        [
          1,
          1.48
        ],
        [
          1,
          4.19
        ],
        [
          1,
          1.76
        ],
        [
          1,
          9.84
        ],
        [
          1,
          5.65
        ],
        [
          1,
          11.71
        ],
        [
          1,
          10.41
        ],
        [
          1,
          4.5
        ],
        [
          1,
          8.76
        ],
        [
          1,
          3.39
        ],
        [
          1,
          8.26
        ],
        [
          1,
          5.08
        ],
        [
          1,
          10.19
        ],
        [
          1,
          11.97
        ],
        [
          1,
          11.61
        ],
        [
          1,
          4.79
        ],
        [
          1,
          9.25
        ],
        [
          1,
          4.78
        ],
        [
          1,
          2.39
        ],
        [
          1,
          4.81
        ],
        [
          1,
          2.59
        ],
        [
          1,
          7.56
        ],
        [
          1,
          4.29
        ],
        [
          1,
          7.59
        ],
        [
          1,
          8.39
        ],
        [
          1,
          10.55
        ],
        [
          1,
          6.6
        ],
        [
          1,
          9.8
        ],
        [
          1,
          9.78
        ],
        [
          1,
          10.13
        ],
        [
          1,
          10.02
        ],
        [
          1,
          6.1
        ],
        [
          1,
          1.16
        ],
        [
          1,
          10.95
        ],
        [
          1,
          5.15
        ],
        [
          1,
          8.94
        ],
        [
          1,
          2.31
        ],
        [
          1,
          7.65
        ],
        [
          1,
          10.6
        ],
        [
          1,
          8.62
        ],
        [
          1,
          6.94
        ],
        [
          1,
          4.16
        ],
        [
          1,
          8.52
        ],
        [
          1,
          8.26
        ],
        [
          1,
          7.84
        ],
        [
          1,
          10
        ],
        [
          1,
          6.41
        ],
        [
          1,
          8.08
        ],
        [
          1,
          7.53
        ],
        [
          1,
          9.37
        ],
        [
          1,
          2.5
        ],
        [
          1,
          7.21
        ],
        [
          1,
          2.53
        ],
        [
          1,
          4.98
        ],
        [
          1,
          7.35
        ],
        [
          1,
          5.76
        ],
        [
          1,
          1.25
        ],
        [
          1,
          7.52
        ],
        [
          1,
          1.36
        ],
        [
          1,
          4.68
        ],
        [
          1,
          8.02
        ],
        [
          1,
          6.32
        ],
        [
          1,
          11.98
        ],
        [
          1,
          10.74
        ],
        [
          1,
          7.83
        ],
        [
          1,
          1.76
        ],
        [
          1,
          11.29
        ],
        [
          1,
          8.06
        ],
        [
          1,
          8.97
        ],
        [
          1,
          10.91
        ],
        [
          1,
          1.09
        ],
        [
          1,
          2.99
        ],
        [
          1,
          4.13
        ],
        [
          1,
          2.41
        ],
        [
          1,
          5.97
        ],
        [
          1,
          9.03
        ],
        [
          1,
          9.21
        ],
        [
          1,
          3.14
        ],
        [
          1,
          2.2
        ],
        [
          1,
          1.26
        ],
        [
          1,
          7.2
        ],
        [
          1,
          4.14
        ],
        [
          1,
          6.85
        ],
        [
          1,
          4.83
        ],
        [
          1,
          10.62
        ],
        [
          1,
          11.35
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -1.254007624143226,
        0.1502609392741857
      ],
      "covariance": [
        [
          0.0849633696511547,
          -0.010149910446861846
        ],
        [
          -0.010149910446861846,
          0.0014636370542523518
        ]
      ],
      "std_errors": [
        0.2914847674427511,
        0.03825750977589043
      ],
      "z_statistics": [
        -4.3021377588436716,
        3.9276194439837515
      ],
      "p_values": [
        1.6915808093635403e-05,
        8.579081692167129e-05
      ],
      "conf_int": [
        [
          -1.8253072703730513,
          -0.6827079779134009
        ],
        [
          0.07527759797525146,
          0.22524428057311996
        ]
      ],
      "fitted": [
        0.1637825523146382,
        0.18946815092212685,
        0.15253749103387387,
        0.29970746179952235,
        0.1939782519395973,
        0.5806370550026221,
        0.6382497770876978,
        0.6455442389639157,
        0.4888795841096844,
        0.26667128135431617,
        0.6981445448813403,
        0.4464784508913207,
        0.708023929524279,
        0.1935655596019874,
        0.16714556072765946,
        0.6010689088670101,
        0.24872475474291436,
        0.17093407198642985,
        0.6399376929632807,
        0.15467298595346074,
        0.3982892777506857,
        0.28067461312704434,
        0.19688208464647472,
        0.5014666830886041,
        0.2588310422478267,
        0.54155470257621,
        0.4500448753550977,
        0.5570204047417948,
        0.21926579624174386,
        0.1448754113044084,
        0.3707366858874774,
        0.5753454356287786,
        0.6438655186082027,
        0.6354306120897124,
        0.15112474768992634,
        0.26617777184812697,
        0.16119745795025164,
        0.5888392143800646,
        0.34272651047717295,
        0.6934129941790947,
        0.6217988929120087,
        0.28168830246447707,
        0.5248293572267569,
        0.2282498177682777,
        0.49487282895001206,
        0.3118256710986974,
        0.6091680519214144,
        0.7069911136750577,
        0.6881176748606179,
        0.2965816181486325,
        0.5540522292665906,
        0.29606209958704544,
        0.18542455584796236,
        0.2976219061125077,
        0.1935655596019874,
        0.4530199932771792,
        0.27113358049864456,
        0.4548063415964266,
        0.5026655753940774,
        0.6297703917548005,
        0.39655069900846496,
        0.5864995340150126,
        0.5853285355347337,
        0.6057025629195656,
        0.5993275714009437,
        0.3679017021718308,
        0.14013679790380798,
        0.652230602079247,
        0.31555546724144057,
        0.5355882555520585,
        0.18222855692483117,
        0.4583817456122471,
        0.6326041033703371,
        0.5164483839271498,
        0.4163668906725431,
        0.2647000229499906,
        0.5104573048357296,
        0.49487282895001206,
        0.469724720807945,
        0.5981655798508149,
        0.38558875654133323,
        0.4840867305768739,
        0.4512345951857745,
        0.561170443567628,
        0.1898754736140949,
        0.43225882726400144,
        0.19110066853745156,
        0.30653077423706176,
        0.4405441593968398,
        0.3488213201415853,
        0.14317081295352432,
        0.450639679831964,
        0.1469388982542079,
        0.2908900443686899,
        0.4804935608175278,
        0.3804273951550693,
        0.7075077334824801,
        0.6404997277337474,
        0.46912702772119375,
        0.16119745795025164,
        0.6709139944921716,
        0.48288884928371645,
        0.5373790918981908,
        0.6500069475233028,
        0.1378074179672246,
        0.21048849767376657,
        0.2632264576373481,
        0.18622896006976333,
        0.36056468730428204,
        0.5409584565553601,
        0.5516754977680917,
        0.2170519671241465,
        0.17789065525836845,
        0.14351064423146903,
        0.43166811164650715,
        0.26371718011549405,
        0.411098478427435,
        0.2986638562525912,
        0.6337355791183402,
        0.6741688274676305
      ],
      "residuals": [
        -0.1637825523146382,
        -0.18946815092212685,
        0.8474625089661261,
        -0.29970746179952235,
        0.8060217480604027,
        0.4193629449973779,
        0.3617502229123022,
        0.35445576103608434,
        0.5111204158903155,
        -0.26667128135431617,
        0.30185545511865974,
        -0.4464784508913207,
        -0.708023929524279,
        -0.1935655596019874,
        -0.16714556072765946,
        -0.6010689088670101,
        -0.24872475474291436,
        -0.17093407198642985,
        0.36006230703671926,
        -0.15467298595346074,
        0.6017107222493143,
        -0.28067461312704434,
        -0.19688208464647472,
        -0.5014666830886041,
        -0.2588310422478267,
        -0.54155470257621,
        0.5499551246449024,
        0.4429795952582052,
        -0.21926579624174386,
        -0.1448754113044084,
        0.6292633141125226,
        -0.5753454356287786,
        0.35613448139179726,
        0.3645693879102876,
        -0.15112474768992634,
        -0.26617777184812697,
        -0.16119745795025164,
        -0.5888392143800646,
        -0.34272651047717295,
        -0.6934129941790947,
        0.37820110708799126,
        -0.28168830246447707,
        -0.5248293572267569,
        -0.2282498177682777,
        -0.49487282895001206,
        -0.3118256710986974,
        0.39083194807858557,
        0.29300888632494226,
        0.3118823251393821,
        -0.2965816181486325,
        -0.5540522292665906,
        -0.29606209958704544,
        -0.18542455584796236,
        0.7023780938874923,
        -0.1935655596019874,
        0.5469800067228208,
        -0.27113358049864456,
        -0.4548063415964266,
        -0.5026655753940774,
        -0.6297703917548005,
        -0.39655069900846496,
        -0.5864995340150126,
        -0.5853285355347337,
        -0.6057025629195656,
        0.4006724285990563,
        0.6320982978281692,
        -0.14013679790380798,
        0.347769397920753,
        0.6844445327585594,
        -0.5355882555520585,
        0.8177714430751688,
        -0.4583817456122471,
        0.3673958966296629,
        -0.5164483839271498,
        0.5836331093274569,
        -0.2647000229499906,
        -0.5104573048357296,
        0.5051271710499879,
        -0.469724720807945,
        0.40183442014918513,
        -0.38558875654133323,
        0.5159132694231261,
        0.5487654048142254,
        -0.561170443567628,
        -0.1898754736140949,
        -0.43225882726400144,
        -0.19110066853745156,
        0.6934692257629382,
        -0.4405441593968398,
        -0.3488213201415853,
        -0.14317081295352432,
        -0.450639679831964,
        -0.1469388982542079,
        0.7091099556313101,
        -0.4804935608175278,
        0.6195726048449307,
        0.2924922665175199,
        0.3595002722662526,
        0.5308729722788063,
        0.8388025420497484,
        0.3290860055078284,
        0.5171111507162836,
        0.4626209081018092,
        -0.6500069475233028,
        -0.1378074179672246,
        0.7895115023262335,
        -0.2632264576373481,
        -0.18622896006976333,
        -0.36056468730428204,
        0.4590415434446399,
        0.44832450223190834,
        0.7829480328758535,
        -0.17789065525836845,
        -0.14351064423146903,
        0.5683318883534929,
        0.736282819884506,
        -0.411098478427435,
        -0.2986638562525912,
        0.3662644208816598,
        0.3258311725323695
      ],
      "log_likelihood": -72.92761152850606,
      "deviance": 145.8552230570121,
      "null_deviance": 162.2990865129829,
      "aic": 149.85522305701213,
      "df_residual": 118
    },
    "statsmodels": {
      "coefficients": [
        -1.2540076241433726,
        0.15026093927419917
      ],
      "covariance": [
        [
          0.08496336964986528,
          -0.010149910446723375
        ],
        [
          -0.010149910446723375,
          0.00146363705423754
        ]
      ],
      "std_errors": [
        0.2914847674405393,
        0.03825750977569685
      ],
      "z_statistics": [
        -4.302137758876819,
        3.927619444003977
      ],
      "p_values": [
        1.691580809110403e-05,
        8.579081691445878e-05
      ],
      "conf_int": [
        [
          -1.825307270368863,
          -0.6827079779178822
        ],
        [
          0.0752775979756443,
          0.22524428057275403
        ]
      ],
      "fitted": [
        0.1637825523146081,
        0.18946815092209618,
        0.15253749103384412,
        0.29970746179949403,
        0.19397825193956675,
        0.5806370550026159,
        0.6382497770876969,
        0.6455442389639153,
        0.48887958410966975,
        0.2666712813542865,
        0.6981445448813446,
        0.44647845089130245,
        0.7080239295242841,
        0.1935655596019567,
        0.1671455607276292,
        0.6010689088670058,
        0.2487247547428843,
        0.17093407198639954,
        0.6399376929632798,
        0.15467298595343093,
        0.39828927775066353,
        0.28067461312701525,
        0.19688208464644402,
        0.5014666830885905,
        0.25883104224779685,
        0.5415547025762002,
        0.4500448753550797,
        0.5570204047417864,
        0.21926579624171327,
        0.14487541130437898,
        0.3707366858874533,
        0.5753454356287717,
        0.6438655186082023,
        0.6354306120897112,
        0.15112474768989664,
        0.2661777718480974,
        0.16119745795022167,
        0.5888392143800592,
        0.3427265104771471,
        0.6934129941790986,
        0.6217988929120063,
        0.281688302464448,
        0.5248293572267455,
        0.2282498177682472,
        0.4948728289499979,
        0.31182567109866977,
        0.6091680519214108,
        0.7069911136750627,
        0.6881176748606215,
        0.29658161814860406,
        0.5540522292665818,
        0.296062099587017,
        0.18542455584793177,
        0.29762190611247946,
        0.1935655596019567,
        0.45301999327716147,
        0.27113358049861513,
        0.454806341596409,
        0.502665575394064,
        0.6297703917547989,
        0.3965506990084427,
        0.5864995340150069,
        0.585328535534728,
        0.6057025629195617,
        0.5993275714009392,
        0.36790170217180657,
        0.14013679790377886,
        0.6522306020792473,
        0.31555546724141303,
        0.535588255552048,
        0.18222855692480072,
        0.45838174561222983,
        0.6326041033703356,
        0.5164483839271375,
        0.4163668906725224,
        0.264700022949961,
        0.5104573048357169,
        0.4948728289499979,
        0.46972472080792865,
        0.5981655798508102,
        0.38558875654131014,
        0.48408673057685886,
        0.4512345951857566,
        0.56117044356762,
        0.1898754736140642,
        0.432258827263982,
        0.19110066853742091,
        0.3065307742370339,
        0.44054415939682096,
        0.34882132014155975,
        0.14317081295349504,
        0.450639679831946,
        0.14693889825417844,
        0.2908900443686613,
        0.4804935608175124,
        0.3804273951550458,
        0.7075077334824851,
        0.6404997277337466,
        0.46912702772117737,
        0.16119745795022167,
        0.6709139944921736,
        0.4828888492837013,
        0.5373790918981806,
        0.6500069475233029,
        0.1378074179671956,
        0.2104884976737359,
        0.26322645763731833,
        0.18622896006973272,
        0.3605646873042573,
        0.5409584565553502,
        0.5516754977680828,
        0.2170519671241159,
        0.17789065525833808,
        0.14351064423143978,
        0.43166811164648766,
        0.2637171801154644,
        0.41109847842741387,
        0.29866385625256286,
        0.633735579118339,
        0.6741688274676327
      ],
      "residuals": [
        -0.1637825523146081,
        -0.18946815092209618,
        0.8474625089661558,
        -0.29970746179949403,
        0.8060217480604333,
        0.41936294499738413,
        0.3617502229123031,
        0.35445576103608467,
        0.5111204158903302,
        -0.2666712813542865,
        0.3018554551186554,
        -0.44647845089130245,
        -0.7080239295242841,
        -0.1935655596019567,
        -0.1671455607276292,
        -0.6010689088670058,
        -0.2487247547428843,
        -0.17093407198639954,
        0.36006230703672015,
        -0.15467298595343093,
        0.6017107222493365,
        -0.28067461312701525,
        -0.19688208464644402,
        -0.5014666830885905,
        -0.25883104224779685,
        -0.5415547025762002,
        0.5499551246449204,
        0.4429795952582136,
        -0.21926579624171327,
        -0.14487541130437898,
        0.6292633141125468,
        -0.5753454356287717,
        0.3561344813917977,
        0.3645693879102888,
        -0.15112474768989664,
        -0.2661777718480974,
        -0.16119745795022167,
        -0.5888392143800592,
        -0.3427265104771471,
        -0.6934129941790986,
        0.3782011070879937,
        -0.281688302464448,
        -0.5248293572267455,
        -0.2282498177682472,
        -0.4948728289499979,
        -0.31182567109866977,
        0.39083194807858923,
        0.29300888632493727,
        0.3118823251393785,
        -0.29658161814860406,
        -0.5540522292665818,
        -0.296062099587017,
        -0.18542455584793177,
        0.7023780938875206,
        -0.1935655596019567,
        0.5469800067228385,
        -0.27113358049861513,
        -0.454806341596409,
        -0.502665575394064,
        -0.6297703917547989,
        -0.3965506990084427,
        -0.5864995340150069,
        -0.585328535534728,
        -0.6057025629195617,
        0.4006724285990608,
        0.6320982978281935,
        -0.14013679790377886,
        0.3477693979207527,
        0.684444532758587,
        -0.535588255552048,
        0.8177714430751992,
        -0.45838174561222983,
        0.36739589662966443,
        -0.5164483839271375,
        0.5836331093274776,
        -0.264700022949961,
        -0.5104573048357169,
        0.505127171050002,
        -0.46972472080792865,
        0.4018344201491898,
        -0.38558875654131014,
        0.5159132694231412,
        0.5487654048142434,
        -0.56117044356762,
        -0.1898754736140642,
        -0.432258827263982,
        -0.19110066853742091,
        0.6934692257629661,
        -0.44054415939682096,
        -0.34882132014155975,
        -0.14317081295349504,
        -0.450639679831946,
        -0.14693889825417844,
        0.7091099556313387,
        -0.4804935608175124,
        0.6195726048449541,
        0.2924922665175149,
        0.35950027226625336,
        0.5308729722788226,
        0.8388025420497783,
        0.3290860055078264,
        0.5171111507162987,
        0.46262090810181944,
        -0.6500069475233029,
        -0.1378074179671956,
        0.7895115023262641,
        -0.26322645763731833,
        -0.18622896006973272,
        -0.3605646873042573,
        0.45904154344464976,
        0.4483245022319172,
        0.7829480328758841,
        -0.17789065525833808,
        -0.14351064423143978,
        0.5683318883535123,
        0.7362828198845356,
        -0.41109847842741387,
        -0.29866385625256286,
        0.366264420881661,
        0.32583117253236726
      ],
      "log_likelihood": -72.92761152850606,
      "deviance": 145.85522305701213,
      "null_deviance": 162.29908651298285,
      "aic": 149.85522305701213,
      "df_residual": 118
    },
    "phit": {
      "coefficients": [
        -1.2540076241991325,
        0.15026093928032871
      ],
      "covariance": [
        [
          0.08496336965531309,
          -0.010149910447329154
        ],
        [
          -0.010149910447329154,
          0.0014636370543056046
        ]
      ],
      "std_errors": [
        0.2914847674498842,
        0.03825750977658641
      ],
      "z_statistics": [
        -4.30213775893019,
        3.9276194440728704
      ],
      "p_values": [
        1.691580808837801e-05,
        8.579081689679435e-05
      ],
      "conf_int": [
        [
          -1.8253072704429385,
          -0.6827079779553265
        ],
        [
          0.07527759798003035,
          0.22524428058062707
        ]
      ],
      "fitted": [
        0.16378255231778682,
        0.18946815092843072,
        0.15253749103581507,
        0.29970746179044705,
        0.19397825194651458,
        0.5806370550040605,
        0.6382497770913793,
        0.6455442389678682,
        0.48887958410737964,
        0.26667128134442375,
        0.6981445448871214,
        0.4464784508873115,
        0.7080239295303736,
        0.19356555960884772,
        0.16714556073118944,
        0.6010689088692612,
        0.2487247547326531,
        0.17093407199040064,
        0.6399376929670251,
        0.15467298595562334,
        0.3982892777448282,
        0.2806746131174779,
        0.1968820846537966,
        0.5014666830868131,
        0.2588310422377661,
        0.5415547025760618,
        0.4500448753512296,
        0.5570204047422779,
        0.21926579625245493,
        0.1448754113055862,
