{ "recorded_at": "2026-10-16T07:49:59.210984+00:00", "backend_label": "nalgebra", "model": "ols", "lapack_symbols": { "extension": [], "numpy": [ "_cgesdd$NEWLAPACK$ILP64", "_dgesdd$NEWLAPACK$ILP64", "_sgesdd$NEWLAPACK$ILP64", "_zgesdd$NEWLAPACK$ILP64" ] }, "platform": "macOS-27.0.1-arm64-arm-64bit-Mach-O", "cpu": "Apple M5 Ultra", "host_memory_bytes": 103079215104, "python": "3.14.7", "numpy_config": "Build Dependencies:\n blas:\n detection method: system\n found: true\n include directory: unknown\n lib directory: unknown\n name: accelerate\n openblas configuration: unknown\n pc file directory: unknown\n version: unknown\n lapack:\n detection method: system\n found: true\n include directory: unknown\n lib directory: unknown\n name: accelerate\n openblas configuration: unknown\n pc file directory: unknown\n version: unknown\nCompilers:\n c:\n commands: cc\n linker: ld64\n name: clang\n version: 15.0.0\n c++:\n commands: c++\n linker: ld64\n name: clang\n version: 15.0.0\n cython:\n commands: cython\n linker: cython\n name: cython\n version: 3.3.0\nMachine Information:\n build:\n cpu: aarch64\n endian: little\n family: aarch64\n system: darwin\n host:\n cpu: aarch64\n endian: little\n family: aarch64\n system: darwin\nPython Information:\n path: /private/var/folders/s6/5hzmn6lx4dz5nxs7k_0slzph0000gn/T/build-env-buaiw__1/bin/python\n version: '3.14'\nSIMD Extensions:\n baseline:\n - NEON\n - NEON_FP16\n - NEON_VFPV4\n - ASIMD\n found:\n - ASIMDHP\n - ASIMDDP\n not found:\n - ASIMDFHM\n\n", "thread_environment": { "OPENBLAS_NUM_THREADS": "1", "OMP_NUM_THREADS": "1", "MKL_NUM_THREADS": "1", "VECLIB_MAXIMUM_THREADS": "1", "BLIS_NUM_THREADS": "1" }, "repeats": 5, "warmups": 1, "extension_sha256": "0b35a5809d64faa2ca62a8b8db6ed67d993392da0d8855110cd667c090b729d8", "rust": "rustc 1.99.0 (b940084d7 2026-09-28) (Homebrew)", "tolerance": { "absolute": 1e-09, "relative": 1e-07 }, "cases": [ { "n": 1000, "p": 3, "data": { "seed": 20261011, "sha256": "79687709d8e6b0f1c66f0aa93f2e08f4460e3728e0337dbaa85102257e3155ad", "true_coefficients": [ 650.0, 18.0, 60.0 ], "error_sd": 180, "sample_correlations": [ [ 1.0, 0.7695104511537801, 0.9221524064722517 ], [ 0.7695104511537801, 0.9999999999999999, 0.7516334539170098 ], [ 0.9221524064722518, 0.7516334539170096, 1.0 ] ], "correlation_order": [ "area_m2", "bedrooms", "monthly_rent" ] }, "implementations": { "R": { "version": "R version 4.6.1 (2026-06-24)", "BLAS": "/opt/homebrew/Cellar/openblas/0.3.34/lib/libopenblasp-r0.3.34.dylib", "load_seconds": 0, "fit_seconds": [ 0.0010000000000000009, 0, 0, 0.0010000000000000009, 0 ], "sample_indices": [ 0, 111, 222, 333, 444, 555, 666, 777, 888, 999 ], "result": { "coefficients": [ 604.2521359905681, 18.868755278842958, 51.22896118036626 ], "covariance": [ [ 434.3508687035226, -5.971204600369764, 16.70712989989845 ], [ -5.971204600369764, 0.17908390913582026, -3.0603285644096627 ], [ 16.70712989989845, -3.0603285644096627, 88.31825930112866 ] ], "std_errors": [ 20.84108607303186, 0.42318306811097756, 9.397779487790116 ], "t_statistics": [ 28.993313202255035, 44.587689585668215, 5.451177189986688 ], "p_values": [ 1.5516073093917476e-134, 1.1907251319726663e-239, 6.307793107873704e-08 ], "conf_int": [ [ 563.3547091791378, 645.1495628019985 ], [ 18.038323577958597, 19.69918697972732 ], [ 32.78726397490269, 69.67065838582982 ] ], "rss": 32998139.139764134, "residual_variance": 33097.43143406633, "sigma": 181.9269947920493, "r_squared": 0.8546958152274078, "adj_r_squared": 0.8544043324094086, "df_residual": 997, "log_likelihood": -6621.041757781942, "fitted_sample": [ 1968.7684741479795, 2212.1958623053088, 2649.0875080330907, 1709.1785592703907, 1429.379449914606, 2688.213196192684, 2189.057653078216, 2052.267997693525, 1651.0797151907234, 2574.893227720435 ], "residuals_sample": [ -76.93035504427765, -98.85581792600189, 107.2803967905404, 50.22021756070289, -94.12493004199969, -184.46503192452977, -248.61746826020484, 128.22321725623073, 11.765221256307699, -164.845207795646 ] }, "process_seconds": 0.1663782501127571, "peak_rss_bytes": 87228416, "median_fit_seconds": 0, "min_fit_seconds": 0 }, "statsmodels": { "version": "0.15.0", "numpy": "2.5.4", "load_seconds": 0.00043708295561373234, "fit_seconds": [ 0.00027520814910531044, 0.00022995797917246819, 0.00021245796233415604, 0.00021137483417987823, 0.0002024590503424406 ], "result": { "coefficients": [ 604.2521359905708, 18.86875527884305, 51.22896118036641 ], "covariance": [ [ 434.3508687035223, -5.971204600369777, 16.707129899898334 ], [ -5.971204600369777, 0.17908390913578623, -3.060328564409127 ], [ 16.707129899898334, -3.060328564409127, 88.31825930112862 ] ], "std_errors": [ 20.841086073031853, 0.4231830681109373, 9.397779487790114 ], "t_statistics": [ 28.99331320225517, 44.58768958567268, 5.451177189986705 ], "p_values": [ 1.5516073093886965e-134, 1.1907251318933731e-239, 6.307793107873135e-08 ], "conf_int": [ [ 563.3547091791404, 645.1495628020011 ], [ 18.038323577958767, 19.699186979727333 ], [ 32.78726397490284, 69.67065838582998 ] ], "rss": 