{
"test": "wls",
"method": "statsmodels",
"dataset": "faithful",
"formula": "Eruption length (mins) ~ Eruption wait (mins)",
"n": 272,
"k": 1,
"df_residual": 270,
"df_model": 1,
"variable_names": [
"Intercept",
"Eruption wait (mins)"
],
"coefficients": [
-1.8740159864107393,
0.07562794795186271
],
"std_errors": [
0.16014330230423843,
0.00221854145151769
],
"t_stats": [
-11.702119036177391,
34.08903985099134
],
"p_values": [
7.359171081984561e-26,
8.129958506618055e-100
],
"r_squared": 0.8114607609733095,
"adj_r_squared": 0.8107624674954329,
"f_statistic": 1162.0626379624757,
"f_p_value": 8.129958506618055e-100,
"mse": 0.24652509523222163,
"rmse": 0.49651293561419085,
"mae": 0.40194339340159724,
"residual_std_error": 0.49651293561419085,
"log_likelihood": -194.50794455190203,
"aic": 393.01588910380406,
"bic": 400.22749323639607,
"conf_int_lower": [
-2.1893043619076096,
0.07126010789763043
],
"conf_int_upper": [
-1.5587276109138688,
0.079995788006095
],
"fitted_values": [
4.100591901786416,
2.2098932029898477,
3.722452162027101,
2.814916786604749,
4.554359589497592,
2.2855211509417104,
4.781243433353179,
4.554359589497592,
1.9830093591342592,
4.554359589497592,
2.2098932029898477,
4.478731641545728,
4.024963953834552,
1.680497567326808,
4.4031036935938666,
2.058637307086122,
2.814916786604749,
4.478731641545728,
2.058637307086122,
4.100591901786416,
1.9830093591342592,
1.680497567326808,
4.024963953834552,
3.344312422267788,
3.722452162027101,
4.4031036935938666,
2.2855211509417104,
3.8737080579308274,
4.024963953834552,
4.100591901786416,
3.6468242140752385,
3.94933600588269,
3.1174285784122,
4.176219849738278,
3.722452162027101,
2.058637307086122,
1.7561255152786708,
4.176219849738278,
2.588032942749161,
4.932499329256904,
4.176219849738278,
2.5124049947972984,
4.478731641545728,
2.5124049947972984,
3.6468242140752385,
4.4031036935938666,
2.9661726825084744,
2.134265255037984,
4.327475745642003,
2.588032942749161,
3.7980801099789647,
4.932499329256904,
2.2098932029898477,
4.176219849738278,
2.2098932029898477,
4.4031036935938666,
3.495568318171513,
2.9661726825084744,
3.94933600588269,
4.251847797690141,
2.588032942749161,
4.478731641545728,
1.7561255152786708,
4.327475745642003,
2.6636608907010237,
5.08375522516063,
4.024963953834552,
4.024963953834552,
3.041800630460337,
3.6468242140752385,
4.327475745642003,
2.361149098893573,
4.100591901786416,
3.495568318171513,
2.814916786604749,
3.8737080579308274,
2.6636608907010237,
4.024963953834552,
3.8737080579308274,
4.4031036935938666,
3.7980801099789647,
4.327475745642003,
3.4199403702196505,
3.041800630460337,
3.6468242140752385,
4.781243433353179,
3.8737080579308274,
4.176219849738278,
1.7561255152786708,
4.629987537449454,
2.6636608907010237,
4.932499329256904,
1.9073814111823966,
4.024963953834552,
2.8905447345566118,
3.571196266123376,
4.478731641545728,
3.7980801099789647,
1.9830093591342592,
4.327475745642003,
2.814916786604749,
4.781243433353179,
1.831753463230534,
4.4031036935938666,
4.251847797690141,
1.680497567326808,
4.478731641545728,
2.058637307086122,
4.629987537449454,
4.251847797690141,
3.7980801099789647,
2.588032942749161,
4.856871381305043,
4.100591901786416,
2.588032942749161,
4.251847797690141,
1.9073814111823966,
4.554359589497592,
2.588032942749161,
4.705615485401317,
2.134265255037984,
3.344312422267788,
3.94933600588269,
2.361149098893573,
4.781243433353179,
4.251847797690141,
1.5292416714230828,
4.327475745642003,
2.2855211509417104,
4.932499329256904,
1.5292416714230828,
4.4031036935938666,
2.361149098893573,
4.856871381305043,
1.6048696193749454,
4.327475745642003,
1.9830093591342592,
4.629987537449454,
2.134265255037984,
4.100591901786416,
4.251847797690141,
2.6636608907010237,
4.327475745642003,
3.94933600588269,
3.8737080579308274,
2.588032942749161,
4.176219849738278,
1.831753463230534,
5.38626701696808,
2.134265255037984,
3.94933600588269,
3.94933600588269,
3.041800630460337,
4.251847797690141,
3.495568318171513,
3.4199403702196505,
4.251847797690141,