        0.3707366858806288,
        0.5753454356300041,
        0.6438655186120932,
        0.635430612093288,
        0.15112474769172315,
        0.2661777718382236,
        0.1611974579531135,
        0.588839214381831,
        0.34272651046938196,
        0.693412994184722,
        0.6217988929150665,
        0.28168830245493537,
        0.5248293572259233,
        0.22824981778049286,
        0.49487282894795154,
        0.3118256710899612,
        0.609168051923983,
        0.70699111368112,
        0.6881176748660702,
        0.29658161813947304,
        0.5540522292669527,
        0.2960620995778721,
        0.18542455585373185,
        0.2976219061033762,
        0.19356555960884772,
        0.45301999327342934,
        0.2711335804888525,
        0.4548063415927478,
        0.5026655753923354,
        0.6297703917581625,
        0.39655069900254336,
        0.5864995340166856,
        0.58532853553636,
        0.6057025629219986,
        0.5993275714031262,
        0.36790170216488366,
        0.14013679789990044,
        0.6522306020834447,
        0.3155554672328124,
        0.5355882555516659,
        0.18222855693018844,
        0.4583817456087109,
        0.6326041033738062,
        0.5164483839259725,
        0.4163668906673643,
        0.2647000229400549,
        0.5104573048343067,
        0.49487282894795154,
        0.46972472080486394,
        0.5981655798529514,
        0.3855887565350119,
        0.48408673057437424,
        0.45123459518195363,
        0.5611704435682799,
        0.1898754736204534,
        0.43225882725943454,
        0.19110066854397537,
        0.3065307742281751,
        0.4405441593925968,
        0.3488213201339931,
        0.14317081294977416,
        0.4506396798281195,
        0.1469388982555867,
        0.29089004435938054,
        0.48049356081488226,
        0.3804273951485627,
        0.7075077334885584,
        0.6404997277375126,
        0.4691270277180887,
        0.1611974579531135,
        0.6709139944970365,
        0.482888849281168,
        0.5373790918978715,
        0.6500069475274193,
        0.13780741796320034,
        0.21048849768308986,
        0.2632264576273804,
        0.18622896007563797,
        0.36056468729708285,
        0.5409584565551876,
        0.551675497768357,
        0.21705196713450012,
        0.17789065526318038,
        0.14351064422773685,
        0.4316681116419173,
        0.263717180105537,
        0.4110984784220565,
        0.2986638562434876,
        0.6337355791218521,
        0.6741688274726085
      ],
      "residuals": [
        -0.16378255231778682,
        -0.18946815092843072,
        0.847462508964185,
        -0.29970746179044705,
        0.8060217480534855,
        0.4193629449959395,
        0.3617502229086207,
        0.35445576103213183,
        0.5111204158926204,
        -0.26667128134442375,
        0.3018554551128786,
        -0.4464784508873115,
        -0.7080239295303736,
        -0.19356555960884772,
        -0.16714556073118944,
        -0.6010689088692612,
        -0.2487247547326531,
        -0.17093407199040064,
        0.3600623070329749,
        -0.15467298595562334,
        0.6017107222551719,
        -0.2806746131174779,
        -0.1968820846537966,
        -0.5014666830868131,
        -0.2588310422377661,
        -0.5415547025760618,
        0.5499551246487704,
        0.4429795952577221,
        -0.21926579625245493,
        -0.1448754113055862,
        0.6292633141193712,
        -0.5753454356300041,
        0.3561344813879068,
        0.364569387906712,
        -0.15112474769172315,
        -0.2661777718382236,
        -0.1611974579531135,
        -0.588839214381831,
        -0.34272651046938196,
        -0.693412994184722,
        0.3782011070849335,
        -0.28168830245493537,
        -0.5248293572259233,
        -0.22824981778049286,
        -0.49487282894795154,
        -0.3118256710899612,
        0.39083194807601696,
        0.29300888631888,
        0.31188232513392977,
        -0.29658161813947304,
        -0.5540522292669527,
        -0.2960620995778721,
        -0.18542455585373185,
        0.7023780938966238,
        -0.19356555960884772,
        0.5469800067265707,
        -0.2711335804888525,
        -0.4548063415927478,
        -0.5026655753923354,
        -0.6297703917581625,
        -0.39655069900254336,
        -0.5864995340166856,
        -0.58532853553636,
        -0.6057025629219986,
        0.4006724285968738,
        0.6320982978351164,
        -0.14013679789990044,
        0.34776939791655526,
        0.6844445327671875,
        -0.5355882555516659,
        0.8177714430698115,
        -0.4583817456087109,
        0.36739589662619376,
        -0.5164483839259725,
        0.5836331093326357,
        -0.2647000229400549,
        -0.5104573048343067,
        0.5051271710520484,
        -0.46972472080486394,
        0.4018344201470486,
        -0.3855887565350119,
        0.5159132694256258,
        0.5487654048180464,
        -0.5611704435682799,
        -0.1898754736204534,
        -0.43225882725943454,
        -0.19110066854397537,
        0.6934692257718249,
        -0.4405441593925968,
        -0.3488213201339931,
        -0.14317081294977416,
        -0.4506396798281195,
        -0.1469388982555867,
        0.7091099556406195,
        -0.48049356081488226,
        0.6195726048514373,
        0.29249226651144156,
        0.3595002722624874,
        0.5308729722819113,
        0.8388025420468865,
        0.3290860055029635,
        0.517111150718832,
        0.4626209081021285,
        -0.6500069475274193,
        -0.13780741796320034,
        0.7895115023169101,
        -0.2632264576273804,
        -0.18622896007563797,
        -0.36056468729708285,
        0.4590415434448124,
        0.448324502231643,
        0.7829480328654999,
        -0.17789065526318038,
        -0.14351064422773685,
        0.5683318883580827,
        0.736282819894463,
        -0.4110984784220565,
        -0.2986638562434876,
        0.3662644208781479,
        0.32583117252739147
      ],
      "log_likelihood": -72.92761152837014,
      "deviance": 145.85522305674027,
      "null_deviance": 162.2990865129829,
      "aic": 149.85522305674027,
      "df_residual": 118,
      "iterations": 8,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 1.4654943925052066e-13,
        "phit": 5.590639062802438e-11
      },
      "covariance": {
        "statsmodels": 1.2894130207996568e-12,
        "phit": 4.158395849884755e-12
      },
      "std_errors": {
        "statsmodels": 2.211786309658237e-12,
        "phit": 7.1331274220653995e-12
      },
      "z_statistics": {
        "statsmodels": 3.3147706801628374e-11,
        "phit": 8.911893445429087e-11
      },
      "p_values": {
        "statsmodels": 7.212505874661101e-15,
        "phit": 2.4876937532516963e-14
      },
      "conf_int": {
        "statsmodels": 4.481304216596982e-12,
        "phit": 6.988720713252405e-11
      },
      "fitted": {
        "statsmodels": 3.069766663088558e-14,
        "phit": 1.2215145561711438e-11
      },
      "residuals": {
        "statsmodels": 3.069766663088558e-14,
        "phit": 1.2215145561711438e-11
      },
      "log_likelihood": {
        "statsmodels": 0.0,
        "phit": 1.3592682535090717e-10
      },
      "deviance": {
        "statsmodels": 2.842170943040401e-14,
        "phit": 2.7182522899238393e-10
      },
      "null_deviance": {
        "statsmodels": 5.684341886080802e-14,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 0.0,
        "phit": 2.7185365070181433e-10
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "no_intercept",
    "input": {
      "x": [
        [
          1.83,
          56.39
        ],
        [
          2.49,
          61.62
        ],
        [
          1.52,
          34.88
        ],
        [
          4.85,
          78.07
        ],
        [
          2.6,
          66.36
        ],
        [
          9.7,
          81.6
        ],
        [
          10.7,
          75.03
        ],
        [
          10.83,
          80.27
        ],
        [
          8.16,
          81.41
        ],
        [
          4.2,
          59.63
        ],
        [
          11.8,
          84.54
        ],
        [
          7.45,
          71.37
        ],
        [
          11.99,
          86.19
        ],
        [
          2.59,
          50.28
        ],
        [
          1.92,
          45.47
        ],
        [
          10.05,
          83.86
        ],
        [
          3.83,
          50.96
        ],
        [
          2.02,
          28.23
        ],
        [
          10.73,
          83.28
        ],
        [
          1.58,
          50.61
        ],
        [
          6.63,
          65.27
        ],
        [
          4.48,
          58.04
        ],
        [
          2.67,
          58.73
        ],
        [
          8.37,
          75.27
        ],
        [
          4.04,
          64.07
        ],
        [
          9.04,
          72.06
        ],
        [
          7.51,
          70.66
        ],
        [
          9.3,
          88.99
        ],
        [
          3.19,
          48.59
        ],
        [
          1.3,
          39.56
        ],
        [
          6.15,
          70.58
        ],
        [
          9.61,
          87.11
        ],
        [
          10.8,
          71.4
        ],
        [
          10.65,
          74.56
        ],
        [
          1.48,
          49.19
        ],
        [
          4.19,
          48.81
        ],
        [
          1.76,
          48.94
        ],
        [
          9.84,
          70.92
        ],
        [
          5.65,
          79.16
        ],
        [
          11.71,
          93.65
        ],
        [
          10.41,
          87.76
        ],
        [
          4.5,
          74.61
        ],
        [
          8.76,
          58.68
        ],
        [
          3.39,
          42.27
        ],
        [
          8.26,
          66.12
        ],
        [
          5.08,
          73.77
        ],
        [
          10.19,
          72.85
        ],
        [
          11.97,
          79.13
        ],
        [
          11.61,
          84.14
        ],
        [
          4.79,
          64.25
        ],
        [
          9.25,
          69.29
        ],
        [
          4.78,
          58.54
        ],
        [
          2.39,
          48.95
        ],
        [
          4.81,
          52.58
        ],
        [
          2.59,
          52.99
        ],
        [
          7.56,
          69.2
        ],
        [
          4.29,
          69.75
        ],
        [
          7.59,
          77.72
        ],
        [
          8.39,
          79.59
        ],
        [
          10.55,
          84.76
        ],
        [
          6.6,
          59.23
        ],
        [
          9.8,
          83.91
        ],
        [
          9.78,
          72.62
        ],
        [
          10.13,
          68.86
        ],
        [
          10.02,
          75.17
        ],
        [
          6.1,
          59.55
        ],
        [
          1.16,
          55.02
        ],
        [
          10.95,
          95
        ],
        [
          5.15,
          60.94
        ],
        [
          8.94,
          60.52
        ],
        [
          2.31,
          53.74
        ],
        [
          7.65,
          72.07
        ],
        [
          10.6,
          74.89
        ],
        [
          8.62,
          70.42
        ],
        [
          6.94,
          70.08
        ],
        [
          4.16,
          51.82
        ],
        [
          8.52,
          75.87
        ],
        [
          8.26,
          80.1
        ],
        [
          7.84,
          77.18
        ],
        [
          10,
          81.56
        ],
        [
          6.41,
          61.14
        ],
        [
          8.08,
          74.06
        ],
        [
          7.53,
          69.84
        ],
        [
          9.37,
          71.92
        ],
        [
          2.5,
          37.32
        ],
        [
          7.21,
          78.28
        ],
        [
          2.53,
          53.38
        ],
        [
          4.98,
          73.13
        ],
        [
          7.35,
          68.11
        ],
        [
          5.76,
          60.89
        ],
        [
          1.25,
          54.01
        ],
        [
          7.52,
          64.25
        ],
        [
          1.36,
          40.08
        ],
        [
          4.68,
          59.68
        ],
        [
          8.02,
          58.34
        ],
        [
          6.32,
          56.81
        ],
        [
          11.98,
          61.9
        ],
        [
          10.74,
          74.75
        ],
        [
          7.83,
          66.12
        ],
        [
          1.76,
          52.3
        ],
        [
          11.29,
          86.01
        ],
        [
          8.06,
          56.46
        ],
        [
          8.97,
          61.82
        ],
        [
          10.91,
          72.69
        ],
        [
          1.09,
          31.47
        ],
        [
          2.99,
          48.2
        ],
        [
          4.13,
          62.12
        ],
        [
          2.41,
          66.31
        ],
        [
          5.97,
          46.22
        ],
        [
          9.03,
          73.07
        ],
        [
          9.21,
          79.32
        ],
        [
          3.14,
          52.42
        ],
        [
          2.2,
          47.49
        ],
        [
          1.26,
          38.22
        ],
        [
          7.2,
          60.45
        ],
        [
          4.14,
          69.24
        ],
        [
          6.85,
          59.9
        ],
        [
          4.83,
          69.45
        ],
        [
          10.62,
          81.19
        ],
        [
          11.35,
          67.69
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        0.20631280059692642,
        -0.024071288878554874
      ],
      "covariance": [
        [
          0.002932884415189059,
          -0.0003126713076411273
        ],
        [
          -0.0003126713076411273,
          3.64674095597328e-05
        ]
      ],
      "std_errors": [
        0.05415611152205316,
        0.006038825180424815
      ],
      "z_statistics": [
        3.8095940568575135,
        -3.9860880484805694
      ],
      "p_values": [
        0.00013919514652938292,
        6.717159381989852e-05
      ],
      "conf_int": [
        [
          0.10016877247096762,
          0.3124568287228852
        ],
        [
          -0.0359071687411211,
          -0.012235409015988647
        ]
      ],
      "fitted": [
        0.16358562404355173,
        0.1661344388027407,
        0.2994402476369399,
        0.18980138517812783,
        0.14435461973481575,
        0.514764271834017,
        0.6559659433768168,
        0.6187369618148391,
        0.3912236585895942,
        0.2847265287455796,
        0.6552391665770979,
        0.4282083079814483,
        0.6550482734320295,
        0.24953484581045865,
        0.24246324804063252,
        0.5218612020437216,
        0.33123886567185845,
        0.3963598338419366,
        0.5828068770492326,
        0.18612312232216116,
        0.41945842280488876,
        0.31817213629922875,
        0.19410952724428224,
        0.4661276056028317,
        0.23924175062634578,
        0.5519108708073789,
        0.43980322084668394,
        0.4116140664904962,
        0.30450536210433177,
        0.24697067670867226,
        0.3335513227711995,
        0.45454598321571504,
        0.6947949735163973,
        0.656333136298083,
        0.18977553765166902,
        0.37810217423986014,
        0.2075538003325606,
        0.6266456200057349,
        0.22970585364566812,
        0.5642079568533963,
        0.5140478197532332,
        0.1928200190908124,
        0.6535036092155958,
        0.3752072016193639,
        0.54480638086789,
        0.23340782370417096,
        0.6363555080071122,
        0.713896162496426,
        0.6442839311115323,
        0.2883054366010495,
        0.5950262650945728,
        0.33616292892780264,
        0.24660823188217657,
        0.3923098478874202,
        0.2292898976602084,
        0.4577878366593035,
        0.21362959478769417,
        0.38021871486137715,
        0.42666570298807677,
        0.5542148948909478,
        0.47445407703104375,
        0.5008152763010707,
        0.606297618882824,
        0.6672745384315355,
        0.601725340358918,
        0.43056450194176443,
        0.13894323064796996,
        0.4889717372630624,
        0.34296171860028,
        0.6508595212044826,
        0.20696178670791124,
        0.43780966071286526,
        0.6495911392617906,
        0.5331999317088774,
        0.3993209670685376,
        0.3485963010928739,
        0.4726923668122896,
        0.4113916826845661,
        0.40503732881122,
        0.5397776959130749,
        0.44067678310222974,
        0.4539403083879296,
        0.449231409562027,
        0.5800196877833147,
        0.35102357307657056,
        0.3457629323226612,
        0.2227454105083267,
        0.2318110508147149,
        0.45101538054455614,
        0.39075988938530787,
        0.14865964108259314,
        0.5019515979212517,
        0.24692701416798365,
        0.3188094367647619,
        0.5988260596387783,
        0.4746471442989292,
        0.8368551164964304,
        0.6614671744992673,
        0.5095081314923149,
        0.18517501959583835,
        0.6021437863610254,
        0.6193660390532315,
        0.6415252614308793,
        0.6918604169600937,
        0.2971405353027648,
        0.2934406877260965,
        0.26003529435122164,
        0.13589421458877438,
        0.5474068654015437,
        0.5414611591342924,
        0.49633227992863427,
        0.2696093919070563,
        0.2453306669396762,
        0.2546107009922279,
        0.5121031492910625,
        0.20823488611899704,
        0.4885808317498458,
        0.24975523726107932,
        0.5935529043248444,
        0.7618495737814377
      ],
      "residuals": [
        -0.16358562404355173,
        -0.1661344388027407,
        0.7005597523630601,
        -0.18980138517812783,
        0.8556453802651842,
        0.48523572816598304,
        0.3440340566231832,
        0.38126303818516094,
        0.6087763414104058,
        -0.2847265287455796,
        0.3447608334229021,
        -0.4282083079814483,
        -0.6550482734320295,
        -0.24953484581045865,
        -0.24246324804063252,
        -0.5218612020437216,
        -0.33123886567185845,
        -0.3963598338419366,
        0.4171931229507674,
        -0.18612312232216116,
        0.5805415771951112,
        -0.31817213629922875,
        -0.19410952724428224,
        -0.4661276056028317,
        -0.23924175062634578,
        -0.5519108708073789,
        0.560196779153316,
        0.5883859335095039,
        -0.30450536210433177,
        -0.24697067670867226,
        0.6664486772288005,
        -0.45454598321571504,
        0.3052050264836027,
        0.343666863701917,
        -0.18977553765166902,
        -0.37810217423986014,
        -0.2075538003325606,
        -0.6266456200057349,
        -0.22970585364566812,
        -0.5642079568533963,
        0.4859521802467668,
        -0.1928200190908124,
        -0.6535036092155958,
        -0.3752072016193639,
        -0.54480638086789,
        -0.23340782370417096,
        0.36364449199288784,
        0.28610383750357404,
        0.35571606888846774,
        -0.2883054366010495,
        -0.5950262650945728,
        -0.33616292892780264,
        -0.24660823188217657,
        0.6076901521125798,
        -0.2292898976602084,
        0.5422121633406964,
        -0.21362959478769417,
        -0.38021871486137715,
        -0.42666570298807677,
        -0.5542148948909478,
        -0.47445407703104375,
        -0.5008152763010707,
        -0.606297618882824,
        -0.6672745384315355,
        0.398274659641082,
        0.5694354980582356,
        -0.13894323064796996,
        0.5110282627369376,
        0.65703828139972,
        -0.6508595212044826,
        0.7930382132920888,
        -0.43780966071286526,
        0.3504088607382094,
        -0.5331999317088774,
        0.6006790329314624,
        -0.3485963010928739,
        -0.4726923668122896,
        0.588608317315434,
        -0.40503732881122,
        0.4602223040869251,
        -0.44067678310222974,
        0.5460596916120704,
        0.550768590437973,
        -0.5800196877833147,
        -0.35102357307657056,
        -0.3457629323226612,
        -0.2227454105083267,
        0.7681889491852851,
        -0.45101538054455614,
        -0.39075988938530787,
        -0.14865964108259314,
        -0.5019515979212517,
        -0.24692701416798365,
        0.6811905632352381,
        -0.5988260596387783,
        0.5253528557010708,
        0.1631448835035696,
        0.3385328255007327,
        0.4904918685076851,
        0.8148249804041616,
        0.3978562136389746,
        0.3806339609467685,
        0.3584747385691207,
        -0.6918604169600937,
        -0.2971405353027648,
        0.7065593122739036,
        -0.26003529435122164,
        -0.13589421458877438,
        -0.5474068654015437,
        0.4585388408657076,
        0.5036677200713657,
        0.7303906080929436,
        -0.2453306669396762,
        -0.2546107009922279,
        0.4878968507089375,
        0.7917651138810029,