32998139.139764123, "residual_variance": 33097.43143406632, "sigma": 181.92699479204927, "r_squared": 0.8546958152274078, "adj_r_squared": 0.8544043324094086, "df_residual": 997, "log_likelihood": -6621.041757781943, "fitted_sample": [ 1968.7684741479598, 2212.1958623053188, 2649.0875080331025, 1709.1785592703973, 1429.3794499146109, 2688.2131961926966, 2189.0576530782255, 2052.267997693534, 1651.0797151907298, 2574.8932277204476 ], "residuals_sample": [ -76.9303550442578, -98.8558179260117, 107.28039679052836, 50.220217560696256, -94.12493004200451, -184.46503192454247, -248.61746826021408, 128.2232172562217, 11.765221256301402, -164.84520779565855 ] }, "sample_indices": [ 0, 111, 222, 333, 444, 555, 666, 777, 888, 999 ], "process_seconds": 7.328707416076213, "peak_rss_bytes": 221675520, "median_fit_seconds": 0.00021245796233415604, "min_fit_seconds": 0.0002024590503424406 }, "PHP": { "version": "8.5.10", "load_seconds": 0.000876083, "fit_seconds": [ 0.000134791, 0.0001315, 0.000129958, 0.000128167, 0.000126875 ], "sample_indices": [ 0, 111, 222, 333, 444, 555, 666, 777, 888, 999 ], "result": { "coefficients": [ 604.2521359905727, 18.868755278842915, 51.228961180366426 ], "covariance": [ [ 434.35086870352336, -5.9712046003697665, 16.70712989989868 ], [ -5.9712046003697665, 0.17908390913581962, -3.0603285644096556 ], [ 16.707129899898675, -3.0603285644096556, 88.31825930112859 ] ], "std_errors": [ 20.841086073031878, 0.4231830681109768, 9.397779487790112 ], "t_statistics": [ 28.993313202255226, 44.5876895856682, 5.451177189986708 ], "p_values": [ 1.551607309387209e-134, 1.1907251319729457e-239, 6.307793107873163e-08 ], "conf_int": [ [ 563.3547091791422, 645.1495628020032 ], [ 18.03832357795855, 19.69918697972728 ], [ 32.787263974902785, 69.67065838583007 ] ], "rss": 32998139.13976413, "residual_variance": 33097.431434066326, "sigma": 181.92699479204927, "r_squared": 0.8546958152274078, "adj_r_squared": 0.8544043324094086, "df_residual": 997, "log_likelihood": -6621.0417577819435, "diagnostics": { "converged": true, "solver": "scaled_svd", "warnings": [] }, "fitted_sample": [ 1968.7684741479525, 2212.19586230531, 2649.0875080330916, 1709.178559270392, 1429.3794499146072, 2688.213196192685, 2189.0576530782173, 2052.2679976935265, 1651.0797151907248, 2574.8932277204362 ], "residuals_sample": [ -76.93035504425052, -98.85581792600306, 107.28039679053927, 50.220217560701485, -94.12493004200087, -184.46503192453065, -248.6174682602059, 128.22321725622942, 11.765221256306404, -164.84520779564718 ] }, "process_seconds": 0.12747012497857213, "peak_rss_bytes": 29802496, "median_fit_seconds": 0.000129958, "min_fit_seconds": 0.000126875 } }, "max_absolute_errors_vs_R": { "statsmodels": { "coefficients": 2.6147972675971687e-12, "covariance": 5.355715870791755e-13, "std_errors": 4.0245584642661925e-14, "t_statistics": 4.462208380573429e-12, "p_values": 5.6910026143648304e-21, "conf_int": 2.6147972675971687e-12, "rss": 1.1175870895385742e-08, "residual_variance": 1.4551915228366852e-11, "sigma": 2.842170943040401e-14, "r_squared": 0.0, "adj_r_squared": 0.0, "df_residual": 0.0, "log_likelihood": 9.094947017729282e-13, "fitted_sample": 1.978150976356119e-11, "residuals_sample": 1.98525640371372e-11 }, "PHP": { "coefficients": 4.547473508864641e-12, "covariance": 7.389644451905042e-13, "std_errors": 1.7763568394002505e-14, "t_statistics": 1.9184653865522705e-13, "p_values": 5.413069928547013e-21, "conf_int": 4.661160346586257e-12, "rss": 3.725290298461914e-09, "residual_variance": 7.275957614183426e-12, "sigma": 2.842170943040401e-14, "r_squared": 0.0, "adj_r_squared": 0.0, "df_residual": 0.0, "log_likelihood": 1.8189894035458565e-12, "fitted_sample": 2.7057467377744615e-11, "residuals_sample": 2.7128521651320625e-11 } }, "agreement_passed": true }, { "n": 100000, "p": 3, "data": { "seed": 20261011, "sha256": "3edd0a251f6d23147067b20aa29ad681fd6b94cb40f3684f2cbee92ac81cb210", "true_coefficients": [ 650.0, 18.0, 60.0 ], "error_sd": 180, "sample_correlations": [ [ 1.0, 0.7967476697702436, 0.9215924911263137 ], [ 0.7967476697702436, 1.0, 0.7817867583651585 ], [ 0.9215924911263138, 0.7817867583651585, 0.9999999999999999 ] ], "correlation_order": [ "area_m2", "bedrooms", "monthly_rent" ] }, "implementations": { "PHP": { "version": "8.5.10", "load_seconds": 0.08246025, "fit_seconds": [ 0.010444083, 0.010328666, 0.011380541, 0.010627291, 0.010934291 ], "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "result": { "coefficients": [ 651.801014964034, 17.921788359844268, 61.87155496695371 ], "covariance": [ [ 4.076312044420639, -0.06123635273574915, 0.2968887483704617 ], [ -0.06123635273574916, 0.001899495671206556, -0.03284932770119199 ], [ 0.2968887483704617, -0.03284932770119199, 0.8948970144428721 ] ], "std_errors": [ 2.0189878762440947, 0.043583204003452475, 0.9459899652971336 ], "t_statistics": [ 322.83552696540886, 411.20860133239813, 65.40402883398448 ], "p_values": [ 0, 0, 0 ], "conf_int": [ [ 647.8438235435573, 655.7582063845108 ], [ 17.836365815712803, 18.007210903975732 ], [ 60.017426262875084, 63.725683671032336 ] ], "rss": 3249145819.046909, "residual_variance": 32492.43296345799, "sigma": 180.25657536816234, "r_squared": 0.8555135818351284, "adj_r_squared": 0.8555106920200706, "df_residual": 99997, "log_likelihood": -661330.4787637006, "diagnostics": { "converged": true, "solver": "scaled_svd", "warnings": [] }, "fitted_sample": [ 2036.1351232735046, 1895.1333265773244, 1567.4771173533084, 1704.471524501248, 2854.933734624018, 1904.9702530824984, 2804.246363718333, 2526.727087821867, 2675.9897031939504, 1444.272640054755 ], "residuals_sample": [ 32.14206807899973, 67.49567612181022, 178.93565999979455, -101.6695202935523, -23.85499542846992, -6.535258905037836, -30.015273767108283, -291.33599991346, 47.00448984454442, 2.0114340271875335 ] }, "process_seconds": 0.19558795914053917, "peak_rss_bytes": 88555520, "median_fit_seconds": 0.010627291, "min_fit_seconds": 0.010328666 }, "statsmodels": { "version": "0.15.0", "numpy": "2.5.4", "load_seconds": 0.02381816692650318, "fit_seconds": [ 0.005225708009675145, 0.0049707910511642694, 0.004864000016823411, 0.004892708035185933, 0.00494383298791945 ], "result": { "coefficients": [ 651.8010149638682, 17.9217883598442, 61.87155496695245 ], "covariance": [ [ 4.076312044418665, -0.06123635273572239, 0.29688874837005863 ], [ -0.06123635273572239, 0.0018994956712065157, -0.03284932770119123 ], [ 0.29688874837005863, -0.03284932770119123, 0.8948970144428612 ] ], "std_errors": [ 2.0189878762436058, 0.04358320400345202, 0.9459899652971279 ], "t_statistics": [ 322.8355269654049, 411.2086013324009, 65.40402883398356 ], "p_values": [ 0.0, 0.0, 0.0 ], "conf_int": [ [ 647.8438235433323, 655.758206384404 ], [ 17.836365815711442, 18.007210903976958 ], [ 60.01742626284571, 63.725683671059194 ] ], "rss": 3249145819.0469036, "residual_variance": 32492.43296345794, "sigma": 180.2565753681622, "r_squared": 0.8555135818351305, "adj_r_squared": 0.8555106920200728, "df_residual": 99997, "log_likelihood": -661330.4787637005, "fitted_sample": [ 2036.1351232733305, 1895.133326577152, 1567.4771173531383, 1704.471524501076, 2854.9337346238394, 1904.9702530823258, 2804.246363718155, 2526.727087821691, 2675.989703193774, 1444.272640054585 ], "residuals_sample": [ 32.142068079173896, 67.49567612198257, 178.93565999996463, -101.66952029338017, -23.854995428291204, -6.535258904865259, -30.015273766930022, -291.335999913284, 47.004489844720865, 2.0114340273573816 ] }, "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "process_seconds": 0.7115188748575747, "peak_rss_bytes": 195608576, "median_fit_seconds": 0.00494383298791945, "min_fit_seconds": 0.004864000016823411 }, "R": { "version": "R version 4.6.1 (2026-06-24)", "BLAS": "/opt/homebrew/Cellar/openblas/0.3.34/lib/libopenblasp-r0.3.34.dylib", "load_seconds": 0.061000000000000006, "fit_seconds": [ 0.014999999999999986, 0.015000000000000013, 0.015000000000000013, 0.014999999999999986, 0.015000000000000013 ], "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "result": { "coefficients": [ 651.8010149638403, 17.921788359844484, 61.87155496695173 ], "covariance": [ [ 4.076312044418676, -0.061236352735719604, 0.2968887483699397 ], [ -0.061236352735719604, 0.0018994956712065632, -0.032849327701191734 ], [ 0.2968887483699397, -0.032849327701191734, 0.8948970144428625 ] ], "std_errors": [ 2.0189878762436084, 0.04358320400345256, 0.9459899652971286 ], "t_statistics": [ 322.83552696539067, 411.20860133240234, 65.40402883398274 ], "p_values": [ 0, 0, 0 ], "conf_int": [ [ 647.8438235433044, 655.7582063843762 ], [ 17.836365815711726, 18.007210903977242 ], [ 60.017426262844985, 63.72568367105847 ] ], "rss": 3249145819.046939, "residual_variance": 32492.432963458294, "sigma": 180.25657536816317, "r_squared": 0.8555135818351274, "adj_r_squared": 0.8555106920200697, "df_residual": 99997, "log_likelihood": -661330.478763701, "fitted_sample": [ 2036.1351232763068, 1895.133326577152, 1567.4771173531376, 1704.4715245010757, 2854.9337346238417, 1904.970253082326, 2804.246363718157, 2526.7270878216927, 2675.9897031937758, 1444.2726400545841 ], "residuals_sample": [ 32.142068076197575, 67.49567612198229, 178.93565999996534, -101.66952029338026, -23.854995428293357, -6.535258904865185, -30.015273766932083, -291.3359999132857, 47.004489844719096, 2.0114340273583085 ] }, "process_seconds": 0.302015749970451, "peak_rss_bytes": 124469248, "median_fit_seconds": 0.015000000000000013, "min_fit_seconds": 0.014999999999999986 } }, "max_absolute_errors_vs_R": { "statsmodels": { "coefficients": 2.7853275241795927e-11, "covariance": 1.1890488593735427e-13, "std_errors": 2.6645352591003757e-15, "t_statistics": 1.4210854715202004e-11, "p_values": 0.0, "conf_int": 2.7853275241795927e-11, "rss": 3.528594970703125e-05, "residual_variance": 3.5288394428789616e-10, "sigma": 9.663381206337363e-13, "r_squared": 3.1086244689504383e-15, "adj_r_squared": 3.1086244689504383e-15, "df_residual": 0.0, "log_likelihood": 5.820766091346741e-10, "fitted_sample": 2.9763214115519077e-09, "residuals_sample": 2.9763214115519077e-09 }, "PHP": { "coefficients": 1.9372237147763371e-10, "covariance": 