{"id":867,"date":"2023-07-28T11:57:38","date_gmt":"2023-07-28T11:57:38","guid":{"rendered":"https:\/\/statorials.org\/my\/breusch-%e1%80%a1%e1%80%9a%e1%80%b0%e1%80%99%e1%80%be%e1%80%ac%e1%80%b8%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python\/"},"modified":"2023-07-28T11:57:38","modified_gmt":"2023-07-28T11:57:38","slug":"breusch-%e1%80%a1%e1%80%9a%e1%80%b0%e1%80%99%e1%80%be%e1%80%ac%e1%80%b8%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/breusch-%e1%80%a1%e1%80%9a%e1%80%b0%e1%80%99%e1%80%be%e1%80%ac%e1%80%b8%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a breusch-pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a\u104a <a href=\"https:\/\/statorials.org\/my\/heteroscedasticity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">heteroskedasticity \u101e\u100a\u103a<\/a> \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1019\u100a\u102e\u1019\u100a\u102c \u1000\u103d\u1032\u1011\u103d\u1000\u103a\u101e\u103d\u102c\u1038\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u101e\u100a\u103a\u104b \u1015\u102d\u102f\u104d\u1010\u102d\u1000\u103b\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u104f \u1021\u1000\u103d\u102c\u1021\u101d\u1031\u1038\u1011\u1000\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u102c\u1010\u103d\u1004\u103a \u1005\u1014\u1005\u103a\u1010\u1000\u103b \u1021\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1021\u101c\u1032\u101b\u103e\u102d\u1014\u1031\u101e\u100a\u1037\u103a \u1000\u102d\u1005\u1039\u1005\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Heteroscedasticity \u101e\u100a\u103a \u101e\u102c\u1019\u102c\u1014\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1015\u102f\u1036\u1019\u103b\u102c\u1038 (OLS) \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u101e\u100a\u103a \u1000\u103b\u1014\u103a\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a <em>\u1019\u103b\u102d\u102f\u1038\u1010\u1030\u101b\u102d\u102f\u1038\u1000\u103b<\/em> \u1016\u103c\u1005\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103e \u1006\u1004\u103a\u1038\u101e\u1000\u103a\u101c\u102c\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1021\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101f\u102f \u1006\u102d\u102f\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1019\u103b\u102d\u102f\u1038\u1000\u103d\u1032\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u1014\u1031\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u104f \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u101b\u1014\u103a \u1001\u1000\u103a\u1001\u1032\u101c\u102c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/linear-regression-python\/\" target=\"_blank\" rel=\"noopener\">\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a<\/a> heteroskedasticity \u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c <a href=\"https:\/\/statorials.org\/my\/pagan-breusch-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a <strong>\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u101b\u103e\u102d Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1018\u1010\u103a\u1005\u1000\u1000\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 10 \u1026\u1038\u104f \u1021\u101b\u100a\u103a\u1021\u1001\u103b\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> pandas <span style=\"color: #107d3f;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#create dataset<\/span>\ndf = pd.DataFrame({'rating': [90, 85, 82, 88, 94, 90, 76, 75, 87, 86],\n                   'points': [25, 20, 14, 16, 27, 20, 12, 15, 14, 19],\n                   'assists': [5, 7, 7, 8, 5, 7, 6, 9, 9, 5],\n                   'rebounds': [11, 8, 10, 6, 6, 9, 6, 10, 10, 7]})\n\n<span style=\"color: #008080;\">#view dataset\n<\/span>df\n\n\trating points assists rebounds\n0 90 25 5 11\n1 85 20 7 8\n2 82 14 7 10\n3 88 16 8 6\n4 94 27 5 6\n5 90 20 7 9\n6 76 12 6 6\n7 75 15 9 10\n8 87 14 9 10\n9 86 19 5 7<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a \u1021\u1019\u103e\u1010\u103a\u1015\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u104a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u103c\u1014\u103a\u101c\u100a\u103a\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a \u1021\u1019\u103e\u1010\u103a\u1015\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036\u101e\u1031\u102c\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101c\u102f\u1015\u103a\u1015\u102b\u1019\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u103d\u1004\u103a heteroskedasticity \u101b\u103e\u102d\u1014\u1031\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1- \u1019\u103b\u1009\u103a\u1038\u1016\u103c\u1031\u102c\u1004\u1037\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1015\u102f\u1036\u1005\u1036\u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036\u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a