        -0.4885808317498458,
        -0.24975523726107932,
        0.4064470956751556,
        0.2381504262185623
      ],
      "log_likelihood": -74.53280174360556,
      "deviance": 149.06560348721115,
      "null_deviance": 166.35532333438687,
      "aic": 153.06560348721112,
      "df_residual": 118
    },
    "statsmodels": {
      "coefficients": [
        0.20631280059692358,
        -0.02407128887855464
      ],
      "covariance": [
        [
          0.0029328844151871535,
          -0.0003126713076409126
        ],
        [
          -0.0003126713076409126,
          3.646740955970793e-05
        ]
      ],
      "std_errors": [
        0.05415611152203557,
        0.006038825180422756
      ],
      "z_statistics": [
        3.8095940568586983,
        -3.9860880484818897
      ],
      "p_values": [
        0.00013919514652871584,
        6.717159381952479e-05
      ],
      "conf_int": [
        [
          0.10016877247099923,
          0.31245682872284797
        ],
        [
          -0.03590716874111684,
          -0.012235409015992443
        ]
      ],
      "fitted": [
        0.16358562404355376,
        0.16613443880274265,
        0.2994402476369412,
        0.1898013851781291,
        0.1443546197348176,
        0.5147642718340137,
        0.6559659433768121,
        0.6187369618148346,
        0.39122365858959274,
        0.28472652874558035,
        0.6552391665770929,
        0.4282083079814466,
        0.6550482734320245,
        0.2495348458104601,
        0.24246324804063424,
        0.5218612020437181,
        0.3312388656718588,
        0.39635983384193696,
        0.5828068770492285,
        0.18612312232216316,
        0.41945842280488743,
        0.31817213629922914,
        0.19410952724428404,
        0.4661276056028294,
        0.23924175062634684,
        0.5519108708073754,
        0.4398032208466821,
        0.4116140664904942,
        0.30450536210433266,
        0.24697067670867406,
        0.33355132277119925,
        0.4545459832157125,
        0.6947949735163924,
        0.6563331362980784,
        0.189775537651671,
        0.37810217423986003,
        0.20755380033256243,
        0.6266456200057305,
        0.22970585364566898,
        0.5642079568533919,
        0.5140478197532298,
        0.1928200190908137,
        0.6535036092155917,
        0.37520720161936405,
        0.544806380867887,
        0.23340782370417185,
        0.6363555080071077,
        0.7138961624964207,
        0.6442839311115274,
        0.28830543660105,
        0.595026265094569,
        0.3361629289278027,
        0.24660823188217806,
        0.39230984788741974,
        0.22928989766021002,
        0.4577878366593014,
        0.21362959478769544,
        0.38021871486137593,
        0.4266657029880748,
        0.5542148948909439,
        0.4744540770310419,
        0.5008152763010677,
        0.60629761888282,
        0.6672745384315308,
        0.6017253403589139,
        0.43056450194176327,
        0.13894323064797215,
        0.488971737263059,
        0.3429617186002799,
        0.6508595212044785,
        0.206961786707913,
        0.43780966071286337,
        0.6495911392617861,
        0.5331999317088743,
        0.3993209670685364,
        0.3485963010928741,
        0.4726923668122871,
        0.4113916826845644,
        0.40503732881121846,
        0.5397776959130712,
        0.4406767831022283,
        0.4539403083879274,
        0.4492314095620251,
        0.580019687783311,
        0.3510235730765711,
        0.3457629323226605,
        0.22274541050832836,
        0.2318110508147158,
        0.45101538054455426,
        0.39075988938530704,
        0.14865964108259533,
        0.5019515979212491,
        0.2469270141679854,
        0.31880943676476226,
        0.5988260596387749,
        0.47464714429892735,
        0.8368551164964257,
        0.6614671744992626,
        0.5095081314923123,
        0.18517501959584026,
        0.602143786361021,
        0.6193660390532278,
        0.6415252614308753,
        0.691860416960089,
        0.2971405353027663,
        0.29344068772609744,
        0.26003529435122263,
        0.13589421458877626,
        0.5474068654015414,
        0.5414611591342892,
        0.4963322799286314,
        0.2696093919070574,
        0.2453306669396778,
        0.2546107009922296,
        0.51210314929106,
        0.20823488611899849,
        0.48858083174984374,
        0.24975523726108018,
        0.5935529043248401,
        0.7618495737814326
      ],
      "residuals": [
        -0.16358562404355376,
        -0.16613443880274265,
        0.7005597523630588,
        -0.1898013851781291,
        0.8556453802651824,
        0.48523572816598626,
        0.34403405662318787,
        0.3812630381851654,
        0.6087763414104073,
        -0.28472652874558035,
        0.3447608334229071,
        -0.4282083079814466,
        -0.6550482734320245,
        -0.2495348458104601,
        -0.24246324804063424,
        -0.5218612020437181,
        -0.3312388656718588,
        -0.39635983384193696,
        0.4171931229507715,
        -0.18612312232216316,
        0.5805415771951126,
        -0.31817213629922914,
        -0.19410952724428404,
        -0.4661276056028294,
        -0.23924175062634684,
        -0.5519108708073754,
        0.5601967791533179,
        0.5883859335095059,
        -0.30450536210433266,
        -0.24697067670867406,
        0.6664486772288007,
        -0.4545459832157125,
        0.3052050264836076,
        0.34366686370192157,
        -0.189775537651671,
        -0.37810217423986003,
        -0.20755380033256243,
        -0.6266456200057305,
        -0.22970585364566898,
        -0.5642079568533919,
        0.4859521802467702,
        -0.1928200190908137,
        -0.6535036092155917,
        -0.37520720161936405,
        -0.544806380867887,
        -0.23340782370417185,
        0.3636444919928923,
        0.28610383750357926,
        0.3557160688884726,
        -0.28830543660105,
        -0.595026265094569,
        -0.3361629289278027,
        -0.24660823188217806,
        0.6076901521125803,
        -0.22928989766021002,
        0.5422121633406987,
        -0.21362959478769544,
        -0.38021871486137593,
        -0.4266657029880748,
        -0.5542148948909439,
        -0.4744540770310419,
        -0.5008152763010677,
        -0.60629761888282,
        -0.6672745384315308,
        0.3982746596410861,
        0.5694354980582368,
        -0.13894323064797215,
        0.511028262736941,
        0.6570382813997201,
        -0.6508595212044785,
        0.793038213292087,
        -0.43780966071286337,
        0.35040886073821387,
        -0.5331999317088743,
        0.6006790329314635,
        -0.3485963010928741,
        -0.4726923668122871,
        0.5886083173154356,
        -0.40503732881121846,
        0.46022230408692877,
        -0.4406767831022283,
        0.5460596916120726,
        0.5507685904379749,
        -0.580019687783311,
        -0.3510235730765711,
        -0.3457629323226605,
        -0.22274541050832836,
        0.7681889491852842,
        -0.45101538054455426,
        -0.39075988938530704,
        -0.14865964108259533,
        -0.5019515979212491,
        -0.2469270141679854,
        0.6811905632352377,
        -0.5988260596387749,
        0.5253528557010727,
        0.16314488350357426,
        0.3385328255007374,
        0.49049186850768767,
        0.8148249804041597,
        0.39785621363897905,
        0.38063396094677215,
        0.3584747385691247,
        -0.691860416960089,
        -0.2971405353027663,
        0.7065593122739026,
        -0.26003529435122263,
        -0.13589421458877626,
        -0.5474068654015414,
        0.45853884086571084,
        0.5036677200713686,
        0.7303906080929425,
        -0.2453306669396778,
        -0.2546107009922296,
        0.48789685070893996,
        0.7917651138810016,
        -0.48858083174984374,
        -0.24975523726108018,
        0.4064470956751599,
        0.2381504262185674
      ],
      "log_likelihood": -74.5328017436056,
      "deviance": 149.0656034872112,
      "null_deviance": 166.35532333438687,
      "aic": 153.0656034872112,
      "df_residual": 118
    },
    "phit": {
      "coefficients": [
        0.2063128006046471,
        -0.024071288879517417
      ],
      "covariance": [
        [
          0.0029328844153219094,
          -0.00031267130765705065
        ],
        [
          -0.00031267130765705065,
          3.64674095616656e-05
        ]
      ],
      "std_errors": [
        0.05415611152327971,
        0.006038825180584847
      ],
      "z_statistics": [
        3.8095940569137956,
        -3.9860880485343286
      ],
      "p_values": [
        0.0001391951465089335,
        6.717159381008443e-05
      ],
      "conf_int": [
        [
          0.10016877247628428,
          0.31245682873300995
        ],
        [
          -0.0359071687423973,
          -0.01223540901663753
        ]
      ],
      "fitted": [
        0.1635856240478011,
        0.16613443880719977,
        0.2994402476293534,
        0.18980138518525205,
        0.14435461973208605,
        0.5147642718325608,
        0.6559659433806415,
        0.61873696181726,
        0.3912236585836958,
        0.28472652873710624,
        0.6552391665806822,
        0.4282083079770615,
        0.6550482734355699,
        0.24953484580144275,
        0.24246324803158492,
        0.5218612020424762,
        0.3312388656647929,
        0.3963598338374749,
        0.5828068770502794,
        0.186123122329255,
        0.4194584228003412,
        0.318172136291638,
        0.1941095272523171,
        0.46612760559972,
        0.2392417506414979,
        0.5519108708075506,
        0.4398032208427278,
        0.4116140664851054,
        0.30450536209658186,
        0.24697067669981915,
        0.3335513227637606,
        0.4545459832118898,
        0.6947949735215332,
        0.6563331363019306,
        0.18977553765927319,
        0.37810217423429743,
        0.20755380034270735,
        0.6266456200086534,
        0.229705853658837,
        0.5642079568535017,
        0.5140478197515985,
        0.19282001909840146,
        0.6535036092197111,
        0.3752072016138594,
        0.5448063808679413,
        0.23340782371808697,
        0.6363555080103227,
        0.7138961625019531,
        0.6442839311147546,
        0.28830543659256286,
        0.5950262650964028,
        0.33616292892070987,
        0.2466082318731339,
        0.39230984788224194,
        0.2292898976737955,
        0.4577878366560349,
        0.21362959479840182,
        0.38021871485520436,
        0.42666570298343637,
        0.5542148948908958,
        0.47445407702863324,
        0.5008152762990346,
        0.6062976188849817,
        0.6672745384358699,
        0.6017253403608502,
        0.430564501937748,
        0.1389432306451087,
        0.4889717372603108,
        0.3429617185933336,
        0.6508595212084681,
        0.20696178671788415,
        0.43780966070880334,
        0.6495911392654052,
        0.5331999317083884,
        0.39932096706318015,
        0.34859630108630496,
        0.4726923668094049,
        0.4113916826793811,
        0.40503732880588733,
        0.5397776959125598,
        0.44067678309853686,
        0.4539403083844017,
        0.44923140955843116,
        0.580019687784533,
        0.3510235730704079,
        0.3457629323154037,
        0.22274541052079797,
        0.23181105082836231,
        0.4510153805410673,
        0.3907598893798804,
        0.14865964108528018,
        0.5019515979197421,
        0.24692701415911955,
        0.3188094367571525,
        0.5988260596410073,
        0.4746471442965851,
        0.836855116490431,
        0.6614671745032801,
        0.5095081314910425,
        0.18517501960278,
        0.6021437863627145,
        0.6193660390562348,
        0.6415252614345217,
        0.6918604169651132,
        0.29714053529519185,
        0.2934406877180734,
        0.260035294342169,
        0.1358942145856053,
        0.547406865402179,
        0.5414611591340482,
        0.4963322799265434,
        0.2696093918983953,
        0.24533066693063932,
        0.25461070098354555,
        0.512103149290027,
        0.20823488612888752,
        0.4885808317479437,
        0.24975523725169152,
        0.5935529043263359,
        0.761849573763967
      ],
      "residuals": [
        -0.1635856240478011,
        -0.16613443880719977,
        0.7005597523706466,
        -0.18980138518525205,
        0.8556453802679139,
        0.4852357281674392,
        0.3440340566193585,
        0.38126303818274,
        0.6087763414163042,
        -0.28472652873710624,
        0.34476083341931785,
        -0.4282083079770615,
        -0.6550482734355699,
        -0.24953484580144275,
        -0.24246324803158492,
        -0.5218612020424762,
        -0.3312388656647929,
        -0.3963598338374749,
        0.41719312294972055,
        -0.186123122329255,
        0.5805415771996588,
        -0.318172136291638,
        -0.1941095272523171,
        -0.46612760559972,
        -0.2392417506414979,
        -0.5519108708075506,
        0.5601967791572722,
        0.5883859335148947,
        -0.30450536209658186,
        -0.24697067669981915,
        0.6664486772362395,
        -0.4545459832118898,
        0.3052050264784668,
        0.3436668636980694,
        -0.18977553765927319,
        -0.37810217423429743,
        -0.20755380034270735,
        -0.6266456200086534,
        -0.229705853658837,
        -0.5642079568535017,
        0.4859521802484015,
        -0.19282001909840146,
        -0.6535036092197111,
        -0.3752072016138594,
        -0.5448063808679413,
        -0.23340782371808697,
        0.3636444919896773,
        0.2861038374980469,
        0.35571606888524543,
        -0.28830543659256286,
        -0.5950262650964028,
        -0.33616292892070987,
        -0.2466082318731339,
        0.607690152117758,
        -0.2292898976737955,
        0.5422121633439652,
        -0.21362959479840182,
        -0.38021871485520436,
        -0.42666570298343637,
        -0.5542148948908958,
        -0.47445407702863324,
        -0.5008152762990346,
        -0.6062976188849817,
        -0.6672745384358699,
        0.39827465963914976,
        0.569435498062252,
        -0.1389432306451087,
        0.5110282627396892,
        0.6570382814066664,
        -0.6508595212084681,
        0.7930382132821159,
        -0.43780966070880334,
        0.35040886073459476,
        -0.5331999317083884,
        0.6006790329368199,
        -0.34859630108630496,
        -0.4726923668094049,
        0.5886083173206189,
        -0.40503732880588733,
        0.46022230408744025,
        -0.44067678309853686,
        0.5460596916155983,
        0.5507685904415689,
        -0.580019687784533,
        -0.3510235730704079,
        -0.3457629323154037,
        -0.22274541052079797,
        0.7681889491716377,
        -0.4510153805410673,
        -0.3907598893798804,
        -0.14865964108528018,
        -0.5019515979197421,
        -0.24692701415911955,
        0.6811905632428474,
        -0.5988260596410073,
        0.5253528557034148,
        0.16314488350956902,
        0.3385328254967199,
        0.49049186850895754,
        0.8148249803972201,
        0.3978562136372855,
        0.3806339609437652,
        0.3584747385654783,
        -0.6918604169651132,
        -0.29714053529519185,
        0.7065593122819266,
        -0.260035294342169,
        -0.1358942145856053,
        -0.547406865402179,
        0.45853884086595176,
        0.5036677200734566,
        0.7303906081016047,
        -0.24533066693063932,
        -0.25461070098354555,
        0.487896850709973,
        0.7917651138711125,
        -0.4885808317479437,
        -0.24975523725169152,
        0.4064470956736641,
        0.238150426236033
      ],
      "log_likelihood": -74.53280174359764,
      "deviance": 149.0656034871953,
      "null_deviance": 166.35532333438687,
      "aic": 153.0656034871953,
      "df_residual": 118,
      "iterations": 8,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 2.831068712794149e-15,
        "phit": 7.720685202272648e-12
      },
      "covariance": {
        "statsmodels": 1.9055937383605226e-15,
        "phit": 1.3285032796073182e-13
      },
      "std_errors": {
        "statsmodels": 1.7590096046404824e-14,
        "phit": 1.2265535809241612e-12
      },
      "z_statistics": {
        "statsmodels": 1.3202772208842362e-12,
        "phit": 5.6282090099557536e-11
      },
      "p_values": {
        "statsmodels": 6.670824916760187e-16,
        "phit": 2.044940822579222e-14
      },
      "conf_int": {
        "statsmodels": 3.7247982476174e-14,
        "phit": 1.0124734384220346e-11
      },
      "fitted": {
        "statsmodels": 5.218048215738236e-15,
        "phit": 1.7470691560106388e-11
      },
      "residuals": {
        "statsmodels": 5.218048215738236e-15,
        "phit": 1.7470691560106388e-11
      },
      "log_likelihood": {
        "statsmodels": 4.263256414560601e-14,
        "phit": 7.915446076367516e-12
      },
      "deviance": {
        "statsmodels": 5.684341886080802e-14,
        "phit": 1.5859313862165436e-11
      },
      "null_deviance": {
        "statsmodels": 0.0,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 8.526512829121202e-14,
        "phit": 1.5830892152735032e-11
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "intercept_only",
    "input": {
      "x": [
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ],
        [
          1
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -0.23183436245301
      ],
      "covariance": [
        [
          0.01334850593779309
        ]
      ],
      "std_errors": [
        0.11553573446251636
      ],
      "z_statistics": [
        -2.006603095843259
      ],
      "p_values": [
        0.044791941423101014
      ],
      "conf_int": [
        [
          -0.4582802409269251,
          -0.005388483979094888
        ]
      ],
      "fitted": [
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327,
        0.40833333333333327
      ],
      "residuals": [
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668,
        -0.40833333333333327,
        -0.40833333333333327,
        0.5916666666666668,
        0.5916666666666668
      ],
      "log_likelihood": -81.14954325649147,
      "deviance": 162.29908651298294,
      "null_deviance": 162.2990865129829,
      "aic": 164.29908651298294,
      "df_residual": 119
    },
    "statsmodels": {
      "coefficients": [
        -0.2318343624530098
      ],
      "covariance": [
        [
          0.0133485059377931
        ]
      ],
      "std_errors": [
        0.1155357344625164
      ],
      "z_statistics": [
        -2.006603095843256
      ],
      "p_values": [
        0.044791941423101306
      ],
      "conf_int": [
        [
          -0.4582802409269251,
          -0.005388483979094527
        ]
      ],
      "fitted": [
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333,
        0.4083333333333333
      ],
      "residuals": [
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667,
        -0.4083333333333333,
        -0.4083333333333333,
        0.5916666666666667,
        0.5916666666666667
      ],
      "log_likelihood": -81.14954325649143,
      "deviance": 162.29908651298285,
      "null_deviance": 162.29908651298285,
      "aic": 164.29908651298285,
      "df_residual": 119
    },
    "phit": {
      "coefficients": [
        -0.23183436245300976
      ],
      "covariance": [
        [
          0.01334850593779309
        ]
      ],
      "std_errors": [
        0.11553573446251636
      ],
      "z_statistics": [
        -2.0066030958432566
      ],
      "p_values": [
        0.044791941421101385
      ],
      "conf_int": [
        [
          -0.45828024092692493,
          -0.005388483979094583
        ]
      ],
      "fitted": [
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334,
        0.4083333333333334
      ],
      "residuals": [
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666,
        -0.4083333333333334,
        -0.4083333333333334,
        0.5916666666666666,
        0.5916666666666666
      ],
      "log_likelihood": -81.14954325649146,
      "deviance": 162.2990865129829,
      "null_deviance": 162.2990865129829,
      "aic": 164.2990865129829,
      "df_residual": 119,
      "iterations": 4,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 1.942890293094024e-16,
        "phit": 2.498001805406602e-16
      },
      "covariance": {
        "statsmodels": 1.0408340855860843e-17,
        "phit": 0.0
      },
      "std_errors": {
        "statsmodels": 4.163336342344337e-17,
        "phit": 0.0
      },
      "z_statistics": {
        "statsmodels": 2.6645352591003757e-15,
        "phit": 2.220446049250313e-15
      },
      "p_values": {
        "statsmodels": 2.914335439641036e-16,
        "phit": 1.9996296285462734e-12
      },
      "conf_int": {
        "statsmodels": 3.608224830031759e-16,
        "phit": 3.0531133177191805e-16
      },
      "fitted": {
        "statsmodels": 5.551115123125783e-17,
        "phit": 1.1102230246251565e-16
      },
      "residuals": {
        "statsmodels": 1.1102230246251565e-16,
        "phit": 2.220446049250313e-16
      },
      "log_likelihood": {
        "statsmodels": 4.263256414560601e-14,
        "phit": 1.4210854715202004e-14
      },
      "deviance": {
        "statsmodels": 8.526512829121202e-14,
        "phit": 2.842170943040401e-14
      },