1.963762485956977e-12, "std_errors": 4.862776847858186e-13, "t_statistics": 1.8189894035458565e-11, "p_values": 0.0, "conf_int": 2.5283952709287405e-10, "rss": 3.0040740966796875e-05, "residual_variance": 3.019522409886122e-10, "sigma": 8.242295734817162e-13, "r_squared": 9.992007221626409e-16, "adj_r_squared": 8.881784197001252e-16, "df_residual": 0.0, "log_likelihood": 4.656612873077393e-10, "fitted_sample": 2.802153176162392e-09, "residuals_sample": 2.802153176162392e-09 } }, "agreement_passed": true }, { "n": 1000000, "p": 3, "data": { "seed": 20261011, "sha256": "21f9eddd10fc6000955d4d9e0019b34cf8d5b6d68b308d64ca151dbb39910e29", "true_coefficients": [ 650.0, 18.0, 60.0 ], "error_sd": 180, "sample_correlations": [ [ 1.0, 0.7966809332060808, 0.9219928562603458 ], [ 0.7966809332060808, 1.0, 0.7803238476037206 ], [ 0.9219928562603458, 0.7803238476037206, 1.0 ] ], "correlation_order": [ "area_m2", "bedrooms", "monthly_rent" ] }, "implementations": { "R": { "version": "R version 4.6.1 (2026-06-24)", "BLAS": "/opt/homebrew/Cellar/openblas/0.3.34/lib/libopenblasp-r0.3.34.dylib", "load_seconds": 1.5490000000000002, "fit_seconds": [ 0.18299999999999983, 0.17100000000000026, 0.16900000000000004, 0.18300000000000027, 0.20000000000000018 ], "sample_indices": [ 0, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999 ], "result": { "coefficients": [ 651.1220923658835, 17.99310335327689, 59.717683018730604 ], "covariance": [ [ 0.4049449001412597, -0.006074300093851262, 0.029143416423860397 ], [ -0.006074300093851262, 0.0001890674996865984, -0.003278837155733925 ], [ 0.029143416423860397, -0.003278837155733925, 0.08958885126251846 ] ], "std_errors": [ 0.6363528110578751, 0.013750181805583458, 0.2993139677036781 ], "t_statistics": [ 1023.2092654442052, 1308.5720325509103, 199.51518960802835 ], "p_values": [ 0, 0, 0 ], "conf_int": [ [ 649.8748622651415, 652.3693224666256 ], [ 17.96615345953777, 18.02005324701601 ], [ 59.13103771190472, 60.30432832555649 ] ], "rss": 32379112950.61594, "residual_variance": 32379.210088246204, "sigma": 179.94224097817113, "r_squared": 0.8558104964198698, "adj_r_squared": 0.8558102080399975, "df_residual": 999997, "log_likelihood": -6611572.949143916, "fitted_sample": [ 2033.7645702550933, 1937.5586100015034, 2185.980200944693, 1496.8068843216843, 2414.736647712703, 1691.787234866754, 2320.6509298665737, 1687.6727972611332, 1996.9934848523735, 2250.3494217736593 ], "residuals_sample": [ 23.307434460750528, 93.21875322936056, -79.83613765911619, 13.647783106654062, 369.6250787618763, -239.9933035864414, -117.90582462642868, -228.1335031251577, 89.07132799560623, -172.35926137650756 ] }, "process_seconds": 2.948457125108689, "peak_rss_bytes": 522108928, "median_fit_seconds": 0.18299999999999983, "min_fit_seconds": 0.16900000000000004 }, "statsmodels": { "version": "0.15.0", "numpy": "2.5.4", "load_seconds": 0.24722754093818367, "fit_seconds": [ 0.09425220894627273, 0.09041399997659028, 0.08978870906867087, 0.09009991609491408, 0.08997033396735787 ], "result": { "coefficients": [ 651.1220923659214, 17.993103353276428, 59.7176830187281 ], "covariance": [ [ 0.40494490014126555, -0.006074300093851174, 0.02914341642385708 ], [ -0.006074300093851174, 0.00018906749968659563, -0.003278837155733871 ], [ 0.02914341642385708, -0.003278837155733871, 0.08958885126251943 ] ], "std_errors": [ 0.6363528110578797, 0.013750181805583359, 0.29931396770367974 ], "t_statistics": [ 1023.2092654442574, 1308.572032550886, 199.5151896080189 ], "p_values": [ 0.0, 0.0, 0.0 ], "conf_int": [ [ 649.8748622651793, 652.3693224666634 ], [ 17.96615345953731, 18.020053247015547 ], [ 59.131037711902216, 60.30432832555399 ] ], "rss": 32379112950.616966, "residual_variance": 32379.21008824723, "sigma": 179.94224097817397, "r_squared": 0.8558104964198698, "adj_r_squared": 0.8558102080399975, "df_residual": 999997, "log_likelihood": -6611572.949143933, "fitted_sample": [ 2033.7645702538905, 1937.5586100014996, 2185.980200944691, 1496.806884321677, 2414.7366477127034, 1691.7872348667483, 2320.6509298665737, 1687.6727972611272, 1996.99348485237, 2250.349421773658 ], "residuals_sample": [ 23.307434461953335, 93.21875322936444, -79.83613765911423, 13.647783106661336, 369.625078761876, -239.9933035864358, -117.90582462642851, -228.13350312515172, 89.07132799560964, -172.3592613765063 ] }, "sample_indices": [ 0, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999 ], "process_seconds": 1.4731278750114143, "peak_rss_bytes": 393658368, "median_fit_seconds": 0.09009991609491408, "min_fit_seconds": 0.08978870906867087 }, "PHP": { "version": "8.5.10", "load_seconds": 0.809957375, "fit_seconds": [ 0.123192875, 0.116670625, 0.113401833, 0.112949875, 0.113148292 ], "sample_indices": [ 0, 111111, 222222, 333333, 444444, 555555, 666666, 777777, 888888, 999999 ], "result": { "coefficients": [ 651.1220923649437, 17.99310335327652, 59.717683018726035 ], "covariance": [ [ 0.4049449001401167, -0.006074300093841107, 0.029143416423784808 ], [ -0.006074300093841106, 0.00018906749968659197, -0.00327883715573382 ], [ 0.02914341642378481, -0.00327883715573382, 0.08958885126251746 ] ], "std_errors": [ 0.636352811056977, 0.013750181805583225, 0.29931396770367646 ], "t_statistics": [ 1023.2092654441724, 1308.5720325509055, 199.51518960801417 ], "p_values": [ 0, 0, 0 ], "conf_int": [ [ 649.8748622644385, 652.3693224654488 ], [ 17.966153459542486, 18.020053247010555 ], [ 59.13103771201079, 60.30432832544128 ] ], "rss": 32379112950.617058, "residual_variance": 32379.210088247324, "sigma": 179.94224097817423, "r_squared": 0.8558104964198643, "adj_r_squared": 0.855810208039992, "df_residual": 999997, "log_likelihood": -6611572.949143934, "diagnostics": { "converged": true, "solver": "scaled_svd", "warnings": [] }, "fitted_sample": [ 2033.7645702529128, 1937.5586100005237, 2185.9802009437167, 1496.8068843207013, 2414.73664771173, 1691.7872348657736, 2320.6509298655997, 1687.67279726015, 1996.9934848513944, 2250.349421772684 ], "residuals_sample": [ 23.30743446293104, 93.21875323034033, -79.8361376581397, 13.647783107636997, 369.6250787628496, -239.99330358546104, -117.90582462545444, -228.13350312417447, 89.0713279965853, -172.35926137553224 ] }, "process_seconds": 1.5910915001295507, "peak_rss_bytes": 903200768, "median_fit_seconds": 0.113401833, "min_fit_seconds": 0.112949875 } }, "max_absolute_errors_vs_R": { "statsmodels": { "coefficients": 3.785771696129814e-11, "covariance": 5.828670879282072e-15, "std_errors": 4.551914400963142e-15, "t_statistics": 5.218225851422176e-11, "p_values": 0.0, "conf_int": 3.785771696129814e-11, "rss": 0.001026153564453125, "residual_variance": 1.025910023599863e-09, "sigma": 2.8421709430404007e-12, "r_squared": 0.0, "adj_r_squared": 0.0, "df_residual": 0.0, "log_likelihood": 1.6763806343078613e-08, "fitted_sample": 1.2028067430946976e-09, "residuals_sample": 1.2028067430946976e-09 }, "PHP": { "coefficients": 9.398490874445997e-10, "covariance": 1.14303011500283e-12, "std_errors": 8.980594046192891e-13, "t_statistics": 3.285549610154703e-11, "p_values": 0.0, "conf_int": 1.1767724572564475e-09, "rss": 0.001117706298828125, "residual_variance": 1.1204974725842476e-09, "sigma": 3.097966327914037e-12, "r_squared": 5.551115123125783e-15, "adj_r_squared": 5.551115123125783e-15, "df_residual": 0.0, "log_likelihood": 1.7695128917694092e-08, "fitted_sample": 2.1805135475005955e-09, "residuals_sample": 2.1805135475005955e-09 } }, "agreement_passed": true }, { "n": 100000, "p": 11, "data": { "seed": 20261011, "sha256": "a40483bcb6a170f74a85351116d323599f08c628bd651cb142d1652d31a0e20f", "true_coefficients": [ 650.0, 18.0, 60.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5 ], "error_sd": 180, "sample_correlations": [ [ 1.0, 0.7967476697702436, 0.921558718600213 ], [ 0.7967476697702436, 1.0, 0.781112783296116 ], [ 0.921558718600213, 0.781112783296116, 0.9999999999999999 ] ], "correlation_order": [ "area_m2", "bedrooms", "monthly_rent" ] }, "implementations": { "PHP": { "version": "8.5.10", "load_seconds": 0.304886166, "fit_seconds": [ 0.028643667, 0.028582666, 0.025713334, 0.027377666, 0.027113417 ], "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "result": { "coefficients": [ 653.4691003477566, 17.931017822685874, 60.95273786650942, 0.0532587010685985, -0.20577496854801175, -0.27985794500410854, 1.2913921359066385, 0.5051834481329632, -0.21848101914366794, -0.49466318500884754, 0.8536450809062963 ], "covariance": [ [ 4.073464919711363, -0.06119307452223954, 0.2966637496504089, 0.003190794866363923, -0.0025591381914664155, 0.0037201982956457397, 0.0025360966630790073, -0.005682951394511834, 0.0014389935212899122, 0.00014384730973477668, 0.001317698560168864 ], [ -0.06119307452223954, 0.0018981854030035916, -0.03282666971732007, -7.56106862002038e-05, -2.984063350877426e-06, -2.0690706753414856e-05, -0.00011889351849453367, 8.903977248714772e-05, 5.073577484946545e-05, -1.204635498369033e-05, 9.191210491118202e-05 ], [ 0.2966637496504089, -0.03282666971732007, 0.8942829584897597, 0.0010713179087015634, 0.0009177209395624902, 2.269208096402473e-05, 0.0013492784816156258, -0.0002770709380041354, -0.0013004053653582156, 0.0004018369222865016, -0.00373348454967378 ], [ 0.0031907948663639227, -7.56106862002038e-05, 0.0010713179087015634, 0.32574185240579506, 0.0006114998422527628, -0.001398529392279365, -0.0012633331786297889, -0.0008825899737035762, 0.0004873490663968262, 0.001255582813617457, 0.0003238222644310912 ], [ -0.0025591381914664155, -2.984063350877426e-06, 0.0009177209395624902, 0.0006114998422527628, 0.3260196281559824, 0.00010304848851758633, -0.001037884285871109, 0.001550316634434471, 0.00012361786282777144, -0.0007782641758644416, -0.0004809290935229789 ], [ 0.00372019829564574, -2.0690706753414852e-05, 2.2692080964024726e-05, -0.001398529392279365, 0.00010304848851758633, 0.3254122453207837, -0.001356882402978376, -0.0010148446796477183, 0.0010290925998725962, -0.001831439494129776, 0.0008616954113418627 ], [ 0.0025360966630790073, -0.00011889351849453366, 0.0013492784816156258, -0.0012633331786297889, -0.001037884285871109, -0.001356882402978376, 