5.159383173112493,
2.134265255037984,
4.856871381305043,
1.5292416714230828,
4.629987537449454,
2.5124049947972984,
4.024963953834552,
3.1174285784122,
3.8737080579308274,
2.8905447345566118,
4.781243433353179,
2.058637307086122,
5.159383173112493,
1.831753463230534,
2.4367770468454357,
3.94933600588269,
3.268684474315925,
4.251847797690141,
4.251847797690141,
3.6468242140752385,
1.9073814111823966,
4.554359589497592,
3.722452162027101,
2.2855211509417104,
3.94933600588269,
4.4031036935938666,
4.4031036935938666,
1.9830093591342592,
4.024963953834552,
4.478731641545728,
1.6048696193749454,
4.4031036935938666,
2.2855211509417104,
4.251847797690141,
2.4367770468454357,
3.8737080579308274,
4.478731641545728,
3.94933600588269,
4.251847797690141,
4.705615485401317,
3.94933600588269,
1.9830093591342592,
4.024963953834552,
2.6636608907010237,
4.327475745642003,
5.008127277208768,
2.134265255037984,
4.024963953834552,
1.6048696193749454,
3.94933600588269,
4.478731641545728,
1.831753463230534,
4.4031036935938666,
3.495568318171513,
4.176219849738278,
1.831753463230534,
3.7980801099789647,
2.9661726825084744,
3.8737080579308274,
2.134265255037984,
5.235011121064355,
2.2855211509417104,
3.8737080579308274,
1.9073814111823966,
4.327475745642003,
2.2098932029898477,
3.7980801099789647,
4.024963953834552,
4.100591901786416,
4.024963953834552,
4.024963953834552,
3.4199403702196505,
4.100591901786416,
3.4199403702196505,
2.2098932029898477,
4.629987537449454,
1.9073814111823966,
4.932499329256904,
2.2098932029898477,
2.2098932029898477,
3.94933600588269,
4.100591901786416,
2.9661726825084744,
3.7980801099789647,
1.680497567326808,
4.629987537449454,
2.8905447345566118,
4.554359589497592,
4.327475745642003,
2.4367770468454357,
4.327475745642003,
3.1930565263640625,
3.722452162027101,
2.2098932029898477,
4.4031036935938666,
3.6468242140752385,
3.6468242140752385,
4.781243433353179,
4.176219849738278,
3.495568318171513,
4.4031036935938666,
2.361149098893573,
4.100591901786416,
4.024963953834552,
4.478731641545728,
2.5124049947972984,
4.4031036935938666,
1.3779857755193574,
2.6636608907010237,
3.7980801099789647,
4.251847797690141,
1.6048696193749454,
4.932499329256904,
1.6048696193749454,
3.722452162027101
],
"residuals": [
-0.5005919017864158,
-0.40989320298984766,
-0.389452162027101,
-0.5319167866047492,
-0.021359589497591536,
0.5974788490582896,
-0.08124343335317885,
-0.9543595894975918,
-0.033009359134259286,
-0.20435958949759225,
-0.37689320298984774,
-0.5617316415457285,
0.17503604616544788,
0.0695024326731919,
0.2968963064061336,
0.1083626929138779,
-1.064916786604749,
0.3212683584542715,
-0.4586373070861218,
0.14940809821358414,
-0.1830093591342592,
0.0695024326731919,
-0.5749639538345521,
-0.27731242226778763,
0.8105478379728992,
-0.8031036935938665,
-0.3185211509417103,
0.2092919420691728,
-0.1749639538345522,
0.33240809821358397,
0.6531757859247613,
0.5176639941173096,
0.2495714215878002,
-0.14321984973827728,
0.11054783797289902,
-0.04163730708612201,
0.11087448472132921,
0.6567801502617225,
-0.7550329427491611,
-0.149499329256904,
0.173780150261722,
-0.6294049947972984,
0.08826835845427183,
-0.7624049947972984,
0.8861757859247619,
-1.0861036935938664,
0.8668273174915258,
-0.034265255037984055,
0.305524254357997,
-0.5880329427491611,
1.001919890021035,
-0.21649932925690418,
-0.37689320298984774,
0.6567801502617225,
-0.4768932029898476,
0.47989630640613345,
0.22143168182848694,
-1.2991726825084744,
0.6176639941173101,
0.06515220230985896,
-0.355032942749161,
0.021268358454271663,
-0.006125515278670779,
0.47252425435799683,
-0.8466608907010238,
-0.6837552251606294,
0.14203604616544752,
0.6750360461654479,
-0.9748006304603369,
1.0531757859247617,
-0.29447574564200263,
-0.39414909889357297,
0.39940809821358414,
0.5044316818284869,
-0.831916786604749,
1.1932919420691728,
-0.6466608907010238,
0.5420360461654479,
0.00929194206917261,
-0.8031036935938665,
0.3349198900210353,
0.005524254357997194,
0.6800596297803492,
-0.4088006304603371,
0.4201757859247617,