      "null_deviance": {
        "statsmodels": 5.684341886080802e-14,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 8.526512829121202e-14,
        "phit": 2.842170943040401e-14
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "correlated",
    "input": {
      "x": [
        [
          1,
          1.83,
          1.9982941969615795
        ],
        [
          1,
          2.49,
          2.6718594853651365
        ],
        [
          1,
          1.52,
          1.5482240016119735
        ],
        [
          1,
          4.85,
          4.698639500938414
        ],
        [
          1,
          2.6,
          2.4082151450673726
        ],
        [
          1,
          9.7,
          9.644116900360213
        ],
        [
          1,
          10.7,
          10.831397319743758
        ],
        [
          1,
          10.83,
          11.027871649324677
        ],
        [
          1,
          8.16,
          8.242423697048352
        ],
        [
          1,
          4.2,
          4.091195777822127
        ],
        [
          1,
          11.8,
          11.60000195868986
        ],
        [
          1,
          7.45,
          7.342685416399913
        ],
        [
          1,
          11.99,
          12.074033407365329
        ],
        [
          1,
          2.59,
          2.788121471138974
        ],
        [
          1,
          1.92,
          2.0500575680314235
        ],
        [
          1,
          10.05,
          9.992419336666988
        ],
        [
          1,
          3.83,
          3.6377205016240888
        ],
        [
          1,
          2.02,
          1.8698025506456648
        ],
        [
          1,
          10.73,
          10.75997544193259
        ],
        [
          1,
          1.58,
          1.7625890501455257
        ],
        [
          1,
          6.63,
          6.797331127707211
        ],
        [
          1,
          4.48,
          4.47822973814192
        ],
        [
          1,
          2.67,
          2.5007559191649658
        ],
        [
          1,
          8.37,
          8.188884327598675
        ],
        [
          1,
          4.04,
          4.013529649980446
        ],
        [
          1,
          9.04,
          9.19251169009592
        ],
        [
          1,
          7.51,
          7.701275185680901
        ],
        [
          1,
          9.3,
          9.354181157661575
        ],
        [
          1,
          3.19,
          3.0572732231574062
        ],
        [
          1,
          1.3,
          1.1023936751814276
        ],
        [
          1,
          6.15,
          6.069192470935388
        ],
        [
          1,
          9.61,
          9.720285336248338
        ],
        [
          1,
          10.8,
          10.999982372021455
        ],
        [
          1,
          10.65,
          10.755816537224005
        ],
        [
          1,
          1.48,
          1.3943634661007698
        ],
        [
          1,
          4.19,
          3.9916442293113774
        ],
        [
          1,
          1.76,
          1.6312923733286002
        ],
        [
          1,
          9.84,
          9.899273715741877
        ],
        [
          1,
          5.65,
          5.842759077256818
        ],
        [
          1,
          11.71,
          11.85902263209587
        ],
        [
          1,
          10.41,
          10.378275466239058
        ],
        [
          1,
          4.5,
          4.316695690416873
        ],
        [
          1,
          8.76,
          8.59364505147428
        ],
        [
          1,
          3.39,
          3.393540385021083
        ],
        [
          1,
          8.26,
          8.430180704906823
        ],
        [
          1,
          5.08,
          5.260357669529762
        ],
        [
          1,
          10.19,
          10.214714624549044
        ],
        [
          1,
          11.97,
          11.816349067735267
        ],
        [
          1,
          11.61,
          11.419249469448104
        ],
        [
          1,
          4.79,
          4.737525029259214
        ],
        [
          1,
          9.25,
          9.384045835168674
        ],
        [
          1,
          4.78,
          4.977325518408097
        ],
        [
          1,
          2.39,
          2.469185030036367
        ],
        [
          1,
          4.81,
          4.698242190229676
        ],
        [
          1,
          2.59,
          2.3900489653282757
        ],
        [
          1,
          7.56,
          7.4556897995826175
        ],
        [
          1,
          4.29,
          4.377232951049565
        ],
        [
          1,
          7.59,
          7.788574529616907
        ],
        [
          1,
          8.39,
          8.517347601427828
        ],
        [
          1,
          10.55,
          10.489037875779557
        ],
        [
          1,
          6.6,
          6.406776445998321
        ],
        [
          1,
          9.8,
          9.652163860670155
        ],
        [
          1,
          9.78,
          9.81347114006056
        ],
        [
          1,
          10.13,
          10.314005207639358
        ],
        [
          1,
          10.02,
          10.18536573589802
        ],
        [
          1,
          6.1,
          6.094689769195206
        ],
        [
          1,
          1.16,
          0.9888960042049355
        ],
        [
          1,
          10.95,
          10.77041446386214
        ],
        [
          1,
          5.15,
          5.127043037243363
        ],
        [
          1,
          8.94,
          9.094778136311577
        ],
        [
          1,
          2.31,
          2.500210930650875
        ],
        [
          1,
          7.65,
          7.700764672552408
        ],
        [
          1,
          10.6,
          10.464645608622538
        ],
        [
          1,
          8.62,
          8.42297074790635
        ],
        [
          1,
          6.94,
          6.862443672918114
        ],
        [
          1,
          4.16,
          4.273221527379636
        ],
        [
          1,
          8.52,
          8.719904031716146
        ],
        [
          1,
          8.26,
          8.362795691197507
        ],
        [
          1,
          7.84,
          7.751177466258498
        ],
        [
          1,
          10,
          9.801222269215325
        ],
        [
          1,
          6.41,
          6.284022401145109
        ],
        [
          1,
          8.08,
          8.142645756486617
        ],
        [
          1,
          7.53,
          7.723672892220037
        ],
        [
          1,
          9.37,
          9.516638064014657
        ],
        [
          1,
          2.5,
          2.4647848760102824
        ],
        [
          1,
          7.21,
          7.025308310599188
        ],
        [
          1,
          2.53,
          2.3656364326738353
        ],
        [
          1,
          4.98,
          4.9870796605467325
        ],
        [
          1,
          7.35,
          7.52201388116249
        ],
        [
          1,
          5.76,
          5.938799332720111
        ],
        [
          1,
          1.25,
          1.2711975023502313
        ],
        [
          1,
          7.52,
          7.364106786076839
        ],
        [
          1,
          1.36,
          1.1703435717460107
        ],
        [
          1,
          4.68,
          4.630949602906469
        ],
        [
          1,
          8.02,
          8.156652342947224
        ],
        [
          1,
          6.32,
          6.516717549086869
        ],
        [
          1,
          11.98,
          12.055921547805506
        ],
        [
          1,
          10.74,
          10.625323625601915
        ],
        [
          1,
          7.83,
          7.630158633162729
        ],
        [
          1,
          1.76,
          1.6587268717780483
        ],
        [
          1,
          11.29,
          11.38040515743567
        ],
        [
          1,
          8.06,
          8.258965358271682
        ],
        [
          1,
          8.97,
          9.09459772628847
        ],
        [
          1,
          10.91,
          10.845675519367495
        ],
        [
          1,
          1.09,
          0.8958929432925031
        ],
        [
          1,
          2.99,
          2.8445714999838296
        ],
        [
          1,
          4.13,
          4.166956348912134
        ],
        [
          1,
          2.41,
          2.5953637010835573
        ],
        [
          1,
          5.97,
          6.133348521327263
        ],
        [
          1,
          9.03,
          9.021151464382985
        ],
        [
          1,
          9.21,
          9.037089710277879
        ],
        [
          1,
          3.14,
          2.9620008791266335
        ],
        [
          1,
          2.2,
          2.1805636188213584
        ],
        [
          1,
          1.26,
          1.416996077736262
        ],
        [
          1,
          7.2,
          7.389087066804954
        ],
        [
          1,
          4.14,
          4.187332278672857
        ],
        [
          1,
          6.85,
          6.712060411812922
        ],
        [
          1,
          4.83,
          4.633609566191184
        ],
        [
          1,
          10.62,
          10.545719179712382
        ],
        [
          1,
          11.35,
          11.466122236842462
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -1.2674857409500127,
        0.47289187281723355,
        -0.3205097627519413
      ],
      "covariance": [
        [
          0.086231899306182,
          -0.041118176110627666,
          0.030769330736453247
        ],
        [
          -0.041118176110627666,
          0.7594398033943222,
          -0.7532226969260434
        ],
        [
          0.030769330736453247,
          -0.7532226969260434,
          0.748500620804782
        ]
      ],
      "std_errors": [
        0.2936526848271304,
        0.8714584346911344,
        0.8651593037150915
      ],
      "z_statistics": [
        -4.316274995735746,
        0.5426442088254475,
        -0.3704632908363076
      ],
      "p_values": [
        1.586842720184488e-05,
        0.5873747942222196,
        0.7110373235510665
      ],
      "conf_int": [
        [
          -1.8430344271746797,
          -0.6919370547253456
        ],
        [
          -1.23513527320104,
          2.180919018835507
        ],
        [
          -2.0161908389232703,
          1.3751713134193877
        ]
      ],
      "fitted": [
        0.14857457590973813,
        0.17198708193547027,
        0.14803205227059002,
        0.3156421434016876,
        0.20902085912016002,
        0.5903835835645369,
        0.6258526361306582,
        0.6252856330739579,
        0.47987579144542747,
        0.2767217408105497,
        0.7239861730916046,
        0.4610282232843853,
        0.7028593687764285,
        0.17455527133850327,
        0.15467263620470156,
        0.611185284114956,
        0.26689374220248385,
        0.18100700562114755,
        0.6398159496902907,
        0.13890689352864102,
        0.3779673594807754,
        0.27952723984385786,
        0.2100115628623011,
        0.5263118282826602,
        0.25998942408945375,
        0.5243869139406441,
        0.4268491843224576,
        0.5526274029849402,
        0.2300000811044515,
        0.1571947392612981,
        0.38039781052120153,
        0.5641733519550977,
        0.6232944466445068,
        0.626072309335236,
        0.1551690450293597,
        0.28589075085968074,
        0.1690209977967697,
        0.5843195216600277,
        0.3197821794303398,
        0.6805172021577075,
        0.628914615451089,
        0.30048175959334744,
        0.5480356421077962,
        0.22601196396136092,
        0.4747422726524043,
        0.29075136912345195,
        0.6092507189323318,
        0.7276678273240585,
        0.7132171717248393,
        0.3012681374914774,
        0.5394649181160108,
        0.27347258568884314,
        0.17652952895337737,
        0.30899244036221485,
        0.20933528663952633,
        0.4673056430302757,
        0.2605257142295597,
        0.43071638363998355,
        0.4881069043174098,
        0.6404584488277476,
        0.4208052911221132,
        0.6076663493048762,
        0.5839790416451434,
        0.5859619002485742,
        0.5817536057318325,
        0.36834008645400634,
        0.15012859985980545,
        0.6767598525355639,
        0.3172652201154351,
        0.5180270170437921,
        0.16442136954225167,
        0.4530206870250109,
        0.6521557202022155,
        0.5434772158917416,
        0.42657673726782297,
        0.25147200052227714,
        0.4867330846829253,
        0.4833463926430156,
        0.4823160924703902,
        0.6255331043793322,
        0.4011624582177785,
        0.4775446906513053,
        0.4277432938625807,
        0.5451177921741881,
        0.19072066698586193,
        0.45635726272259186,
        0.20347331102579275,
        0.30471336505207913,
        0.4197201866769811,
        0.32741163902931614,
        0.13922627478335578,
        0.4714573440429489,
        0.15878611453577152,
        0.295075807052396,
        0.46446957758356017,
        0.35663024263746135,
        0.7032317908944773,
        0.6575747000847398,
        0.4958978644870813,
        0.1668134621002929,
        0.6641924961758708,
        0.45895915439422064,
        0.5237019601405648,
        0.6611558469663982,
        0.14936143711003713,
        0.222060756896777,
        0.2578485340726256,
        0.16861425499006052,
        0.3408592032382507,
        0.5443348602890812,
        0.5758832860695539,
        0.2320978770663733,
        0.1772189498801699,
        0.13012444477839408,
        0.40868117388471215,
        0.25726695165645064,
        0.42878932041944096,
        0.31970098888145876,
        0.6460284501958199,
        0.6645207530413423
      ],
      "residuals": [
        -0.14857457590973813,
        -0.17198708193547027,
        0.85196794772941,
        -0.3156421434016876,
        0.79097914087984,
        0.4096164164354631,
        0.3741473638693418,
        0.3747143669260421,
        0.5201242085545725,
        -0.2767217408105497,
        0.2760138269083954,
        -0.4610282232843853,
        -0.7028593687764285,
        -0.17455527133850327,
        -0.15467263620470156,
        -0.611185284114956,
        -0.26689374220248385,
        -0.18100700562114755,
        0.36018405030970935,
        -0.13890689352864102,
        0.6220326405192246,
        -0.27952723984385786,
        -0.2100115628623011,
        -0.5263118282826602,
        -0.25998942408945375,
        -0.5243869139406441,
        0.5731508156775424,
        0.4473725970150598,
        -0.2300000811044515,
        -0.1571947392612981,
        0.6196021894787984,
        -0.5641733519550977,
        0.37670555335549316,
        0.37392769066476395,
        -0.1551690450293597,
        -0.28589075085968074,
        -0.1690209977967697,
        -0.5843195216600277,
        -0.3197821794303398,
        -0.6805172021577075,
        0.37108538454891105,
        -0.30048175959334744,
        -0.5480356421077962,
        -0.22601196396136092,
        -0.4747422726524043,
        -0.29075136912345195,
        0.39074928106766815,
        0.27233217267594145,
        0.28678282827516066,
        -0.3012681374914774,
        -0.5394649181160108,
        -0.27347258568884314,
        -0.17652952895337737,
        0.6910075596377852,
        -0.20933528663952633,
        0.5326943569697242,
        -0.2605257142295597,
        -0.43071638363998355,
        -0.4881069043174098,
        -0.6404584488277476,
        -0.4208052911221132,
        -0.6076663493048762,
        -0.5839790416451434,
        -0.5859619002485742,
        0.41824639426816745,
        0.6316599135459937,
        -0.15012859985980545,
        0.3232401474644361,
        0.6827347798845649,
        -0.5180270170437921,
        0.8355786304577484,
        -0.4530206870250109,
        0.34784427979778454,
        -0.5434772158917416,
        0.573423262732177,
        -0.25147200052227714,
        -0.4867330846829253,
        0.5166536073569844,
        -0.4823160924703902,
        0.3744668956206678,
        -0.4011624582177785,
        0.5224553093486948,
        0.5722567061374193,
        -0.5451177921741881,
        -0.19072066698586193,
        -0.45635726272259186,
        -0.20347331102579275,
        0.6952866349479209,
        -0.4197201866769811,
        -0.32741163902931614,
        -0.13922627478335578,
        -0.4714573440429489,
        -0.15878611453577152,
        0.704924192947604,
        -0.46446957758356017,
        0.6433697573625387,
        0.2967682091055227,
        0.34242529991526016,
        0.5041021355129187,
        0.8331865378997071,
        0.33580750382412916,
        0.5410408456057794,
        0.4762980398594352,
        -0.6611558469663982,
        -0.14936143711003713,
        0.777939243103223,
        -0.2578485340726256,
        -0.16861425499006052,
        -0.3408592032382507,
        0.4556651397109188,
        0.42411671393044614,
        0.7679021229336267,
        -0.1772189498801699,
        -0.13012444477839408,
        0.5913188261152879,
        0.7427330483435494,
        -0.42878932041944096,
        -0.31970098888145876,
        0.3539715498041801,
        0.3354792469586577
      ],
      "log_likelihood": -72.86030716042045,
      "deviance": 145.72061432084087,
      "null_deviance": 162.2990865129829,
      "aic": 151.7206143208409,
      "df_residual": 117
    },
    "statsmodels": {
      "coefficients": [
        -1.26748574094394,
        0.47289187278540545,
        -0.32050976272119275
      ],
      "covariance": [
        [
          0.08623189930015931,
          -0.041118176093466234,
          0.030769330720076715
        ],
        [
          -0.041118176093466234,
          0.7594398033552715,
          -0.7532226968891778
        ],
        [
          0.030769330720076715,
          -0.7532226968891778,
          0.7485006207699914
        ]
      ],
      "std_errors": [
        0.2936526848168757,
        0.8714584346687291,
        0.8651593036949851
      ],
      "z_statistics": [
        -4.316274995865796,
        0.5426442088028762,
        -0.3704632908093763
      ],
      "p_values": [
        1.5868427192500586e-05,
        0.5873747942377634,
        0.7110373235711294
      ],
      "conf_int": [
        [
          -1.8430344271485082,
          -0.6919370547393717
        ],
        [
          -1.235135273188955,
          2.180919018759766
        ],
        [
          -2.0161908388531145,
          1.3751713134107288
        ]
      ],
      "fitted": [
        0.14857457591188622,
        0.1719870819377588,
        0.14803205227181482,
        0.3156421434003305,
        0.20902085911940382,
        0.5903835835621593,
        0.6258526361301134,
        0.6252856330741342,
        0.479875791445347,
        0.27672174080994494,
        0.7239861730873209,
        0.46102822328229315,
        0.7028593687749445,
        0.17455527134091442,
        0.15467263620660499,
        0.6111852841124462,
        0.26689374220117734,
        0.18100700562095634,
        0.6398159496885736,
        0.13890689353085084,
        0.37796735948231913,
        0.2795272398442554,
        0.21001156286172074,
        0.5263118282792636,
        0.2599894240897449,
        0.5243869139410435,
        0.42684918432396635,
        0.5526274029840306,
        0.23000008110401066,
        0.15719473926095978,
        0.3803978105200394,
        0.5641733519547392,
        0.623294446644721,
        0.6260723093344133,
        0.1551690450297989,
        0.2858907508581338,
        0.169020997796824,
        0.5843195216589636,
        0.31978217943244924,
        0.6805172021569977,
        0.6289146154487683,
        0.300481759591809,
        0.5480356421044303,
        0.2260119639621193,
        0.47474227265335506,
        0.29075136912555444,
        0.6092507189307321,
        0.7276678273202156,
        0.7132171717206423,
        0.3012681374912296,
        0.5394649181160937,
        0.2734725856911657,
        0.17652952895491375,
        0.30899244036131424,
        0.20933528663870032,
        0.4673056430281702,
        0.26052571423089876,
        0.4307163836415495,
        0.4881069043177813,
        0.6404584488250582,
        0.42080529111937837,
        0.6076663493013973,
        0.5839790416437954,
        0.585961900248884,
        0.5817536057319654,
        0.3683400864537516,
        0.15012859985970256,
        0.6767598525315168,
        0.3172652201153665,
        0.5180270170442625,
        0.16442136954458664,
        0.45302068702476334,
        0.6521557201986928,
        0.543477215888057,
        0.4265767372663313,
        0.2514720005238911,
        0.4867330846841303,
        0.4833463926431416,
        0.4823160924683487,
        0.6255331043752257,
        0.40116245821595337,
        0.47754469065101723,
        0.4277432938641109,
        0.545117792174373,
        0.1907206669864851,
        0.4563572627196612,
        0.20347331102530836,
        0.3047133650523994,
        0.41972018667832045,