0.32643645186309284, 0.0005092331886757512, 0.0007813166845775073, -0.0009224479946724267, -0.0022545886788930885 ], [ -0.005682951394511834, 8.903977248714772e-05, -0.00027707093800413533, -0.0008825899737035761, 0.001550316634434471, -0.0010148446796477183, 0.0005092331886757513, 0.31983724658879875, 0.0003051313316441368, -0.0010412841196088495, -0.0013736897948884524 ], [ 0.0014389935212899122, 5.073577484946544e-05, -0.0013004053653582154, 0.0004873490663968263, 0.00012361786282777144, 0.0010290925998725962, 0.0007813166845775073, 0.00030513133164413673, 0.32528279579907, 0.0014876059400061514, 0.0008643879322506907 ], [ 0.00014384730973477665, -1.204635498369033e-05, 0.00040183692228650154, 0.001255582813617457, -0.0007782641758644416, -0.0018314394941297762, -0.0009224479946724267, -0.0010412841196088495, 0.0014876059400061514, 0.3265841419287733, 0.0015288989603068344 ], [ 0.001317698560168864, 9.191210491118202e-05, -0.00373348454967378, 0.0003238222644310912, -0.0004809290935229789, 0.0008616954113418627, -0.0022545886788930885, -0.0013736897948884524, 0.0008643879322506906, 0.0015288989603068344, 0.32392925926652516 ] ], "std_errors": [ 2.018282665959197, 0.043568169608139286, 0.9456653522730754, 0.5707379892786137, 0.570981285293995, 0.5704491610308352, 0.5713461751539891, 0.5655415516023546, 0.5703356869415327, 0.5714754079825074, 0.5691478360378129 ], "t_statistics": [ 323.7748167634353, 411.56233975310386, 64.45487055225048, 0.0933155004031097, -0.3603882891574273, -0.4905922632936978, 2.26026215290333, 0.8932737951820194, -0.3830744316830121, -0.8655896266038257, 1.4998652842977374 ], "p_values": [ 0, 0, 0, 0.9256531052366139, 0.7185575442372081, 0.623715936074704, 0.02380712678841629, 0.37171271750471613, 0.7016653911920312, 0.38671732305150763, 0.1336524594581041 ], "conf_int": [ [ 649.5132911268739, 657.4249095686392 ], [ 17.845624745700324, 18.016410899671424 ], [ 59.09924539814239, 62.80623033487645 ], [ -1.0653807436314753, 1.1718981457686724 ], [ -1.3248912704481604, 0.913341333352137 ], [ -1.397931289888193, 0.838215399879976 ], [ 0.17156065436534407, 2.411223617447933 ], [ -0.6032710425850981, 1.6136379388510247 ], [ -1.3363319562072995, 0.8993699179199637 ], [ -1.6147479613057856, 0.6254215912880904 ], [ -0.2618776829845575, 1.9691678447971501 ] ], "rss": 3246436795.012876, "residual_variance": 32467.93942346534, "sigma": 180.18862179245764, "r_squared": 0.8552978396712653, "adj_r_squared": 0.8552833678633336, "df_residual": 99989, "log_likelihood": -661288.7731253913, "diagnostics": { "converged": true, "solver": "scaled_svd", "warnings": [] }, "fitted_sample": [ 2037.1774688546677, 1893.7957337141781, 1569.3347490014135, 1705.2369087812704, 2853.022203607671, 1904.7721538709795, 2806.261481662618, 2526.168747613301, 2678.477775745674, 1446.9667177673555 ], "residuals_sample": [ 72.32602150400703, 134.80277088823073, -45.598612892474875, -15.348928972168324, -12.300096963685974, -412.82572155863863, -277.4190790269922, 309.51726312378287, 75.27968067758366, -205.99467143118795 ] }, "process_seconds": 0.5212112909648567, "peak_rss_bytes": 147570688, "median_fit_seconds": 0.027377666, "min_fit_seconds": 0.025713334 }, "statsmodels": { "version": "0.15.0", "numpy": "2.5.4", "load_seconds": 0.11988145904615521, "fit_seconds": [ 0.01211566710844636, 0.011115708155557513, 0.01141608296893537, 0.01111033302731812, 0.011210208060219884 ], "result": { "coefficients": [ 653.46910034759, 17.9310178226858, 60.95273786650771, 0.05325870106853009, -0.20577496854762095, -0.279857945004596, 1.2913921359060219, 0.5051834481324069, -0.21848101914418594, -0.4946631850090253, 0.8536450809060132 ], "covariance": [ [ 4.073464919709347, -0.06119307452221063, 0.296663749649939, 0.0031907948663619443, -0.0025591381914643226, 0.0037201982956415786, 0.002536096663075174, -0.0056829513945137085, 0.0014389935212873706, 0.0001438473097329779, 0.0013176985601688763 ], [ -0.06119307452221063, 0.0018981854030035465, -0.03282666971731921, -7.561068620018134e-05, -2.9840633509251973e-06, -2.0690706753335695e-05, -0.00011889351849446392, 8.903977248724137e-05, 5.073577484954534e-05, -1.2046354983631558e-05, 9.191210491121509e-05 ], [ 0.296663749649939, -0.03282666971731921, 0.8942829584897458, 0.0010713179087011126, 0.0009177209395633554, 2.269208096249315e-05, 0.0013492784816143675, -0.0002770709380056653, -0.0013004053653595392, 0.000401836922285754, -0.0037334845496743876 ], [ 0.0031907948663619443, -7.561068620018134e-05, 0.0010713179087011126, 0.32574185240579895, 0.000611499842252845, -0.0013985293922793018, -0.0012633331786296759, -0.0008825899737032794, 0.00048734906639670333, 0.0012555828136176597, 0.0003238222644313546 ], [ -0.0025591381914643226, -2.9840633509251973e-06, 0.0009177209395633554, 0.000611499842252845, 0.3260196281559824, 0.00010304848851699634, -0.0010378842858711978, 0.0015503166344342139, 0.00012361786282778678, -0.0007782641758645154, -0.00048092909352309845 ], [ 0.0037201982956415786, -2.0690706753335695e-05, 2.269208096249315e-05, -0.0013985293922793018, 0.00010304848851699634, 