multiple linear regression model \u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1019\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> statsmodels.formula.api <span style=\"color: #107d3f;\">as<\/span> smf\n\n<span style=\"color: #008080;\">#fit regression model<\/span>\nfit = smf.ols('rating ~ points+assists+rebounds', data=df). <span style=\"color: #008000;\">fit<\/span> ()\n\n<span style=\"color: #008080;\">#view model summary\n<\/span><span style=\"color: #008000;\">print<\/span> (fit.summary())\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101c\u102d\u102f\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">from<\/span> statsmodels.compat <span style=\"color: #107d3f;\">import<\/span> lzip\n<span style=\"color: #107d3f;\">import<\/span> statsmodels.stats.api <span style=\"color: #107d3f;\">as<\/span> sms\n\n<span style=\"color: #008080;\">#perform Bresuch-Pagan test<\/span>\nnames = ['Lagrange multiplier statistic', 'p-value',\n        'f-value', 'f p-value']\ntest = sms.het_breuschpagan(fit.resid, fit.model.exog)\n\nlzip(names, test)\n\n[('Lagrange multiply statistic', 6.003951995818433),\n ('p-value', 0.11141811013399583),\n ('f-value', 3.004944880309618),\n ('f p-value', 0.11663863538255281)]<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b null \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1021\u101a\u1030\u1021\u1006\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>null hypothesis (H <sub>0<\/sub> ):<\/strong> Homoscedasticity \u101b\u103e\u102d\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u101a\u1030\u1006\u1001\u103b\u1000\u103a- (\u101f\u102c)-<\/strong> \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u1017\u102e\u1007\u101b\u103e\u102d\u1001\u103c\u1004\u103a\u1038 <em>\u1019\u101b\u103e\u102d\u1015\u102b<\/em> (\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101c\u102d\u102f\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1001\u103c\u1004\u103a\u1038)\u104a<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a Lagrange \u1019\u103c\u103e\u1031\u102c\u1000\u103a\u1000\u102d\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a <strong>6.004<\/strong> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a <strong>0.1114<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024 p-value \u101e\u100a\u103a 0.05 \u1011\u1000\u103a\u1019\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u103d\u1004\u103a \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101c\u102d\u102f\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u103b\u102d\u102f\u1038 \u101b\u103e\u102d\u1014\u1031\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1001\u102d\u102f\u1004\u103a\u1021\u1019\u102c\u1006\u102d\u102f\u101b\u1014\u103a \u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u101e\u1031\u102c \u1021\u1011\u1031\u102c\u1000\u103a\u1021\u1011\u102c\u1038 \u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Heteroscedasticity \u1000\u102d\u102f \u1018\u101a\u103a\u101c\u102d\u102f\u1015\u103c\u1004\u103a\u1019\u101c\u1032\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u101a\u1001\u1004\u103a\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a\u104a regression model \u1010\u103d\u1004\u103a heteroscedasticity \u1019\u1015\u102b\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1001\u1032\u1037\u101b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1019\u103b\u102d\u102f\u1038\u1000\u103d\u1032\u1021\u1019\u103e\u1014\u103a\u1010\u1000\u101a\u103a\u101b\u103e\u102d\u1014\u1031\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1000\u102d\u102f \u1000\u102f\u1005\u102c\u1038\u101b\u1014\u103a \u1018\u102f\u1036\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> <strong>\u1019\u103e\u102e\u1001\u102d\u102f\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1015\u102b\u104b<\/strong> heteroskedasticity \u1021\u1010\u103d\u1000\u103a \u1015\u103c\u102f\u1015\u103c\u1004\u103a\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1019\u103e\u102e\u1001\u102d\u102f variable \u1000\u102d\u102f \u1010\u1005\u103a\u1014\u100a\u103a\u1038\u1014\u100a\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u101b\u1014\u103a \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u1030\u101a\u103b\u1021\u101e\u103d\u1004\u103a\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103e\u102e\u1001\u102d\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1000\u102d\u102f \u101b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101b\u103e\u1004\u103a\u1038\u101a\u1030\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u1019\u103e\u102e\u1001\u102d\u102f\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u101c\u100a\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/strong> heteroscedasticity \u1000\u102d\u102f \u1015\u103c\u102f\u1015\u103c\u1004\u103a\u101b\u1014\u103a \u1021\u1001\u103c\u102c\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103e\u102c \u1019\u103e\u102e\u1001\u102d\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u101c\u100a\u103a\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u1000\u102d\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u1014\u103a \u1018\u102f\u1036\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103e\u102c \u1000\u102f\u1014\u103a\u1000\u103c\u1019\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1011\u1000\u103a \u1019\u103e\u102e\u1001\u102d\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1010\u103d\u1000\u103a <em>\u1014\u103e\u102f\u1014\u103a\u1038\u1011\u102c\u1038\u1000\u102d\u102f<\/em> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/strong> \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101c\u102d\u102f\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103c\u102f\u1015\u103c\u1004\u103a\u101b\u1014\u103a \u1014\u1031\u102c\u1000\u103a\u1010\u1005\u103a\u1014\u100a\u103a\u1038\u1019\u103e\u102c \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u101e\u100a\u103a \u104e\u1004\u103a\u1038\u104f\u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u104f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1012\u1031\u1010\u102c\u1021\u1019\u103e\u1010\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u102c\u1038 \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1015\u1031\u1038\u101e\u100a\u103a\u104b \u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u101e\u1031\u102c\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u1000\u103d\u1032\u1001\u103c\u1004\u103a\u1038\u1015\u103c\u103f\u1014\u102c\u1000\u102d\u102f \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1015\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/heteroscedasticity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1024\u1006\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u1038\u1010\u103d\u1004\u103a<\/a> \u1024\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u1021\u1014\u1000\u103a \u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u101e\u1031\u1038\u1005\u102d\u1010\u103a\u1000\u102d\u102f \u1006\u1000\u103a\u101c\u1000\u103a\u1016\u1010\u103a\u101b\u103e\u102f\u1015\u102b\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a\u104a heteroskedasticity \u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1019\u100a\u102e\u1019\u100a\u102c \u1000\u103d\u1032\u1011\u103d\u1000\u103a\u101e\u103d\u102c\u1038\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u101e\u100a\u103a\u104b \u1015\u102d\u102f\u104d\u1010\u102d\u1000\u103b\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u104f \u1021\u1000\u103d\u102c\u1021\u101d\u1031\u1038\u1011\u1000\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u102c\u1010\u103d\u1004\u103a \u1005\u1014\u1005\u103a\u1010\u1000\u103b \u1021\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1021\u101c\u1032\u101b\u103e\u102d\u1014\u1031\u101e\u100a\u1037\u103a \u1000\u102d\u1005\u1039\u1005\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b Heteroscedasticity \u101e\u100a\u103a \u101e\u102c\u1019\u102c\u1014\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1015\u102f\u1036\u1019\u103b\u102c\u1038 (OLS) \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u101e\u100a\u103a \u1000\u103b\u1014\u103a\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u1010\u1030\u101b\u102d\u102f\u1038\u1000\u103b \u1016\u103c\u1005\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103e \u1006\u1004\u103a\u1038\u101e\u1000\u103a\u101c\u102c\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1021\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101f\u102f \u1006\u102d\u102f\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1019\u103b\u102d\u102f\u1038\u1000\u103d\u1032\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u1014\u1031\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u104f \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u101b\u1014\u103a \u1001\u1000\u103a\u1001\u1032\u101c\u102c\u101e\u100a\u103a\u104b \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a heteroskedasticity \u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a \u104b \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u101b\u103e\u102d Breusch-Pagan \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python - Statorials \u1010\u103d\u1004\u103a Breusch-Pagan 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