        0.32741163903124826,
        0.13922627478454763,
        0.4714573440402276,
        0.15878611453547448,
        0.2950758070522277,
        0.4644695775842025,
        0.3566302426394373,
        0.7032317908929115,
        0.6575747000814158,
        0.49589786448368056,
        0.16681346210055759,
        0.6641924961746549,
        0.4589591543956053,
        0.5237019601406527,
        0.6611558469635872,
        0.14936143710978778,
        0.2220607568962928,
        0.25784853407351394,
        0.16861425499236904,
        0.34085920323995633,
        0.5443348602875159,
        0.5758832860659558,
        0.23209787706552176,
        0.17721894988097542,
        0.13012444478041357,
        0.40868117388631015,
        0.2572669516574374,
        0.4287893204172568,
        0.3197009888796071,
        0.6460284501929653,
        0.6645207530403915
      ],
      "residuals": [
        -0.14857457591188622,
        -0.1719870819377588,
        0.8519679477281852,
        -0.3156421434003305,
        0.7909791408805962,
        0.40961641643784075,
        0.37414736386988656,
        0.3747143669258658,
        0.520124208554653,
        -0.27672174080994494,
        0.27601382691267906,
        -0.46102822328229315,
        -0.7028593687749445,
        -0.17455527134091442,
        -0.15467263620660499,
        -0.6111852841124462,
        -0.26689374220117734,
        -0.18100700562095634,
        0.3601840503114264,
        -0.13890689353085084,
        0.6220326405176808,
        -0.2795272398442554,
        -0.21001156286172074,
        -0.5263118282792636,
        -0.2599894240897449,
        -0.5243869139410435,
        0.5731508156760337,
        0.44737259701596943,
        -0.23000008110401066,
        -0.15719473926095978,
        0.6196021894799606,
        -0.5641733519547392,
        0.376705553355279,
        0.37392769066558673,
        -0.1551690450297989,
        -0.2858907508581338,
        -0.169020997796824,
        -0.5843195216589636,
        -0.31978217943244924,
        -0.6805172021569977,
        0.37108538455123175,
        -0.300481759591809,
        -0.5480356421044303,
        -0.2260119639621193,
        -0.47474227265335506,
        -0.29075136912555444,
        0.3907492810692679,
        0.2723321726797844,
        0.28678282827935775,
        -0.3012681374912296,
        -0.5394649181160937,
        -0.2734725856911657,
        -0.17652952895491375,
        0.6910075596386858,
        -0.20933528663870032,
        0.5326943569718299,
        -0.26052571423089876,
        -0.4307163836415495,
        -0.4881069043177813,
        -0.6404584488250582,
        -0.42080529111937837,
        -0.6076663493013973,
        -0.5839790416437954,
        -0.585961900248884,
        0.41824639426803456,
        0.6316599135462484,
        -0.15012859985970256,
        0.3232401474684832,
        0.6827347798846335,
        -0.5180270170442625,
        0.8355786304554134,
        -0.45302068702476334,
        0.34784427980130717,
        -0.543477215888057,
        0.5734232627336687,
        -0.2514720005238911,
        -0.4867330846841303,
        0.5166536073568584,
        -0.4823160924683487,
        0.3744668956247743,
        -0.40116245821595337,
        0.5224553093489828,
        0.5722567061358891,
        -0.545117792174373,
        -0.1907206669864851,
        -0.4563572627196612,
        -0.20347331102530836,
        0.6952866349476006,
        -0.41972018667832045,
        -0.32741163903124826,
        -0.13922627478454763,
        -0.4714573440402276,
        -0.15878611453547448,
        0.7049241929477723,
        -0.4644695775842025,
        0.6433697573605627,
        0.29676820910708845,
        0.34242529991858417,
        0.5041021355163194,
        0.8331865378994424,
        0.3358075038253451,
        0.5410408456043947,
        0.47629803985934727,
        -0.6611558469635872,
        -0.14936143710978778,
        0.7779392431037072,
        -0.25784853407351394,
        -0.16861425499236904,
        -0.34085920323995633,
        0.4556651397124841,
        0.42411671393404415,
        0.7679021229344782,
        -0.17721894988097542,
        -0.13012444478041357,
        0.5913188261136899,
        0.7427330483425626,
        -0.4287893204172568,
        -0.3197009888796071,
        0.3539715498070347,
        0.3354792469596085
      ],
      "log_likelihood": -72.86030716042043,
      "deviance": 145.72061432084087,
      "null_deviance": 162.29908651298285,
      "aic": 151.72061432084087,
      "df_residual": 117
    },
    "phit": {
      "coefficients": [
        -1.2674857409989277,
        0.4728918727659627,
        -0.3205097626957522
      ],
      "covariance": [
        [
          0.08623189930561985,
          -0.04111817609376781,
          0.030769330719771226
        ],
        [
          -0.04111817609376781,
          0.759439803372646,
          -0.7532226969064859
        ],
        [
          0.030769330719771226,
          -0.7532226969064859,
          0.7485006207873016
        ]
      ],
      "std_errors": [
        0.29365268482617324,
        0.8714584346786978,
        0.8651593037049892
      ],
      "z_statistics": [
        -4.316274995916389,
        0.5426442087743581,
        -0.3704632907756869
      ],
      "p_values": [
        1.5868427190131056e-05,
        0.5873747942574024,
        0.7110373235962271
      ],
      "conf_int": [
        [
          -1.8430344272217187,
          -0.6919370547761367
        ],
        [
          -1.235135273227936,
          2.1809190187598615
        ],
        [
          -2.0161908388472813,
          1.3751713134557768
        ]
      ],
      "fitted": [
        0.14857457591517162,
        0.17198708194386872,
        0.14803205227381094,
        0.31564214338975316,
        0.20902085912662718,
        0.5903835835628467,
        0.625852636134862,
        0.6252856330798217,
        0.4798757914437738,
        0.2767217407990453,
        0.7239861730908971,
        0.461028223277118,
        0.7028593687815439,
        0.17455527134750679,
        0.15467263621020405,
        0.6111852841139126,
        0.2668937421890448,
        0.1810070056248976,
        0.6398159496923644,
        0.13890689352868352,
        0.37796735947815063,
        0.27952723983478295,
        0.2100115628693359,
        0.5263118282755241,
        0.2599894240795503,
        0.5243869139422828,
        0.42684918432197444,
        0.5526274029848884,
        0.23000008111519732,
        0.15719473926183755,
        0.3803978105123621,
        0.5641733519568878,
        0.6232944466503699,
        0.626072309338801,
        0.15516904503149492,
        0.2858907508462664,
        0.16902099779958757,
        0.5843195216611237,
        0.31978217942665876,
        0.6805172021638011,
        0.6289146154512786,
        0.3004817595804447,
        0.5480356421017849,
        0.22601196397419804,
        0.47474227265291075,
        0.2907513691187237,
        0.6092507189333262,
        0.7276678273244981,
        0.7132171717239774,
        0.3012681374816172,
        0.5394649181176426,
        0.27347258568407873,
        0.17652952896058627,
        0.3089924403511043,
        0.20933528664588003,
        0.4673056430232802,
        0.26052571422211934,
        0.43071638363981546,
        0.48810690431721215,
        0.6404584488275782,
        0.42080529111143283,
        0.6076663493014084,
        0.5839790416455592,
        0.585961900252956,
        0.5817536057356044,
        0.36834008644676314,
        0.15012859986014024,
        0.6767598525337142,
        0.3172652201065711,
        0.5180270170452866,
        0.16442136954985404,
        0.4530206870216679,
        0.652155720200594,
        0.5434772158847657,
        0.4265767372603169,
        0.25147200051523455,
        0.48673308468460835,
        0.48334639264201334,
        0.48231609246427365,
        0.6255331043752002,
        0.40116245820831825,
        0.47754469064905275,
        0.42774329386218907,
        0.5451177921763315,
        0.1907206669928303,
        0.4563572627131409,
        0.20347331103203548,
        0.3047133650436674,
        0.4197201866757694,
        0.3274116390255113,
        0.13922627478103677,
        0.4714573440347161,
        0.15878611453658342,
        0.29507580704250813,
        0.4644695775828482,
        0.35663024263493376,
        0.7032317908994148,
        0.6575747000838079,
        0.4958978644784511,
        0.166813462103339,
        0.6641924961801344,
        0.45895915439497703,
        0.5237019601414421,
        0.6611558469668111,
        0.1493614371099502,
        0.22206075690602492,
        0.25784853406405833,
        0.16861425499809624,
        0.34085920323444563,
        0.5443348602870984,
        0.5758832860643311,
        0.23209787707654098,
        0.17721894988575893,
        0.1301244447775602,
        0.4086811738835939,
        0.25726695164809743,
        0.4287893204104212,
        0.31970098886852005,
        0.6460284501955013,
        0.6645207530462385
      ],
      "residuals": [
        -0.14857457591517162,
        -0.17198708194386872,
        0.851967947726189,
        -0.31564214338975316,
        0.7909791408733728,
        0.4096164164371533,
        0.374147363865138,
        0.37471436692017834,
        0.5201242085562262,
        -0.2767217407990453,
        0.2760138269091029,
        -0.461028223277118,
        -0.7028593687815439,
        -0.17455527134750679,
        -0.15467263621020405,
        -0.6111852841139126,
        -0.2668937421890448,
        -0.1810070056248976,
        0.36018405030763556,
        -0.13890689352868352,
        0.6220326405218494,
        -0.27952723983478295,
        -0.2100115628693359,
        -0.5263118282755241,
        -0.2599894240795503,
        -0.5243869139422828,
        0.5731508156780256,
        0.44737259701511156,
        -0.23000008111519732,
        -0.15719473926183755,
        0.6196021894876379,
        -0.5641733519568878,
        0.3767055533496301,
        0.373927690661199,
        -0.15516904503149492,
        -0.2858907508462664,
        -0.16902099779958757,
        -0.5843195216611237,
        -0.31978217942665876,
        -0.6805172021638011,
        0.3710853845487214,
        -0.3004817595804447,
        -0.5480356421017849,
        -0.22601196397419804,
        -0.47474227265291075,
        -0.2907513691187237,
        0.39074928106667384,
        0.2723321726755019,
        0.28678282827602264,
        -0.3012681374816172,
        -0.5394649181176426,
        -0.27347258568407873,
        -0.17652952896058627,
        0.6910075596488957,
        -0.20933528664588003,
        0.5326943569767197,
        -0.26052571422211934,
        -0.43071638363981546,
        -0.48810690431721215,
        -0.6404584488275782,
        -0.42080529111143283,
        -0.6076663493014084,
        -0.5839790416455592,
        -0.585961900252956,
        0.4182463942643956,
        0.6316599135532368,
        -0.15012859986014024,
        0.3232401474662858,
        0.6827347798934289,
        -0.5180270170452866,
        0.835578630450146,
        -0.4530206870216679,
        0.347844279799406,
        -0.5434772158847657,
        0.5734232627396831,
        -0.25147200051523455,
        -0.48673308468460835,
        0.5166536073579866,
        -0.48231609246427365,
        0.37446689562479984,
        -0.40116245820831825,
        0.5224553093509472,
        0.572256706137811,
        -0.5451177921763315,
        -0.1907206669928303,
        -0.4563572627131409,
        -0.20347331103203548,
        0.6952866349563326,
        -0.4197201866757694,
        -0.3274116390255113,
        -0.13922627478103677,
        -0.4714573440347161,
        -0.15878611453658342,
        0.7049241929574919,
        -0.4644695775828482,
        0.6433697573650663,
        0.2967682091005852,
        0.3424252999161921,
        0.5041021355215489,
        0.833186537896661,
        0.33580750381986557,
        0.541040845605023,
        0.4762980398585579,
        -0.6611558469668111,
        -0.1493614371099502,
        0.7779392430939751,
        -0.25784853406405833,
        -0.16861425499809624,
        -0.34085920323444563,
        0.45566513971290157,
        0.42411671393566885,
        0.767902122923459,
        -0.17721894988575893,
        -0.1301244447775602,
        0.5913188261164062,
        0.7427330483519026,
        -0.4287893204104212,
        -0.31970098886852005,
        0.35397154980449874,
        0.3354792469537615
      ],
      "log_likelihood": -72.86030716028475,
      "deviance": 145.7206143205695,
      "null_deviance": 162.2990865129829,
      "aic": 151.7206143205695,
      "df_residual": 117,
      "iterations": 10,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 3.182809571455891e-11,
        "phit": 5.618910892124518e-11
      },
      "covariance": {
        "statsmodels": 3.905065160125787e-11,
        "phit": 2.167610535508402e-11
      },
      "std_errors": {
        "statsmodels": 2.2405299837657822e-11,
        "phit": 1.2436607299548541e-11
      },
      "z_statistics": {
        "statsmodels": 1.3004974874775144e-10,
        "phit": 1.8064305606912967e-10
      },
      "p_values": {
        "statsmodels": 2.0062840278001204e-11,
        "phit": 4.516054197267749e-11
      },
      "conf_int": {
        "statsmodels": 7.574119109676758e-11,
        "phit": 7.598899287586391e-11
      },
      "fitted": {
        "statsmodels": 4.283684518213704e-12,
        "phit": 1.3439027668482595e-11
      },
      "residuals": {
        "statsmodels": 4.283684518213704e-12,
        "phit": 1.3439027668482595e-11
      },
      "log_likelihood": {
        "statsmodels": 1.4210854715202004e-14,
        "phit": 1.3569945167546393e-10
      },
      "deviance": {
        "statsmodels": 0.0,
        "phit": 2.7137048164149746e-10
      },
      "null_deviance": {
        "statsmodels": 5.684341886080802e-14,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 2.842170943040401e-14,
        "phit": 2.7139890335092787e-10
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "imbalanced",
    "input": {
      "x": [
        [
          1,
          1.83,
          56.39
        ],
        [
          1,
          2.49,
          61.62
        ],
        [
          1,
          1.52,
          34.88
        ],
        [
          1,
          4.85,
          78.07
        ],
        [
          1,
          2.6,
          66.36
        ],
        [
          1,
          9.7,
          81.6
        ],
        [
          1,
          10.7,
          75.03
        ],
        [
          1,
          10.83,
          80.27
        ],
        [
          1,
          8.16,
          81.41
        ],
        [
          1,
          4.2,
          59.63
        ],
        [
          1,
          11.8,
          84.54
        ],
        [
          1,
          7.45,
          71.37
        ],
        [
          1,
          11.99,
          86.19
        ],
        [
          1,
          2.59,
          50.28
        ],
        [
          1,
          1.92,
          45.47
        ],
        [
          1,
          10.05,
          83.86
        ],
        [
          1,
          3.83,
          50.96
        ],
        [
          1,
          2.02,
          28.23
        ],
        [
          1,
          10.73,
          83.28
        ],
        [
          1,
          1.58,
          50.61
        ],
        [
          1,
          6.63,
          65.27
        ],
        [
          1,
          4.48,
          58.04
        ],
        [
          1,
          2.67,
          58.73
        ],
        [
          1,
          8.37,
          75.27
        ],
        [
          1,
          4.04,
          64.07
        ],
        [
          1,
          9.04,
          72.06
        ],
        [
          1,
          7.51,
          70.66
        ],
        [
          1,
          9.3,
          88.99
        ],
        [
          1,
          3.19,
          48.59
        ],
        [
          1,
          1.3,
          39.56
        ],
        [
          1,
          6.15,
          70.58
        ],
        [
          1,
          9.61,
          87.11
        ],
        [
          1,
          10.8,
          71.4
        ],
        [
          1,
          10.65,
          74.56
        ],
        [
          1,
          1.48,
          49.19
        ],
        [
          1,
          4.19,
          48.81
        ],
        [
          1,
          1.76,
          48.94
        ],
        [
          1,
          9.84,
          70.92
        ],
        [
          1,
          5.65,
          79.16
        ],
        [
          1,
          11.71,
          93.65
        ],
        [
          1,
          10.41,
          87.76
        ],
        [
          1,
          4.5,
          74.61
        ],
        [
          1,
          8.76,
          58.68
        ],
        [
          1,
          3.39,
          42.27
        ],
        [
          1,
          8.26,
          66.12
        ],
        [
          1,
          5.08,
          73.77
        ],
        [
          1,
          10.19,
          72.85
        ],
        [
          1,
          11.97,
          79.13
        ],
        [
          1,
          11.61,
          84.14
        ],
        [
          1,
          4.79,
          64.25
        ],
        [
          1,
          9.25,
          69.29
        ],
        [
          1,
          4.78,
          58.54
        ],
        [
          1,
          2.39,
          48.95
        ],
        [
          1,
          4.81,
          52.58
        ],
        [
          1,
          2.59,
          52.99
        ],
        [
          1,
          7.56,
          69.2
        ],
        [
          1,
          4.29,
          69.75
        ],
        [
          1,
          7.59,
          77.72
        ],
        [
          1,
          8.39,
          79.59
        ],
        [
          1,
          10.55,
          84.76
        ],
        [
          1,
          6.6,
          59.23
        ],
        [
          1,
          9.8,
          83.91
        ],
        [
          1,
          9.78,
          72.62
        ],
        [
          1,
          10.13,
          68.86
        ],
        [
          1,
          10.02,
          75.17
        ],
        [
          1,
          6.1,
          59.55
        ],
        [
          1,
          1.16,
          55.02
        ],
        [
          1,
          10.95,
          95
        ],
        [
          1,
          5.15,
          60.94
        ],
        [
          1,
          8.94,
          60.52
        ],
        [
          1,
          2.31,
          53.74
        ],
        [
          1,
          7.65,
          72.07
        ],
        [
          1,
          10.6,
          74.89
        ],
        [
          1,
          8.62,
          70.42
        ],
        [
          1,
          6.94,
          70.08
        ],
        [
          1,
          4.16,
          51.82
        ],
        [
          1,
          8.52,
          75.87
        ],
        [
          1,
          8.26,
          80.1
        ],
        [
          1,
          7.84,
          77.18
        ],
        [
          1,
          10,
          81.56
        ],
        [
          1,
          6.41,
          61.14
        ],
        [
          1,
          8.08,
          74.06
        ],
        [
          1,
          7.53,
          69.84
        ],
        [
          1,
          9.37,
          71.92
        ],
        [
          1,
          2.5,
          37.32
        ],
        [
          1,
          7.21,
          78.28
        ],
        [
          1,
          2.53,
          53.38
        ],
        [
          1,
          4.98,
          73.13
        ],
        [
          1,
          7.35,
          68.11
        ],
        [
          1,
          5.76,
          60.89
        ],
        [
          1,
          1.25,
          54.01
        ],
        [
          1,
          7.52,
          64.25
        ],
        [
          1,
          1.36,
          40.08
        ],
        [
          1,
          4.68,
          59.68
        ],
        [
          1,
          8.02,
          58.34
        ],
        [
          1,
          6.32,
          56.81
        ],
        [
          1,
          11.98,
          61.9
        ],
        [
          1,
          10.74,
          74.75
        ],
        [
          1,
          7.83,
          66.12
        ],
        [
          1,
          1.76,
          52.3
        ],
        [
          1,
          11.29,
          86.01
        ],
        [
          1,
          8.06,
          56.46
        ],
        [
          1,
          8.97,
          61.82
        ],
        [
          1,
          10.91,
          72.69
        ],
        [
          1,
          1.09,
          31.47
        ],
        [
          1,
          2.99,
          48.2
        ],
        [
          1,
          4.13,
          62.12
        ],
        [
          1,
          2.41,
          66.31
        ],
        [
          1,
          5.97,
          46.22
        ],
        [
          1,
          9.03,
          73.07
        ],
        [
          1,
          9.21,