0.32541224532078344, -0.0013568824029785084, -0.0010148446796480499, 0.0010290925998726642, -0.0018314394941295437, 0.0008616954113421371 ], [ 0.002536096663075174, -0.00011889351849446392, 0.0013492784816143675, -0.0012633331786296759, -0.0010378842858711978, -0.0013568824029785084, 0.32643645186309395, 0.0005092331886753515, 0.000781316684577811, -0.0009224479946727628, -0.002254588678893017 ], [ -0.0056829513945137085, 8.903977248724137e-05, -0.0002770709380056653, -0.0008825899737032794, 0.0015503166344342139, -0.0010148446796480499, 0.0005092331886753515, 0.3198372465887985, 0.0003051313316442697, -0.0010412841196089627, -0.0013736897948880909 ], [ 0.0014389935212873706, 5.073577484954534e-05, -0.0013004053653595392, 0.00048734906639670333, 0.00012361786282778678, 0.0010290925998726642, 0.000781316684577811, 0.0003051313316442697, 0.32528279579907193, 0.001487605940005945, 0.0008643879322506391 ], [ 0.0001438473097329779, -1.2046354983631558e-05, 0.000401836922285754, 0.0012555828136176597, -0.0007782641758645154, -0.0018314394941295437, -0.0009224479946727628, -0.0010412841196089627, 0.001487605940005945, 0.32658414192877444, 0.0015288989603073873 ], [ 0.0013176985601688763, 9.191210491121509e-05, -0.0037334845496743876, 0.0003238222644313546, -0.00048092909352309845, 0.0008616954113421371, -0.002254588678893017, -0.0013736897948880909, 0.0008643879322506391, 0.0015288989603073873, 0.3239292592665243 ] ], "std_errors": [ 2.0182826659586977, 0.043568169608138765, 0.945665352273068, 0.5707379892786172, 0.570981285293995, 0.570449161030835, 0.5713461751539901, 0.5655415516023544, 0.5703356869415344, 0.5714754079825084, 0.5691478360378122 ], "t_statistics": [ 323.7748167634328, 411.56233975310704, 64.45487055224918, 0.09331550040298928, -0.36038828915674287, -0.4905922632945525, 2.260262152902247, 0.8932737951810361, -0.3830744316839192, -0.8655896266041352, 1.499865284297242 ], "p_values": [ 0.0, 0.0, 0.0, 0.9256531052358694, 0.7185575442473128, 0.6237159360824712, 0.023807126788185053, 0.37171271751103746, 0.7016653911981122, 0.3867173230573286, 0.133652459465676 ], "conf_int": [ [ 649.5132911267134, 657.4249095684667 ], [ 17.84562474570036, 18.01641089967124 ], [ 59.09924539814307, 62.80623033487235 ], [ -1.0653807436301181, 1.1718981457671784 ], [ -1.3248912704463367, 0.9133413333510949 ], [ -1.3979312898872487, 0.8382153998780568 ], [ 0.1715606543661592, 2.4112236174458843 ], [ -0.6032710425842349, 1.6136379388490487 ], [ -1.3363319562063896, 0.8993699179180177 ], [ -1.614747961304531, 0.6254215912864804 ], [ -0.26187768298341085, 1.9691678447954373 ] ], "rss": 3246436795.0128813, "residual_variance": 32467.939423465396, "sigma": 180.18862179245778, "r_squared": 0.8552978396712636, "adj_r_squared": 0.8552833678633318, "df_residual": 99989, "log_likelihood": -661288.7731253915, "fitted_sample": [ 2037.1774688544886, 1893.795733714004, 1569.3347490012409, 1705.2369087810969, 2853.0222036074915, 1904.7721538708045, 2806.261481662435, 2526.1687476131215, 2678.477775745494, 1446.9667177671843 ], "residuals_sample": [ 72.3260215041862, 134.8027708884049, -45.5986128923023, -15.348928971994837, -12.300096963506348, -412.82572155846356, -277.4190790268094, 309.5172631239625, 75.27968067776374, -205.99467143101674 ] }, "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "process_seconds": 0.8636084171012044, "peak_rss_bytes": 227557376, "median_fit_seconds": 0.011210208060219884, "min_fit_seconds": 0.01111033302731812 }, "R": { "version": "R version 4.6.1 (2026-06-24)", "BLAS": "/opt/homebrew/Cellar/openblas/0.3.34/lib/libopenblasp-r0.3.34.dylib", "load_seconds": 0.7, "fit_seconds": [ 0.020000000000000018, 0.020000000000000018, 0.020000000000000018, 0.020999999999999908, 0.02200000000000002 ], "sample_indices": [ 0, 11111, 22222, 33333, 44444, 55555, 66666, 77777, 88888, 99999 ], "result": { "coefficients": [ 653.4691003475657, 17.93101782268606, 60.95273786650741, 0.05325870106850358, -0.20577496854765356, -0.27985794500476646, 1.2913921359060703, 0.5051834481323613, -0.21848101914421453, -0.4946631850091334, 0.8536450809060374 ], "covariance": [ [ 4.073464919709417, -0.06119307452221023, 0.2966637496498886, 0.003190794866361827, -0.002559138191464399, 0.003720198295641564, 0.002536096663075092, -0.005682951394514027, 0.0014389935212874663, 0.00014384730973294286, 0.001317698560169152 ], [ -0.06119307452221023, 0.0018981854030036076, -0.03282666971731999, -7.561068620017495e-05, -2.9840633509392013e-06, -2.069070675330919e-05, -0.00011889351849444797, 8.903977248726143e-05, 5.073577484955539e-05, -1.2046354983640662e-05, 9.191210491122429e-05 ], [ 0.2966637496498886, -0.03282666971731999, 0.8942829584897544, 0.0010713179087010285, 0.0009177209395635621, 2.26920809622238e-05, 0.0013492784816141292, -0.00027707093800607004, -0.001300405365359761, 0.0004018369222856645, -0.003733484549674511 ], [ 0.003190794866361827, -7.561068620017495e-05, 0.0010713179087010285, 0.3257418524057946, 0.0006114998422528272, -0.0013985293922792027, -0.0012633331786297685, -0.000882589973703503, 