0.1517565666468208,
0.07629194206917278,
0.3407801502617227,
0.41087448472132904,
-0.6299875374494537,
-0.46366089070102356,
-0.5994993292569042,
-0.040381411182396576,
0.7920360461654479,
-1.0575447345566118,
0.728803733876624,
0.18826835845427148,
-0.048080109978964725,
-0.11600935913425925,
0.5725242543579974,
-0.331916786604749,
-0.41424343335317904,
0.2682465367694662,
0.09689630640613345,
-0.20184779769014138,
0.1865024326731919,
0.22126835845427184,
-0.275637307086122,
0.22001246255054596,
-0.5688477976901414,
0.9349198900210349,
-0.28803294274916125,
0.043128618694957765,
0.31640809821358395,
-0.8880329427491611,
0.3811522023098588,
0.4096185888176036,
0.04564041050240775,
-0.7710329427491611,
-0.28861548540131743,
0.48273474496201585,
0.7226875777322124,
0.30066399411730993,
-0.39414909889357297,
-0.18124343335317938,
-0.4848477976901413,
0.3877583285769173,
0.172524254357997,
-0.018521150941710474,
-0.282499329256904,
0.33775832857691723,
-0.23610369359386674,
0.43885090110642677,
-0.5238713813050424,
0.22813038062505453,
0.055524254357997016,
-0.10000935913425923,
0.30301246255054615,
-0.10126525503798423,
-0.36759190178641576,
-0.018847797690141554,
-0.43066089070102365,
0.20552425435799737,
0.8676639941173101,
0.4592919420691728,
-0.605032942749161,
0.45678015026172236,
0.185246536769466,
-0.28626701696808077,
-0.3342652550379841,
1.0836639941173103,
0.05066399411730993,
-0.6418006304603372,
0.34815220230985844,
0.07143168182848703,
0.5800596297803495,
0.2481522023098588,
-1.076383173112493,
-0.3342652550379841,
-0.8898713813050425,
0.6707583285769174,
-0.4799875374494533,
-0.5124049947972984,
-0.19196395383455211,
0.3825714215878002,
0.7092919420691728,
-0.5235447345566118,
0.21875656664682097,
-0.12563730708612186,
-0.5423831731124933,
0.08524653676946614,
-0.35377704684543554,
0.6336639941173101,
0.06431552568407506,
-0.08484779769014139,
0.08115220230985898,
0.8531757859247615,
0.5096185888176032,
-0.5543595894975919,
0.44454783797289865,
-0.40252115094171037,
0.6336639941173101,
-0.15310369359386655,
-0.6361036935938666,
0.049990640865740676,
0.40803604616544753,
-0.39573164154572815,
0.22813038062505453,
0.013896306406133263,
-0.10252115094171055,
0.5481522023098586,
-0.6037770468454358,
0.9262919420691724,
-0.3787316415457287,
0.01666399411731012,
-0.018847797690141554,
-1.2056154854013172,
0.4166639941173096,
0.26699064086574076,
0.6420360461654475,
-0.5636608907010237,
0.022524254357996654,
-0.8751272772087679,
-0.26726525503798415,
0.5750360461654473,
0.17813038062505449,
0.4176639941173099,
-0.6287316415457282,
0.10124653676946616,
0.09689630640613345,
-1.1125683181715131,
0.5237801502617225,
0.0352465367694661,
0.03491989002103546,
0.4508273174915254,
0.35929194206917225,
0.26573474496201577,
-0.43501112106435524,
-0.2855211509417104,
0.27629194206917296,
-0.040381411182396576,
-0.06047574564200264,
-0.4598932029898477,
0.6849198900210349,
-0.0249639538345523,
0.016408098213584132,
0.058036046165447885,
0.24203604616544805,
0.49705962978034934,
0.44940809821358396,
0.6630596297803497,
0.2071067970101521,
-0.44698753744945385,
0.3096185888176035,
-0.4824993292569042,
-0.3268932029898477,
-0.3598932029898476,
0.3336639941173103,
-0.15059190178641568,
-0.6331726825084742,
0.35191989002103563,
0.669502432673192,
0.30301246255054615,
0.00945526544338815,
0.028640410502408287,
-0.4944757456420028,
-0.35377704684543554,
0.039524254357997,
-1.0600565263640624,
0.6275478379728985,
-0.009893202989847527,
0.046896306406133625,
-0.07982421407523832,
0.8531757859247615,
-0.6312434333531787,
-0.3592198497382775,
0.42143168182848667,
0.046896306406133625,
-0.36114909889357305,
0.1824080982135845,
0.742036046165448,
0.054268358454272025,
-0.6624049947972983,
-0.15310369359386655,
0.6050142244806427,
-0.41366089070102374,
0.9519198900210353,
-0.1348477976901412,
0.5451303806250545,
-0.5154993292569046,
0.21213038062505452,
0.7445478379728985
],
"weights": [
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0,
1.0
]
}