          79.32
        ],
        [
          1,
          3.14,
          52.42
        ],
        [
          1,
          2.2,
          47.49
        ],
        [
          1,
          1.26,
          38.22
        ],
        [
          1,
          7.2,
          60.45
        ],
        [
          1,
          4.14,
          69.24
        ],
        [
          1,
          6.85,
          59.9
        ],
        [
          1,
          4.83,
          69.45
        ],
        [
          1,
          10.62,
          81.19
        ],
        [
          1,
          11.35,
          67.69
        ]
      ],
      "y": [
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -3.913864161684334,
        -0.27666920692495445,
        0.05556198665857749
      ],
      "covariance": [
        [
          2.7032230327276534,
          0.14832536087677903,
          -0.05152684752298278
        ],
        [
          0.14832536087677903,
          0.02003190909640469,
          -0.0038135289441228884
        ],
        [
          -0.05152684752298278,
          -0.0038135289441228884,
          0.0010767590501680425
        ]
      ],
      "std_errors": [
        1.6441481176365023,
        0.14153412696733142,
        0.0328140069203388
      ],
      "z_statistics": [
        -2.3804814905062184,
        -1.954787957174559,
        1.6932399262748685
      ],
      "p_values": [
        0.01729002963554516,
        0.05060810318849025,
        0.0904098076601998
      ],
      "conf_int": [
        [
          -7.136335257501202,
          -0.6913930658674667
        ],
        [
          -0.5540709983642431,
          0.000732584514334278
        ],
        [
          -0.00875228509373463,
          0.11987625841088961
        ]
      ],
      "fitted": [
        0.09904219777965047,
        0.11919095117901743,
        0.008278522023780027,
        0.17931322416941994,
        0.172046072322568,
        0.019523210031841067,
        0.0034110187227051566,
        0.007138229531589868,
        0.04965750505712448,
        0.03897440575302848,
        0.006544280975804159,
        0.02223725971432535,
        0.007298213167075732,
        0.03312113674214875,
        0.02751333982267879,
        0.02092737400035246,
        0.016093989790625544,
        0.0018408404409786766,
        0.012056546573573518,
        0.06190100513118016,
        0.01693356449896421,
        0.026894959736809266,
        0.08235322474166518,
        0.02030771172250719,
        0.0705440281919815,
        0.007951000006814021,
        0.019431245659265073,
        0.06148498169077316,
        0.01801086747841667,
        0.018970019696065876,
        0.04515024366703726,
        0.04157889646730542,
        0.0016689979031532984,
        0.0032869750112683315,
        0.05589030637337743,
        0.009109730979464752,
        0.04632337647891584,
        0.003510642235648412,
        0.14034774055553204,
        0.02557134633628583,
        0.027563706887177332,
        0.15543557994767157,
        0.0010450941401592623,
        0.006154362086580051,
        0.005778444273235739,
        0.11113087987557216,
        0.003621798576078691,
        0.0023348705094661843,
        0.007122837444076671,
        0.04753372229891173,
        0.0043558628791503405,
        0.023642177740343526,
        0.03177353658403781,
        0.010084372158936662,
        0.045877897333800474,
        0.015363361936932973,
        0.1102261157265223,
        0.04498975175116951,
        0.03492051563324264,
        0.016864766281907796,
        0.007163776998535861,
        0.02482215229087102,
        0.004872092341867154,
        0.0019229957599700737,
        0.006045195028027231,
        0.010928896535328017,
        0.1194421747755592,
        0.047956054217036685,
        0.02542383580166532,
        0.0012445003457060746,
        0.058549297715552076,
        0.0213807929223848,
        0.003620845804565664,
        0.008514578098867853,
        0.026179854752585125,
        0.014422957052033959,
        0.019910646310322678,
        0.04017692088748492,
        0.03635261934623071,
        0.01582034730919151,
        0.011003300859355527,
        0.020954098523600077,
        0.01714120875931277,
        0.006032515534909682,
        0.005671284432724135,
        0.05946780270393174,
        0.04968265548592765,
        0.10964303458258702,
        0.015268439392264117,
        0.01682213902699346,
        0.10405169285246278,
        0.007663497250528601,
        0.01954634697840222,
        0.02919644753707725,
        0.0019184727668946535,
        0.006106367390801756,
        7.560484800182257e-05,
        0.0031472423589712153,
        0.008054744823799783,
        0.06746895774702073,
        0.01195497835273879,
        0.0013201182320463267,
        0.0015344799364463931,
        0.0019047234626691594,
        0.006814461047881545,
        0.019555490681099092,
        0.05424719117416052,
        0.1850405090256593,
        0.0013610000770970132,
        0.009329544034789888,
        0.019948642502944196,
        0.030738706054376234,
        0.029789409202188675,
        0.016222360658806032,
        0.00543017572881631,
        0.1127250490213935,
        0.006552828191073496,
        0.08205261910262408,
        0.009615737335582714,
        0.0004955011368362835
      ],
      "residuals": [
        -0.09904219777965047,
        -0.11919095117901743,
        -0.008278522023780027,
        -0.17931322416941994,
        0.827953927677432,
        -0.019523210031841067,
        -0.0034110187227051566,
        -0.007138229531589868,
        -0.04965750505712448,
        -0.03897440575302848,
        -0.006544280975804159,
        -0.02223725971432535,
        -0.007298213167075732,
        -0.03312113674214875,
        -0.02751333982267879,
        -0.02092737400035246,
        -0.016093989790625544,
        -0.0018408404409786766,
        -0.012056546573573518,
        -0.06190100513118016,
        -0.01693356449896421,
        -0.026894959736809266,
        0.9176467752583348,
        -0.02030771172250719,
        -0.0705440281919815,
        -0.007951000006814021,
        -0.019431245659265073,
        -0.06148498169077316,
        -0.01801086747841667,
        -0.018970019696065876,
        -0.04515024366703726,
        -0.04157889646730542,
        -0.0016689979031532984,
        -0.0032869750112683315,
        -0.05589030637337743,
        -0.009109730979464752,
        -0.04632337647891584,
        -0.003510642235648412,
        -0.14034774055553204,
        -0.02557134633628583,
        -0.027563706887177332,
        -0.15543557994767157,
        -0.0010450941401592623,
        -0.006154362086580051,
        -0.005778444273235739,
        -0.11113087987557216,
        -0.003621798576078691,
        -0.0023348705094661843,
        -0.007122837444076671,
        -0.04753372229891173,
        -0.0043558628791503405,
        -0.023642177740343526,
        -0.03177353658403781,
        -0.010084372158936662,
        -0.045877897333800474,
        -0.015363361936932973,
        0.8897738842734777,
        -0.04498975175116951,
        -0.03492051563324264,
        -0.016864766281907796,
        -0.007163776998535861,
        -0.02482215229087102,
        -0.004872092341867154,
        -0.0019229957599700737,
        -0.006045195028027231,
        -0.010928896535328017,
        -0.1194421747755592,
        -0.047956054217036685,
        -0.02542383580166532,
        -0.0012445003457060746,
        -0.058549297715552076,
        -0.0213807929223848,
        -0.003620845804565664,
        0.9914854219011322,
        -0.026179854752585125,
        -0.014422957052033959,
        -0.019910646310322678,
        -0.04017692088748492,
        -0.03635261934623071,
        -0.01582034730919151,
        -0.011003300859355527,
        -0.020954098523600077,
        -0.01714120875931277,
        -0.006032515534909682,
        -0.005671284432724135,
        -0.05946780270393174,
        -0.04968265548592765,
        -0.10964303458258702,
        -0.015268439392264117,
        -0.01682213902699346,
        -0.10405169285246278,
        -0.007663497250528601,
        -0.01954634697840222,
        -0.02919644753707725,
        -0.0019184727668946535,
        -0.006106367390801756,
        -7.560484800182257e-05,
        -0.0031472423589712153,
        -0.008054744823799783,
        -0.06746895774702073,
        -0.01195497835273879,
        -0.0013201182320463267,
        -0.0015344799364463931,
        -0.0019047234626691594,
        -0.006814461047881545,
        -0.019555490681099092,
        -0.05424719117416052,
        -0.1850405090256593,
        -0.0013610000770970132,
        -0.009329544034789888,
        -0.019948642502944196,
        -0.030738706054376234,
        -0.029789409202188675,
        -0.016222360658806032,
        -0.00543017572881631,
        -0.1127250490213935,
        -0.006552828191073496,
        -0.08205261910262408,
        -0.009615737335582714,
        -0.0004955011368362835
      ],
      "log_likelihood": -14.993593075492754,
      "deviance": 29.987186150985508,
      "null_deviance": 35.07473904205548,
      "aic": 35.98718615098551,
      "df_residual": 117
    },
    "statsmodels": {
      "coefficients": [
        -3.9138641616836787,
        -0.2766692069249371,
        0.055561986658566154
      ],
      "covariance": [
        [
          2.7032230327238267,
          0.1483253608766156,
          -0.0515268475229194
        ],
        [
          0.1483253608766156,
          0.02003190909640174,
          -0.0038135289441202855
        ],
        [
          -0.0515268475229194,
          -0.0038135289441202855,
          0.0010767590501669958
        ]
      ],
      "std_errors": [
        1.6441481176353385,
        0.141534126967321,
        0.03281400692032285
      ],
      "z_statistics": [
        -2.3804814905075045,
        -1.9547879571745803,
        1.6932399262753457
      ],
      "p_values": [
        0.017290029635484806,
        0.050608103188487706,
        0.09040980766010899
      ],
      "conf_int": [
        [
          -7.136335257498266,
          -0.6913930658690912
        ],
        [
          -0.5540709983642056,
          0.0007325845143312804
        ],
        [
          -0.008752285093714729,
          0.11987625841084704
        ]
      ],
      "fitted": [
        0.09904219777965867,
        0.11919095117901735,
        0.008278522023786483,
        0.1793132241693816,
        0.17204607232255487,
        0.019523210031836227,
        0.0034110187227050556,
        0.007138229531588532,
        0.049657505057111584,
        0.03897440575303286,
        0.006544280975802327,
        0.02223725971432404,
        0.007298213167073429,
        0.03312113674215834,
        0.02751333982268979,
        0.02092737400034636,
        0.01609398979063135,
        0.0018408404409808508,
        0.012056546573570262,
        0.061901005131193475,
        0.01693356449896548,
        0.02689495973681391,
        0.08235322474167067,
        0.020307711722504607,
        0.07054402819198136,
        0.007951000006813893,
        0.019431245659264313,
        0.06148498169074978,
        0.018010867478423783,
        0.018970019696076482,
        0.04515024366703362,
        0.04157889646729075,
        0.0016689979031534767,
        0.0032869750112682777,
        0.05589030637339132,
        0.009109730979469046,
        0.04632337647892855,
        0.003510642235648648,
        0.1403477405554998,
        0.025571346336273747,
        0.027563706887167194,
        0.15543557994764468,
        0.0010450941401597591,
        0.0061543620865841375,
        0.00577844427323654,
        0.11113087987555453,
        0.0036217985760787553,
        0.002334870509465927,
        0.007122837444074748,
        0.04753372229891265,
        0.00435586287915073,
        0.023642177740347662,
        0.031773536584047954,
        0.010084372158940477,
        0.045877897333810015,
        0.015363361936933023,
        0.1102261157265107,
        0.04498975175116061,
        0.03492051563323473,
        0.016864766281902612,
        0.007163776998537819,
        0.024822152290863715,
        0.004872092341867176,
        0.0019229957599703742,
        0.006045195028026833,
        0.010928896535330496,
        0.11944217477556962,
        0.04795605421701348,
        0.02542383580166848,
        0.0012445003457065837,
        0.05854929771556211,
        0.021380792922383346,
        0.0036208458045655506,
        0.008514578098867994,
        0.02617985475258393,
        0.01442295705203907,
        0.019910646310319906,
        0.04017692088747545,
        0.036352619346224045,
        0.015820347309187723,
        0.011003300859357648,
        0.02095409852359787,
        0.01714120875931251,
        0.006032515534909721,
        0.005671284432728593,
        0.05946780270391904,
        0.04968265548593729,
        0.10964303458257069,
        0.015268439392264507,
        0.016822139026996186,
        0.10405169285247462,
        0.007663497250529806,
        0.01954634697841291,
        0.02919644753708128,
        0.001918472766895464,
        0.006106367390803838,
        7.560484800187177e-05,
        0.0031472423589711533,
        0.0080547448238007,
        0.06746895774703279,
        0.01195497835273493,
        0.0013201182320469972,
        0.0015344799364469402,
        0.0019047234626692832,
        0.006814461047887582,
        0.019555490681106718,
        0.054247191174163094,
        0.18504050902564478,
        0.001361000077098063,
        0.009329544034789462,
        0.019948642502940112,
        0.030738706054384255,
        0.029789409202199156,
        0.01622236065881591,
        0.005430175728817778,
        0.11272504902138247,
        0.006552828191075251,
        0.0820526191026168,
        0.009615737335580616,
        0.0004955011368364315
      ],
      "residuals": [
        -0.09904219777965867,
        -0.11919095117901735,
        -0.008278522023786483,
        -0.1793132241693816,
        0.8279539276774451,
        -0.019523210031836227,
        -0.0034110187227050556,
        -0.007138229531588532,
        -0.049657505057111584,
        -0.03897440575303286,
        -0.006544280975802327,
        -0.02223725971432404,
        -0.007298213167073429,
        -0.03312113674215834,
        -0.02751333982268979,
        -0.02092737400034636,
        -0.01609398979063135,
        -0.0018408404409808508,
        -0.012056546573570262,
        -0.061901005131193475,
        -0.01693356449896548,
        -0.02689495973681391,
        0.9176467752583293,
        -0.020307711722504607,
        -0.07054402819198136,
        -0.007951000006813893,
        -0.019431245659264313,
        -0.06148498169074978,
        -0.018010867478423783,
        -0.018970019696076482,
        -0.04515024366703362,
        -0.04157889646729075,
        -0.0016689979031534767,
        -0.0032869750112682777,
        -0.05589030637339132,
        -0.009109730979469046,
        -0.04632337647892855,
        -0.003510642235648648,
        -0.1403477405554998,
        -0.025571346336273747,
        -0.027563706887167194,
        -0.15543557994764468,
        -0.0010450941401597591,
        -0.0061543620865841375,
        -0.00577844427323654,
        -0.11113087987555453,
        -0.0036217985760787553,
        -0.002334870509465927,
        -0.007122837444074748,
        -0.04753372229891265,
        -0.00435586287915073,
        -0.023642177740347662,
        -0.031773536584047954,
        -0.010084372158940477,
        -0.045877897333810015,
        -0.015363361936933023,
        0.8897738842734892,
        -0.04498975175116061,
        -0.03492051563323473,
        -0.016864766281902612,
        -0.007163776998537819,
        -0.024822152290863715,
        -0.004872092341867176,
        -0.0019229957599703742,
        -0.006045195028026833,
        -0.010928896535330496,
        -0.11944217477556962,
        -0.04795605421701348,
        -0.02542383580166848,
        -0.0012445003457065837,
        -0.05854929771556211,
        -0.021380792922383346,
        -0.0036208458045655506,
        0.991485421901132,
        -0.02617985475258393,
        -0.01442295705203907,
        -0.019910646310319906,
        -0.04017692088747545,
        -0.036352619346224045,
        -0.015820347309187723,
        -0.011003300859357648,
        -0.02095409852359787,
        -0.01714120875931251,
        -0.006032515534909721,
        -0.005671284432728593,
        -0.05946780270391904,
        -0.04968265548593729,
        -0.10964303458257069,
        -0.015268439392264507,
        -0.016822139026996186,
        -0.10405169285247462,
        -0.007663497250529806,
        -0.01954634697841291,
        -0.02919644753708128,
        -0.001918472766895464,
        -0.006106367390803838,
        -7.560484800187177e-05,
        -0.0031472423589711533,
        -0.0080547448238007,
        -0.06746895774703279,
        -0.01195497835273493,
        -0.0013201182320469972,
        -0.0015344799364469402,
        -0.0019047234626692832,
        -0.006814461047887582,
        -0.019555490681106718,
        -0.054247191174163094,
        -0.18504050902564478,
        -0.001361000077098063,
        -0.009329544034789462,
        -0.019948642502940112,
        -0.030738706054384255,
        -0.029789409202199156,
        -0.01622236065881591,
        -0.005430175728817778,
        -0.11272504902138247,
        -0.006552828191075251,
        -0.0820526191026168,
        -0.009615737335580616,
        -0.0004955011368364315
      ],
      "log_likelihood": -14.993593075492758,
      "deviance": 29.987186150985515,
      "null_deviance": 35.07473904205531,
      "aic": 35.987186150985515,
      "df_residual": 117
    },
    "phit": {
      "coefficients": [
        -3.913864161581427,
        -0.2766692069076056,
        0.05556198665547299
      ],
      "covariance": [
        [
          2.703223032670612,
          0.14832536087220813,
          -0.05152684752204233
        ],
        [
          0.14832536087220813,
          0.020031909095976894,
          -0.003813528944060592
        ],
        [
          -0.05152684752204233,
          -0.003813528944060592,
          0.0010767590501565226
        ]
      ],
      "std_errors": [
        1.6441481176191555,
        0.14153412696582013,
        0.032814006920163265
      ],
      "z_statistics": [
        -2.380481490468744,
        -1.954787957072855,
        1.6932399261893172
      ],
      "p_values": [
        0.0172900296365614,
        0.050608103198224764,
        0.09040980768026723
      ],
      "conf_int": [
        [
          -7.136335257364296,
          -0.6913930657985583
        ],
        [
          -0.5540709983439323,
          0.000732584528721103
        ],
        [
          -0.008752285096495102,
          0.11987625840744108
        ]
      ],
      "fitted": [
        0.09904219777717528,
        0.11919095117571464,
        0.008278522023899244,
        0.17931322417096643,
        0.17204607232292676,
        0.0195232100318228,
        0.003411018723133296,
        0.0071382295321098365,
        0.04965750505837569,
        0.038974405753854,
        0.0065442809763548646,
        0.022237259713893606,
        0.007298213167640256,
        0.03312113674002528,
        0.027513339821122897,
        0.020927374000272662,
        0.01609398979036679,
        0.0018408404411982683,
        0.012056546574006899,
        0.06190100513058366,
        0.016933564498861232,
        0.026894959735623718,
        0.0823532247403242,
        0.020307711722313295,
        0.0705440281915771,
        0.00795100000725902,
        0.019431245659057274,
        0.06148498169196879,
        0.018010867477949055,
        0.018970019695348457,
        0.045150243668025475,
        0.04157889646896493,
        0.0016689979034533156,
        0.003286975011688946,
        0.05589030637304857,
        0.009109730979664214,
        0.046323376479067445,
        0.0035106422360644874,
        0.14034774055250862,
        0.025571346336048552,
        0.027563706886633284,
        0.15543557994882035,
        0.001045094140371288,
        0.006154362086848694,
        0.005778444273663749,
        0.11113087987361205,
        0.0036217985765068465,
        0.0023348705098426474,
        0.007122837444625813,
        0.04753372229958014,
        0.004355862879584001,
        0.02364217773951337,
        0.03177353658204762,
        0.010084372159122201,
        0.0458778973341214,
        0.015363361937002683,
        0.11022611572432238,
        0.04498975175241996,
        0.03492051563174675,
        0.01686476628211979,
        0.007163776998896881,
        0.024822152290478478,
        0.004872092342327234,
        0.0019229957602872796,
        0.006045195028512833,
        0.01092889653554223,
        0.11944217477174242,
        0.04795605421885261,
        0.025423835800703905,
        0.0012445003459433527,
        0.05854929771527961,
        0.02138079292204143,
        0.0036208458050021666,
        0.00851457809928581,
        0.026179854751754997,
        0.014422957051923141,
        0.019910646310171243,
        0.040176920888939975,
        0.0363526193445037,
        0.015820347309416186,
        0.011003300859583268,
        0.020954098523330897,
        0.017141208759267494,
        0.006032515535374186,
        0.005671284432975576,