0.0004873490663968241, 0.0012555828136178843, 0.0003238222644314661 ], [ -0.002559138191464399, -2.9840633509392013e-06, 0.0009177209395635621, 0.0006114998422528272, 0.3260196281559874, 0.0001030484885174452, -0.0010378842858713392, 0.0015503166344344856, 0.0001236178628279321, -0.0007782641758645284, -0.0004809290935229724 ], [ 0.003720198295641564, -2.069070675330919e-05, 2.26920809622238e-05, -0.0013985293922792027, 0.0001030484885174452, 0.32541224532078805, -0.0013568824029787088, -0.0010148446796481737, 0.0010290925998726254, -0.0018314394941294945, 0.000861695411342153 ], [ 0.002536096663075092, -0.00011889351849444797, 0.0013492784816141292, -0.0012633331786297685, -0.0010378842858713392, -0.0013568824029787088, 0.32643645186309406, 0.0005092331886752904, 0.0007813166845777747, -0.0009224479946725172, -0.002254588678893007 ], [ -0.005682951394514027, 8.903977248726143e-05, -0.00027707093800607004, -0.000882589973703503, 0.0015503166344344856, -0.0010148446796481737, 0.0005092331886752904, 0.3198372465888033, 0.0003051313316444451, -0.0010412841196088599, -0.0013736897948884287 ], [ 0.0014389935212874663, 5.073577484955539e-05, -0.001300405365359761, 0.0004873490663968241, 0.0001236178628279321, 0.0010290925998726254, 0.0007813166845777747, 0.0003051313316444451, 0.32528279579907765, 0.0014876059400059914, 0.0008643879322504808 ], [ 0.00014384730973294286, -1.2046354983640662e-05, 0.0004018369222856645, 0.0012555828136178843, -0.0007782641758645284, -0.0018314394941294945, -0.0009224479946725172, -0.0010412841196088599, 0.0014876059400059914, 0.326584141928775, 0.0015288989603073017 ], [ 0.001317698560169152, 9.191210491122429e-05, -0.003733484549674511, 0.0003238222644314661, -0.0004809290935229724, 0.000861695411342153, -0.002254588678893007, -0.0013736897948884287, 0.0008643879322504808, 0.0015288989603073017, 0.3239292592665309 ] ], "std_errors": [ 2.0182826659587145, 0.043568169608139466, 0.9456653522730725, 0.5707379892786133, 0.5709812852939993, 0.5704491610308389, 0.5713461751539901, 0.5655415516023586, 0.5703356869415394, 0.5714754079825088, 0.5691478360378178 ], "t_statistics": [ 323.7748167634181, 411.56233975310636, 64.45487055224855, 0.09331550040294347, -0.36038828915679727, -0.490592263294848, 2.2602621529023317, 0.8932737951809487, -0.383074431683966, -0.8655896266043238, 1.4998652842972695 ], "p_values": [ 0, 0, 0, 0.9256531052359056, 0.718557544247272, 0.6237159360822622, 0.023807126788179794, 0.3717127175110838, 0.7016653911980772, 0.3867173230572246, 0.13365245946566898 ], "conf_int": [ [ 649.5132911266891, 657.4249095684423 ], [ 17.845624745700615, 18.016410899671502 ], [ 59.09924539814276, 62.80623033487206 ], [ -1.0653807436301372, 1.1718981457671442 ], [ -1.3248912704463778, 0.9133413333510707 ], [ -1.3979312898874268, 0.8382153998778938 ], [ 0.1715606543662076, 2.411223617445933 ], [ -0.6032710425842885, 1.6136379388490112 ], [ -1.336331956206428, 0.8993699179179988 ], [ -1.61474796130464, 0.6254215912863732 ], [ -0.26187768298339775, 1.9691678447954726 ] ], "rss": 3246436795.0129185, "residual_variance": 32467.939423465767, "sigma": 180.18862179245883, "r_squared": 0.8552978396712632, "adj_r_squared": 0.8552833678633314, "df_residual": 99989, "log_likelihood": -661288.773125392, "fitted_sample": [ 2037.1774688575256, 1893.7957337140076, 1569.3347490012436, 1705.2369087811003, 2853.022203607497, 1904.7721538708074, 2806.261481662441, 2526.1687476131265, 2678.4777757454995, 1446.9667177671872 ], "residuals_sample": [ 72.32602150114906, 134.80277088840117, -45.59861289230499, -15.348928971998298, -12.30009696351175, -412.82572155846657, -277.4190790268155, 309.51726312395755, 75.27968067775849, -205.9946714310196 ] }, "process_seconds": 1.153698458801955, "peak_rss_bytes": 230457344, "median_fit_seconds": 0.020000000000000018, "min_fit_seconds": 0.020000000000000018 } }, "max_absolute_errors_vs_R": { "statsmodels": { "coefficients": 2.432898327242583e-11, "covariance": 6.927791673660977e-14, "std_errors": 1.687538997430238e-14, "t_statistics": 1.4722445484949276e-11, "p_values": 2.0905499553691698e-13, "conf_int": 2.432898327242583e-11, "rss": 3.719329833984375e-05, "residual_variance": 3.710738383233547e-10, "sigma": 1.0516032489249483e-12, "r_squared": 4.440892098500626e-16, "adj_r_squared": 4.440892098500626e-16, "df_residual": 0.0, "log_likelihood": 5.820766091346741e-10, "fitted_sample": 3.0370301828952506e-09, "residuals_sample": 3.0371438697329722e-09 }, "PHP": { "coefficients": 1.9088020053459331e-10, "covariance": 1.9459989175629744e-12, "std_errors": 4.82280881897168e-13, "t_statistics": 1.722355591482483e-11, "p_values": 1.0063949673622119e-11, "conf_int": 1.9690560293383896e-10, "rss": 4.2438507080078125e-05, "residual_variance": 4.256435204297304e-10, "sigma": 1.1937117960769683e-12, "r_squared": 2.1094237467877974e-15, "adj_r_squared": 2.220446049250313e-15, "df_residual": 0.0, "log_likelihood": 6.984919309616089e-10, "fitted_sample": 2.8578597266459838e-09, "residuals_sample": 2.8579734134837054e-09 } }, "agreement_passed": true } ] }