        0.05946780270471268,
        0.0496826554860863,
        0.10964303458065969,
        0.015268439392324255,
        0.016822139026829497,
        0.10405169284952044,
        0.00766349725091642,
        0.019546346977633997,
        0.02919644753567537,
        0.001918472767187105,
        0.006106367391167149,
        7.56048480440125e-05,
        0.003147242359385695,
        0.008054744824192966,
        0.06746895774619016,
        0.011954978353208363,
        0.0013201182322848707,
        0.0015344799367148535,
        0.0019047234629936646,
        0.006814461048050024,
        0.01955549068047631,
        0.054247191174459794,
        0.1850405090260774,
        0.001361000077322175,
        0.009329544035209096,
        0.019948642502853102,
        0.030738706052606344,
        0.029789409200406396,
        0.016222360658340474,
        0.005430175729211059,
        0.11272504901902036,
        0.006552828191452321,
        0.08205261910191688,
        0.009615737336072348,
        0.0004955011370350108
      ],
      "residuals": [
        -0.09904219777717528,
        -0.11919095117571464,
        -0.008278522023899244,
        -0.17931322417096643,
        0.8279539276770732,
        -0.0195232100318228,
        -0.003411018723133296,
        -0.0071382295321098365,
        -0.04965750505837569,
        -0.038974405753854,
        -0.0065442809763548646,
        -0.022237259713893606,
        -0.007298213167640256,
        -0.03312113674002528,
        -0.027513339821122897,
        -0.020927374000272662,
        -0.01609398979036679,
        -0.0018408404411982683,
        -0.012056546574006899,
        -0.06190100513058366,
        -0.016933564498861232,
        -0.026894959735623718,
        0.9176467752596758,
        -0.020307711722313295,
        -0.0705440281915771,
        -0.00795100000725902,
        -0.019431245659057274,
        -0.06148498169196879,
        -0.018010867477949055,
        -0.018970019695348457,
        -0.045150243668025475,
        -0.04157889646896493,
        -0.0016689979034533156,
        -0.003286975011688946,
        -0.05589030637304857,
        -0.009109730979664214,
        -0.046323376479067445,
        -0.0035106422360644874,
        -0.14034774055250862,
        -0.025571346336048552,
        -0.027563706886633284,
        -0.15543557994882035,
        -0.001045094140371288,
        -0.006154362086848694,
        -0.005778444273663749,
        -0.11113087987361205,
        -0.0036217985765068465,
        -0.0023348705098426474,
        -0.007122837444625813,
        -0.04753372229958014,
        -0.004355862879584001,
        -0.02364217773951337,
        -0.03177353658204762,
        -0.010084372159122201,
        -0.0458778973341214,
        -0.015363361937002683,
        0.8897738842756776,
        -0.04498975175241996,
        -0.03492051563174675,
        -0.01686476628211979,
        -0.007163776998896881,
        -0.024822152290478478,
        -0.004872092342327234,
        -0.0019229957602872796,
        -0.006045195028512833,
        -0.01092889653554223,
        -0.11944217477174242,
        -0.04795605421885261,
        -0.025423835800703905,
        -0.0012445003459433527,
        -0.05854929771527961,
        -0.02138079292204143,
        -0.0036208458050021666,
        0.9914854219007142,
        -0.026179854751754997,
        -0.014422957051923141,
        -0.019910646310171243,
        -0.040176920888939975,
        -0.0363526193445037,
        -0.015820347309416186,
        -0.011003300859583268,
        -0.020954098523330897,
        -0.017141208759267494,
        -0.006032515535374186,
        -0.005671284432975576,
        -0.05946780270471268,
        -0.0496826554860863,
        -0.10964303458065969,
        -0.015268439392324255,
        -0.016822139026829497,
        -0.10405169284952044,
        -0.00766349725091642,
        -0.019546346977633997,
        -0.02919644753567537,
        -0.001918472767187105,
        -0.006106367391167149,
        -7.56048480440125e-05,
        -0.003147242359385695,
        -0.008054744824192966,
        -0.06746895774619016,
        -0.011954978353208363,
        -0.0013201182322848707,
        -0.0015344799367148535,
        -0.0019047234629936646,
        -0.006814461048050024,
        -0.01955549068047631,
        -0.054247191174459794,
        -0.1850405090260774,
        -0.001361000077322175,
        -0.009329544035209096,
        -0.019948642502853102,
        -0.030738706052606344,
        -0.029789409200406396,
        -0.016222360658340474,
        -0.005430175729211059,
        -0.11272504901902036,
        -0.006552828191452321,
        -0.08205261910191688,
        -0.009615737336072348,
        -0.0004955011370350108
      ],
      "log_likelihood": -14.993593075459064,
      "deviance": 29.987186150918127,
      "null_deviance": 35.07473904205548,
      "aic": 35.98718615091813,
      "df_residual": 117,
      "iterations": 16,
      "converged": true,
      "n_input": 120,
      "n_observations": 120,
      "n_dropped": 0,
      "retained_rows": [
        0,
        1,
        2,
        3,
        4,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": []
    },
    "warnings": [],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 6.554756737386924e-13,
        "phit": 1.0290701624171561e-10
      },
      "covariance": {
        "statsmodels": 3.8267167212779896e-12,
        "phit": 5.704148264840114e-11
      },
      "std_errors": {
        "statsmodels": 1.163735774412089e-12,
        "phit": 1.734679067055822e-11
      },
      "z_statistics": {
        "statsmodels": 1.2860823517257813e-12,
        "phit": 1.0170397857223179e-10
      },
      "p_values": {
        "statsmodels": 9.08162434143378e-14,
        "phit": 2.0067419947977783e-11
      },
      "conf_int": {
        "statsmodels": 2.935429677108914e-12,
        "phit": 1.369055979694167e-10
      },
      "fitted": {
        "statsmodels": 3.833044992518353e-14,
        "phit": 3.8167802252075944e-12
      },
      "residuals": {
        "statsmodels": 3.833044992518353e-14,
        "phit": 3.8167802252075944e-12
      },
      "log_likelihood": {
        "statsmodels": 3.552713678800501e-15,
        "phit": 3.369038381606515e-11
      },
      "deviance": {
        "statsmodels": 7.105427357601002e-15,
        "phit": 6.73807676321303e-11
      },
      "null_deviance": {
        "statsmodels": 1.6342482922482304e-13,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 7.105427357601002e-15,
        "phit": 6.73807676321303e-11
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  },
  {
    "name": "listwise_missing",
    "input": {
      "x": [
        [
          1,
          1.83,
          56.39
        ],
        [
          1,
          null,
          61.62
        ],
        [
          1,
          1.52,
          34.88
        ],
        [
          1,
          4.85,
          78.07
        ],
        [
          1,
          2.6,
          66.36
        ],
        [
          1,
          9.7,
          81.6
        ],
        [
          1,
          10.7,
          75.03
        ],
        [
          1,
          10.83,
          80.27
        ],
        [
          1,
          8.16,
          81.41
        ],
        [
          1,
          4.2,
          59.63
        ],
        [
          1,
          11.8,
          84.54
        ],
        [
          1,
          7.45,
          71.37
        ],
        [
          1,
          11.99,
          86.19
        ],
        [
          1,
          2.59,
          50.28
        ],
        [
          1,
          1.92,
          45.47
        ],
        [
          1,
          10.05,
          83.86
        ],
        [
          1,
          3.83,
          50.96
        ],
        [
          1,
          2.02,
          28.23
        ],
        [
          1,
          10.73,
          83.28
        ],
        [
          1,
          1.58,
          50.61
        ],
        [
          1,
          6.63,
          65.27
        ],
        [
          1,
          4.48,
          58.04
        ],
        [
          1,
          2.67,
          58.73
        ],
        [
          1,
          8.37,
          75.27
        ],
        [
          1,
          4.04,
          64.07
        ],
        [
          1,
          9.04,
          72.06
        ],
        [
          1,
          7.51,
          70.66
        ],
        [
          1,
          9.3,
          88.99
        ],
        [
          1,
          3.19,
          48.59
        ],
        [
          1,
          1.3,
          39.56
        ],
        [
          1,
          6.15,
          70.58
        ],
        [
          1,
          9.61,
          87.11
        ],
        [
          1,
          10.8,
          71.4
        ],
        [
          1,
          10.65,
          74.56
        ],
        [
          1,
          1.48,
          49.19
        ],
        [
          1,
          4.19,
          48.81
        ],
        [
          1,
          1.76,
          48.94
        ],
        [
          1,
          9.84,
          70.92
        ],
        [
          1,
          5.65,
          79.16
        ],
        [
          1,
          11.71,
          93.65
        ],
        [
          1,
          10.41,
          87.76
        ],
        [
          1,
          4.5,
          74.61
        ],
        [
          1,
          8.76,
          58.68
        ],
        [
          1,
          3.39,
          42.27
        ],
        [
          1,
          8.26,
          66.12
        ],
        [
          1,
          5.08,
          73.77
        ],
        [
          1,
          10.19,
          72.85
        ],
        [
          1,
          11.97,
          79.13
        ],
        [
          1,
          11.61,
          84.14
        ],
        [
          1,
          4.79,
          64.25
        ],
        [
          1,
          9.25,
          69.29
        ],
        [
          1,
          4.78,
          58.54
        ],
        [
          1,
          2.39,
          48.95
        ],
        [
          1,
          4.81,
          52.58
        ],
        [
          1,
          2.59,
          52.99
        ],
        [
          1,
          7.56,
          69.2
        ],
        [
          1,
          4.29,
          69.75
        ],
        [
          1,
          7.59,
          77.72
        ],
        [
          1,
          8.39,
          79.59
        ],
        [
          1,
          10.55,
          84.76
        ],
        [
          1,
          6.6,
          59.23
        ],
        [
          1,
          9.8,
          83.91
        ],
        [
          1,
          9.78,
          72.62
        ],
        [
          1,
          10.13,
          68.86
        ],
        [
          1,
          10.02,
          75.17
        ],
        [
          1,
          6.1,
          59.55
        ],
        [
          1,
          1.16,
          55.02
        ],
        [
          1,
          10.95,
          95
        ],
        [
          1,
          5.15,
          60.94
        ],
        [
          1,
          8.94,
          60.52
        ],
        [
          1,
          2.31,
          53.74
        ],
        [
          1,
          7.65,
          72.07
        ],
        [
          1,
          10.6,
          74.89
        ],
        [
          1,
          8.62,
          70.42
        ],
        [
          1,
          6.94,
          70.08
        ],
        [
          1,
          4.16,
          51.82
        ],
        [
          1,
          8.52,
          75.87
        ],
        [
          1,
          8.26,
          80.1
        ],
        [
          1,
          7.84,
          77.18
        ],
        [
          1,
          10,
          81.56
        ],
        [
          1,
          6.41,
          61.14
        ],
        [
          1,
          8.08,
          74.06
        ],
        [
          1,
          7.53,
          69.84
        ],
        [
          1,
          9.37,
          71.92
        ],
        [
          1,
          2.5,
          37.32
        ],
        [
          1,
          7.21,
          78.28
        ],
        [
          1,
          2.53,
          53.38
        ],
        [
          1,
          4.98,
          73.13
        ],
        [
          1,
          7.35,
          68.11
        ],
        [
          1,
          5.76,
          60.89
        ],
        [
          1,
          1.25,
          54.01
        ],
        [
          1,
          7.52,
          64.25
        ],
        [
          1,
          1.36,
          40.08
        ],
        [
          1,
          4.68,
          59.68
        ],
        [
          1,
          8.02,
          58.34
        ],
        [
          1,
          6.32,
          56.81
        ],
        [
          1,
          11.98,
          61.9
        ],
        [
          1,
          10.74,
          74.75
        ],
        [
          1,
          7.83,
          66.12
        ],
        [
          1,
          1.76,
          52.3
        ],
        [
          1,
          11.29,
          86.01
        ],
        [
          1,
          8.06,
          56.46
        ],
        [
          1,
          8.97,
          61.82
        ],
        [
          1,
          10.91,
          72.69
        ],
        [
          1,
          1.09,
          31.47
        ],
        [
          1,
          2.99,
          48.2
        ],
        [
          1,
          4.13,
          62.12
        ],
        [
          1,
          2.41,
          66.31
        ],
        [
          1,
          5.97,
          46.22
        ],
        [
          1,
          9.03,
          73.07
        ],
        [
          1,
          9.21,
          79.32
        ],
        [
          1,
          3.14,
          52.42
        ],
        [
          1,
          2.2,
          47.49
        ],
        [
          1,
          1.26,
          38.22
        ],
        [
          1,
          7.2,
          60.45
        ],
        [
          1,
          4.14,
          69.24
        ],
        [
          1,
          6.85,
          59.9
        ],
        [
          1,
          4.83,
          69.45
        ],
        [
          1,
          10.62,
          81.19
        ],
        [
          1,
          11.35,
          67.69
        ]
      ],
      "y": [
        0,
        0,
        1,
        0,
        null,
        1,
        1,
        1,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        1,
        0,
        1,
        0,
        1,
        0,
        1,
        0,
        0,
        1,
        0,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        0,
        1,
        0,
        0,
        0,
        0,
        0,
        1,
        0,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1,
        0,
        0,
        0,
        1,
        1,
        1,
        0,
        0,
        1,
        1,
        0,
        0,
        1,
        1
      ]
    },
    "versions": {
      "R": "R version 4.6.1 (2026-06-24)",
      "statsmodels": "0.15.0",
      "numpy": "2.5.4",
      "Python": "3.14.7",
      "PHP": "8.5.10"
    },
    "R": {
      "coefficients": [
        -1.1506454760972136,
        0.17113350314072232,
        -0.0039719007316424155
      ],
      "covariance": [
        [
          0.5021289462937406,
          0.021825855440521374,
          -0.00956957806166563
        ],
        [
          0.021825855440521374,
          0.004120547420184586,
          -0.0007587304701377976
        ],
        [
          -0.00956957806166563,
          -0.0007587304701377976,
          0.00022262703225923598
        ]
      ],
      "std_errors": [
        0.7086105745003674,
        0.06419149024741976,
        0.014920691413578527
      ],
      "z_statistics": [
        -1.6238051159602291,
        2.6659842680253276,
        -0.26620084964881724
      ],
      "p_values": [
        0.10441740786065411,
        0.007676328504637051,
        0.7900845287019268
      ],
      "conf_int": [
        [
          -2.53949668118217,
          0.23820572898774284
        ],
        [
          0.04532049414182551,
          0.2969465121396191
        ],
        [
          -0.033215918526692347,
          0.02527211706340752
        ]
      ],
      "fitted": [
        0.1442434835545658,
        0.1517251652028594,
        0.264107141798966,
        0.573480544757757,
        0.6489440918976452,
        0.6494759001005193,
        0.46909359344537427,
        0.25183411750093043,
        0.7029643023634585,
        0.43676532938265256,
        0.7118874390530743,
        0.18217249846176045,
        0.15800969831277775,
        0.5933467638156668,
        0.2427098685574811,
        0.1795496902390769,
        0.6386441909768886,
        0.13978797215828037,
        0.3915519813686903,
        0.26944364243713526,
        0.1769661869906518,
        0.49312934765497224,
        0.23769218901533842,
        0.5438691569229415,
        0.4419262070984366,
        0.5348377835667155,
        0.21251526184452735,
        0.1388943332282035,
        0.35252544301844657,
        0.5588109443314117,
        0.6605639153365441,
        0.6464602967760646,
        0.13725273683747477,
        0.26517737590191237,
        0.14828079078440556,
        0.5993329854761761,
        0.30918674833364457,
        0.6848694360557079,
        0.6111356986644941,
        0.24923843762598819,
        0.5459410633967469,
        0.23013718218535162,
        0.500117761164532,
        0.282884300000841,
        0.6193796578474431,
        0.7202303876213334,
        0.6921728403557996,
        0.2789005906753843,
        0.56242739444139,
        0.2859884555438485,
        0.1746209050579306,
        0.2958632233738553,
        0.1793406574901418,
        0.4475982464269394,
        0.24399075384617253,
        0.4362679058899767,
        0.48765113298719776,
        0.624816194452814,
        0.39881325932432254,
        0.576591259414765,
        0.5927406876630081,
        0.6215034682064323,
        0.60470496282911,
        0.3657022641737221,
        0.12086681175658262,
        0.6353045235568415,
        0.30455105155523365,
        0.5552388163134807,
        0.1663282249985864,
        0.4491816948402762,
        0.6427853796114829,
        0.517876230936142,
        0.4046497706891985,
        0.25960812675573935,
        0.5024191161696405,
        0.47797682223910287,
        0.45402040377065267,
        0.5935712658768608,
        0.383415836648752,
        0.4752632038814136,
        0.444563976428974,
        0.5664000890481342,
        0.19186532285896551,
        0.4099423377299404,
        0.17626379361932812,
        0.27797567387960564,
        0.4351252183864951,
        0.3420901016521032,
        0.12481450377275058,
        0.4526708915739337,
        0.14071831178093758,
        0.2786744869765636,
        0.4960603216769038,
        0.3841018226729855,
        0.7433388251623552,
        0.6518902406563396,
        0.4707867901492443,
        0.14521451323227305,
        0.6699693713397837,
        0.5017701186069274,
        0.5552271739797733,
        0.6655665280648221,
        0.13805364409817983,
        0.20315579107016016,
        0.24490891955148186,
        0.15827071254500585,
        0.37730759450315426,
        0.5415991427902821,
        0.5439709426799149,
        0.2056826658620408,
        0.16782963863566205,
        0.13855745241190526,
        0.4369976666075163,
        0.23663547386753891,
        0.4143777988925909,
        0.2742800557003809,
        0.634694811395636,
        0.6994647936234712
      ],
      "residuals": [
        -0.1442434835545658,
        0.8482748347971406,
        -0.264107141798966,
        0.426519455242243,
        0.35105590810235476,
        0.35052409989948075,
        0.5309064065546257,
        -0.25183411750093043,
        0.2970356976365415,
        -0.43676532938265256,
        -0.7118874390530743,
        -0.18217249846176045,
        -0.15800969831277775,
        -0.5933467638156668,
        -0.2427098685574811,
        -0.1795496902390769,
        0.3613558090231114,
        -0.13978797215828037,
        0.6084480186313097,
        -0.26944364243713526,
        -0.1769661869906518,
        -0.49312934765497224,
        -0.23769218901533842,
        -0.5438691569229415,
        0.5580737929015633,
        0.4651622164332845,
        -0.21251526184452735,
        -0.1388943332282035,
        0.6474745569815534,
        -0.5588109443314117,
        0.3394360846634559,
        0.35353970322393535,
        -0.13725273683747477,
        -0.26517737590191237,
        -0.14828079078440556,
        -0.5993329854761761,
        -0.30918674833364457,
        -0.6848694360557079,
        0.38886430133550587,
        -0.24923843762598819,
        -0.5459410633967469,
        -0.23013718218535162,
        -0.500117761164532,
        -0.282884300000841,
        0.3806203421525569,
        0.2797696123786666,
        0.3078271596442004,
        -0.2789005906753843,
        -0.56242739444139,
        -0.2859884555438485,
        -0.1746209050579306,
        0.7041367766261447,
        -0.1793406574901418,
        0.5524017535730605,
        -0.24399075384617253,
        -0.4362679058899767,
        -0.48765113298719776,
        -0.624816194452814,
        -0.39881325932432254,
        -0.576591259414765,
        -0.5927406876630081,
        -0.6215034682064323,
        0.39529503717089,
        0.6342977358262779,
        -0.12086681175658262,
        0.3646954764431585,
        0.6954489484447663,
        -0.5552388163134807,
        0.8336717750014135,
        -0.4491816948402762,
        0.35721462038851715,
        -0.517876230936142,
        0.5953502293108015,
        -0.25960812675573935,
        -0.5024191161696405,
        0.5220231777608971,
        -0.45402040377065267,
        0.4064287341231392,
        -0.383415836648752,
        0.5247367961185865,
        0.5554360235710261,
        -0.5664000890481342,
        -0.19186532285896551,
        -0.4099423377299404,
        -0.17626379361932812,
        0.7220243261203944,
        -0.4351252183864951,
        -0.3420901016521032,
        -0.12481450377275058,
        -0.4526708915739337,
        -0.14071831178093758,
        0.7213255130234364,
        -0.4960603216769038,
        0.6158981773270145,
        0.25666117483764483,
        0.3481097593436604,
        0.5292132098507557,
        0.8547854867677269,
        0.33003062866021626,
        0.49822988139307256,
        0.4447728260202267,
        -0.6655665280648221,
        -0.13805364409817983,
        0.7968442089298399,
        -0.24490891955148186,
        -0.15827071254500585,
        -0.37730759450315426,
        0.4584008572097179,
        0.45602905732008514,
        0.7943173341379592,
        -0.16782963863566205,
        -0.13855745241190526,
        0.5630023333924836,
        0.7633645261324611,
        -0.4143777988925909,
        -0.2742800557003809,
        0.365305188604364,
        0.30053520637652875
      ],
      "log_likelihood": -71.01719103308002,
      "deviance": 142.03438206616005,
      "null_deviance": 159.45694043982934,
      "aic": 148.03438206616005,
      "df_residual": 115
    },
    "statsmodels": {
      "coefficients": [
        -1.1506454760971743,
        0.17113350314072825,
        -0.003971900731643608
      ],
      "covariance": [
        [
          0.5021289462937336,
          0.02182585544052383,
          -0.009569578061665814
        ],
        [
          0.02182585544052383,
          0.004120547420185368,
          -0.000758730470137922
        ],
        [
          -0.009569578061665814,
          -0.000758730470137922,
          0.00022262703225925298
        ]
      ],
      "std_errors": [
        0.7086105745003624,
        0.06419149024742585,
        0.014920691413579096
      ],
      "z_statistics": [
        -1.6238051159601852,
        2.6659842680251673,
        -0.266200849648887
      ],
      "p_values": [
        0.1044174078606635,
        0.007676328504640711,
        0.7900845287018731
      ],
      "conf_int": [
        [
          -2.539496681182121,
          0.2382057289877728
        ],
        [
          0.04532049414181946,
          0.2969465121396371
        ],
        [
          -0.033215918526694664,
          0.02527211706340745
        ]
      ],
      "fitted": [
        0.14424348355456185,
        0.151725165202861,
        0.2641071417989578,
        0.5734805447577569,
        0.6489440918976501,
        0.6494759001005223,
        0.4690935934453706,
        0.2518341175009282,
        0.7029643023634614,
        0.4367653293826519,
        0.7118874390530769,
        0.1821724984617591,
        0.15800969831277695,
        0.5933467638156664,
        0.2427098685574815,
        0.17954969023908157,
        0.6386441909768901,
        0.13978797215827776,
        0.3915519813686906,
        0.26944364243713415,
        0.17696618699064798,
        0.49312934765497196,
        0.2376921890153344,
        0.5438691569229441,
        0.4419262070984365,
        0.5348377835667109,
        0.21251526184452746,
        0.13889433322820344,
        0.35252544301844346,
        0.5588109443314088,
        0.6605639153365508,
        0.6464602967760698,
        0.1372527368374724,
        0.26517737590191437,
        0.14828079078440365,
        0.5993329854761812,
        0.30918674833363696,
        0.6848694360557068,
        0.6111356986644927,
        0.2492384376259809,
        0.5459410633967553,
        0.2301371821853544,
        0.5001177611645359,
        0.28288430000083464,
        0.6193796578474481,
        0.7202303876213388,
        0.6921728403558024,
        0.2789005906753813,
        0.5624273944413944,
        0.2859884555438478,
        0.17462090505792938,
        0.2958632233738571,
        0.1793406574901396,
        0.44759824642694,
        0.2439907538461668,
        0.43626790588997344,
        0.4876511329871954,
        0.6248161944528143,
        0.3988132593243256,
        0.576591259414764,
        0.5927406876630124,
        0.6215034682064389,
        0.6047049628291135,
        0.36570226417372376,
        0.12086681175657871,
        0.6353045235568382,
        0.30455105155523265,
        0.5552388163134887,
        0.16632822499858363,
        0.4491816948402757,
        0.6427853796114876,
        0.5178762309361445,
        0.4046497706891973,
        0.25960812675574,
        0.5024191161696403,
        0.47797682223910004,
        0.4540204037706502,
        0.5935712658768614,
        0.38341583664875367,
        0.47526320388141313,
        0.4445639764289743,
        0.5664000890481379,
        0.19186532285896818,
        0.40994233772993605,
        0.17626379361932565,
        0.2779756738795996,
        0.43512521838649576,
        0.3420901016521034,
        0.12481450377274689,
        0.45267089157393664,
        0.14071831178093747,
        0.2786744869765622,
        0.49606032167691066,
        0.384101822672989,
        0.743338825162367,
        0.6518902406563448,
        0.4707867901492471,
        0.1452145132322702,
        0.6699693713397851,
        0.5017701186069354,
        0.5552271739797807,
        0.6655665280648285,
        0.13805364409818166,
        0.20315579107016013,
        0.2449089195514787,
        0.1582707125449997,
        0.37730759450316165,
        0.5415991427902844,
        0.5439709426799145,
        0.20568266586203948,
        0.16782963863566092,
        0.13855745241190554,
        0.43699766660752026,
        0.23663547386753309,
        0.41437779889259424,
        0.27428005570037595,
        0.6346948113956381,
        0.6994647936234804
      ],
      "residuals": [
        -0.14424348355456185,
        0.8482748347971389,
        -0.2641071417989578,
        0.4265194552422431,
        0.3510559081023499,
        0.35052409989947775,
        0.5309064065546294,
        -0.2518341175009282,
        0.2970356976365386,
        -0.4367653293826519,
        -0.7118874390530769,
        -0.1821724984617591,
        -0.15800969831277695,
        -0.5933467638156664,
        -0.2427098685574815,
        -0.17954969023908157,
        0.36135580902310993,
        -0.13978797215827776,
        0.6084480186313094,
        -0.26944364243713415,
        -0.17696618699064798,
        -0.49312934765497196,
        -0.2376921890153344,
        -0.5438691569229441,
        0.5580737929015636,
        0.46516221643328914,
        -0.21251526184452746,
        -0.13889433322820344,
        0.6474745569815565,
        -0.5588109443314088,
        0.3394360846634492,
        0.35353970322393025,
        -0.1372527368374724,
        -0.26517737590191437,
        -0.14828079078440365,
        -0.5993329854761812,
        -0.30918674833363696,
        -0.6848694360557068,
        0.3888643013355073,
        -0.2492384376259809,
        -0.5459410633967553,
        -0.2301371821853544,
        -0.5001177611645359,
        -0.28288430000083464,
        0.3806203421525519,
        0.27976961237866116,
        0.3078271596441976,
        -0.2789005906753813,
        -0.5624273944413944,
        -0.2859884555438478,
        -0.17462090505792938,
        0.7041367766261428,
        -0.1793406574901396,
        0.55240175357306,
        -0.2439907538461668,
        -0.43626790588997344,
        -0.4876511329871954,
        -0.6248161944528143,
        -0.3988132593243256,
        -0.576591259414764,
        -0.5927406876630124,
        -0.6215034682064389,
        0.39529503717088654,
        0.6342977358262762,
        -0.12086681175657871,
        0.3646954764431618,
        0.6954489484447673,
        -0.5552388163134887,
        0.8336717750014164,
        -0.4491816948402757,
        0.35721462038851237,
        -0.5178762309361445,
        0.5953502293108027,
        -0.25960812675574,
        -0.5024191161696403,
        0.5220231777608999,
        -0.4540204037706502,
        0.4064287341231386,
        -0.38341583664875367,
        0.5247367961185869,
        0.5554360235710257,
        -0.5664000890481379,
        -0.19186532285896818,
        -0.40994233772993605,
        -0.17626379361932565,
        0.7220243261204005,
        -0.43512521838649576,
        -0.3420901016521034,
        -0.12481450377274689,
        -0.45267089157393664,
        -0.14071831178093747,
        0.7213255130234377,
        -0.49606032167691066,
        0.615898177327011,
        0.25666117483763295,
        0.3481097593436552,
        0.5292132098507529,
        0.8547854867677298,
        0.33003062866021493,
        0.49822988139306457,
        0.4447728260202193,
        -0.6655665280648285,
        -0.13805364409818166,
        0.7968442089298399,
        -0.2449089195514787,
        -0.1582707125449997,
        -0.37730759450316165,
        0.4584008572097156,
        0.4560290573200855,
        0.7943173341379606,
        -0.16782963863566092,
        -0.13855745241190554,
        0.5630023333924797,
        0.7633645261324669,
        -0.41437779889259424,
        -0.27428005570037595,
        0.3653051886043619,
        0.30053520637651965
      ],
      "log_likelihood": -71.01719103308001,
      "deviance": 142.03438206616002,
      "null_deviance": 159.4569404398291,
      "aic": 148.03438206616002,
      "df_residual": 115
    },
    "phit": {
      "coefficients": [
        -1.1506454761566869,
        0.17113350314657896,
        -0.003971900731569102
      ],
      "covariance": [
        [
          0.5021289463122656,
          0.021825855440645265,
          -0.009569578061932706
        ],
        [
          0.021825855440645265,
          0.00412054742029246,
          -0.0007587304701526854
        ],
        [
          -0.009569578061932706,
          -0.0007587304701526854,
          0.00022262703226470087
        ]
      ],
      "std_errors": [
        0.7086105745134387,
        0.06419149024826001,
        0.014920691413761658
      ],
      "z_statistics": [
        -1.6238051160142053,
        2.6659842680816674,
        -0.2662008496406364
      ],
      "p_values": [
        0.10441740785356485,
        0.007676328503028093,
        0.790084528708227
      ],
      "conf_int": [
        [
          -2.539496681267263,
          0.23820572895388903
        ],
        [
          0.045320494146035256,
          0.29694651214712264
        ],
        [
          -0.03321591852697797,
          0.025272117063839767
        ]
      ],
      "fitted": [
        0.14424348355164765,
        0.15172516520441107,
        0.26410714179067857,
        0.5734805447590582,
        0.6489440919008687,
        0.6494759001041654,
        0.46909359344310125,
        0.25183411749119944,
        0.7029643023689385,
        0.43676532937847334,
        0.7118874390588982,
        0.18217249846740294,
        0.15800969831547118,
        0.5933467638178137,
        0.24270986854706372,
        0.1795496902431939,
        0.6386441909804375,
        0.13978797215487426,
        0.3915519813625987,
        0.2694436424275628,
        0.17696618699613006,
        0.4931293476530037,
        0.23769218903006803,
        0.5438691569224471,
        0.44192620709436725,
        0.5348377835673186,
        0.21251526185417108,
        0.1388943332242442,
        0.3525254430116578,
        0.5588109443326725,
        0.6605639153398444,
        0.6464602967791748,
        0.13725273683388756,
        0.2651773758916385,
        0.1482807907863185,
        0.5993329854774729,
        0.30918674832639237,
        0.6848694360613834,
        0.6111356986675335,
        0.24923843761721637,
        0.5459410633952143,
        0.23013718219737966,
        0.5001177611620385,
        0.28288429999261594,
        0.6193796578495561,
        0.7202303876268625,
        0.6921728403609665,
        0.2789005906664104,
        0.5624273944413033,
        0.2859884555346033,
        0.17462090506260478,
        0.295863223364372,
        0.17934065749559097,
        0.44759824642293544,
        0.24399075383700253,
        0.43626790588630465,
        0.4876511329854028,
        0.6248161944560482,
        0.3988132593179617,
        0.57659125941636,
        0.5927406876642223,
        0.6215034682082967,
        0.6047049628309281,
        0.36570226416643203,
        0.12086681175259428,
        0.6353045235612086,
        0.30455105154653694,
        0.5552388163124224,
        0.16632822500258193,
        0.44918169483656184,
        0.6427853796145041,
        0.5178762309346169,
        0.4046497706838935,
        0.2596081267455911,
        0.5024191161680398,
        0.4779768222370214,
        0.4540204037675223,
        0.5935712658788285,
        0.3834158366420898,
        0.47526320387873694,
        0.4445639764249233,
        0.5664000890484001,
        0.19186532286508923,
        0.4099423377254668,
        0.17626379362443298,
        0.27797567387123784,
        0.4351252183819941,
        0.3420901016442895,
        0.12481450376886433,
        0.4526708915696867,
        0.14071831177708288,
        0.27867448696726427,
        0.4960603216736222,
        0.3841018226659972,
        0.7433388251672612,
        0.6518902406596322,
        0.47078679014575553,
        0.14521451323406057,
        0.669969371344475,
        0.5017701186036841,
        0.555227173978822,
        0.6655665280683725,
        0.1380536440938111,
        0.2031557910784281,
        0.24490891954182298,
        0.15827071254877922,
        0.37730759449513,
        0.5415991427897936,
        0.5439709426800263,
        0.205682665870917,
        0.16782963863949485,
        0.13855745240786946,
        0.4369976666024446,
        0.23663547388241413,
        0.41437779888675913,
        0.2742800556916852,
        0.634694811398898,
        0.6994647936276337
      ],
      "residuals": [
        -0.14424348355164765,
        0.848274834795589,
        -0.26410714179067857,
        0.4265194552409418,
        0.35105590809913134,
        0.35052409989583455,
        0.5309064065568987,
        -0.25183411749119944,
        0.2970356976310615,
        -0.43676532937847334,
        -0.7118874390588982,
        -0.18217249846740294,
        -0.15800969831547118,
        -0.5933467638178137,
        -0.24270986854706372,
        -0.1795496902431939,
        0.36135580901956255,
        -0.13978797215487426,
        0.6084480186374013,
        -0.2694436424275628,
        -0.17696618699613006,
        -0.4931293476530037,
        -0.23769218903006803,
        -0.5438691569224471,
        0.5580737929056327,
        0.4651622164326814,
        -0.21251526185417108,
        -0.1388943332242442,
        0.6474745569883422,
        -0.5588109443326725,
        0.3394360846601556,
        0.3535397032208252,
        -0.13725273683388756,
        -0.2651773758916385,
        -0.1482807907863185,
        -0.5993329854774729,
        -0.30918674832639237,
        -0.6848694360613834,
        0.3888643013324665,
        -0.24923843761721637,
        -0.5459410633952143,
        -0.23013718219737966,
        -0.5001177611620385,
        -0.28288429999261594,
        0.38062034215044394,
        0.27976961237313747,
        0.3078271596390335,
        -0.2789005906664104,
        -0.5624273944413033,
        -0.2859884555346033,
        -0.17462090506260478,
        0.704136776635628,
        -0.17934065749559097,
        0.5524017535770646,
        -0.24399075383700253,
        -0.43626790588630465,
        -0.4876511329854028,
        -0.6248161944560482,
        -0.3988132593179617,
        -0.57659125941636,
        -0.5927406876642223,
        -0.6215034682082967,
        0.3952950371690719,
        0.634297735833568,
        -0.12086681175259428,
        0.3646954764387914,
        0.6954489484534631,
        -0.5552388163124224,
        0.8336717749974181,
        -0.44918169483656184,
        0.3572146203854959,
        -0.5178762309346169,
        0.5953502293161065,
        -0.2596081267455911,
        -0.5024191161680398,
        0.5220231777629786,
        -0.4540204037675223,
        0.40642873412117153,
        -0.3834158366420898,
        0.524736796121263,
        0.5554360235750767,
        -0.5664000890484001,
        -0.19186532286508923,
        -0.4099423377254668,
        -0.17626379362443298,
        0.7220243261287622,
        -0.4351252183819941,
        -0.3420901016442895,
        -0.12481450376886433,
        -0.4526708915696867,
        -0.14071831177708288,
        0.7213255130327357,
        -0.4960603216736222,
        0.6158981773340029,
        0.25666117483273876,
        0.3481097593403678,
        0.5292132098542445,
        0.8547854867659395,
        0.330030628655525,
        0.49822988139631585,
        0.44477282602117796,
        -0.6655665280683725,
        -0.1380536440938111,
        0.7968442089215719,
        -0.24490891954182298,
        -0.15827071254877922,
        -0.37730759449513,
        0.4584008572102064,
        0.4560290573199737,
        0.794317334129083,
        -0.16782963863949485,
        -0.13855745240786946,
        0.5630023333975553,
        0.7633645261175859,
        -0.41437779888675913,
        -0.2742800556916852,
        0.36530518860110195,
        0.3005352063723663
      ],
      "log_likelihood": -71.01719103289383,
      "deviance": 142.03438206578767,
      "null_deviance": 159.45694043982934,
      "aic": 148.03438206578767,
      "df_residual": 115,
      "iterations": 10,
      "converged": true,
      "n_input": 120,
      "n_observations": 118,
      "n_dropped": 2,
      "retained_rows": [
        0,
        2,
        3,
        5,
        6,
        7,
        8,
        9,
        10,
        11,
        12,
        13,
        14,
        15,
        16,
        17,
        18,
        19,
        20,
        21,
        22,
        23,
        24,
        25,
        26,
        27,
        28,
        29,
        30,
        31,
        32,
        33,
        34,
        35,
        36,
        37,
        38,
        39,
        40,
        41,
        42,
        43,
        44,
        45,
        46,
        47,
        48,
        49,
        50,
        51,
        52,
        53,
        54,
        55,
        56,
        57,
        58,
        59,
        60,
        61,
        62,
        63,
        64,
        65,
        66,
        67,
        68,
        69,
        70,
        71,
        72,
        73,
        74,
        75,
        76,
        77,
        78,
        79,
        80,
        81,
        82,
        83,
        84,
        85,
        86,
        87,
        88,
        89,
        90,
        91,
        92,
        93,
        94,
        95,
        96,
        97,
        98,
        99,
        100,
        101,
        102,
        103,
        104,
        105,
        106,
        107,
        108,
        109,
        110,
        111,
        112,
        113,
        114,
        115,
        116,
        117,
        118,
        119
      ],
      "dropped_rows": [
        1,
        4
      ]
    },
    "warnings": [
      {
        "severity": 2,
        "message": "stats_probit(): stats_probit dropped 2 of 120 observations with missing values (listwise deletion)"
      }
    ],
    "max_absolute_errors_vs_R": {
      "coefficients": {
        "statsmodels": 3.930189507173054e-14,
        "phit": 5.947331516154009e-11
      },
      "covariance": {
        "statsmodels": 6.994405055138486e-15,
        "phit": 1.8524959344290437e-11
      },
      "std_errors": {
        "statsmodels": 6.0923488476305465e-15,
        "phit": 1.3071321802726743e-11
      },
      "z_statistics": {
        "statsmodels": 1.603162047558726e-13,
        "phit": 5.6339821696838044e-11
      },
      "p_values": {
        "statsmodels": 5.3734794391857577e-14,
        "phit": 7.089259734804898e-12
      },
      "conf_int": {
        "statsmodels": 4.884981308350689e-14,
        "phit": 8.50928216777902e-11
      },
      "fitted": {
        "statsmodels": 1.1879386363489175e-14,
        "phit": 1.4875212173137697e-11
      },
      "residuals": {
        "statsmodels": 1.1879386363489175e-14,
        "phit": 1.4875212173137697e-11
      },
      "log_likelihood": {
        "statsmodels": 1.4210854715202004e-14,
        "phit": 1.8619061847857665e-10
      },
      "deviance": {
        "statsmodels": 2.842170943040401e-14,
        "phit": 3.723812369571533e-10
      },
      "null_deviance": {
        "statsmodels": 2.2737367544323206e-13,
        "phit": 0.0
      },
      "aic": {
        "statsmodels": 2.842170943040401e-14,
        "phit": 3.723812369571533e-10
      },
      "df_residual": {
        "statsmodels": 0.0,
        "phit": 0.0
      }
    }
  }
]