{"id":3813,"date":"2023-07-15T09:50:14","date_gmt":"2023-07-15T09:50:14","guid":{"rendered":"https:\/\/statorials.org\/my\/goldfeld-%e1%80%9e%e1%80%8a%e1%80%ba-python-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%b7%e1%80%ba%e1%80%a1%e1%80%81%e1%80%ab\/"},"modified":"2023-07-15T09:50:14","modified_gmt":"2023-07-15T09:50:14","slug":"goldfeld-%e1%80%9e%e1%80%8a%e1%80%ba-python-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%b7%e1%80%ba%e1%80%a1%e1%80%81%e1%80%ab","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/goldfeld-%e1%80%9e%e1%80%8a%e1%80%ba-python-%e1%80%80%e1%80%ad%e1%80%af%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%9e%e1%80%8a%e1%80%b7%e1%80%ba%e1%80%a1%e1%80%81%e1%80%ab\/","title":{"rendered":"Python \u101b\u103e\u102d goldfeld-quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong> \u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u103d\u1004\u103a <a href=\"https:\/\/statorials.org\/my\/heteroscedasticity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">heteroskedasticity<\/a> \u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Heteroscedasticity \u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f <a href=\"https:\/\/statorials.org\/my\/\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c-\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a-\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f<\/a> \u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u104f \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a <a href=\"https:\/\/statorials.org\/my\/\u1021\u1000\u103c\u103d\u1004\u103a\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038<\/a> \u1019\u100a\u102e\u1019\u103b\u103e\u1005\u103d\u102c \u1015\u103b\u1036\u1037\u1014\u103e\u1036\u1037\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<\/span><\/p>\n<p> <span style=\"color: #000000;\">heteroskedasticity \u101b\u103e\u102d\u1014\u1031\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1021\u100a\u102e\u1021\u1019\u103b\u103e \u1001\u103d\u1032\u101d\u1031\u1015\u1031\u1038\u101e\u100a\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/linear-regression-\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u104f \u1021\u1013\u102d\u1000 \u101a\u1030\u1006\u1001\u103b\u1000\u103a<\/a> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1001\u103b\u102d\u102f\u1038\u1016\u1031\u102c\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a Python \u101b\u103e\u102d Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102f\u1036\u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a\u104a \u1021\u1010\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u1014\u103a\u1038\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1041\u1043 \u1026\u1038\u1019\u103e\u101b\u101b\u103e\u102d\u101e\u1031\u102c \u1014\u102c\u101b\u102e\u1019\u103b\u102c\u1038\u104a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1015\u103c\u1004\u103a\u1006\u1004\u103a\u1019\u103e\u102f\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u1014\u103a\u1012\u102b DataFrame \u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6],\n                   ' <span style=\"color: #ff0000;\">exams<\/span> ': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours exam score\n0 1 1 76\n1 2 3 78\n2 2 3 85\n3 4 5 88\n4 2 2 72\n5 1 2 69\n6 5 1 94\n7 4 1 94\n8 2 0 88\n9 4 3 92\n10 4 4 90\n11 3 3 75\n12 6 2 96<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- linear regression model \u1000\u102d\u102f \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/h2>\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 \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1016\u103c\u1005\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a <strong>\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a<\/strong> <strong>\u1014\u102c\u101b\u102e\u1019\u103b\u102c\u1038<\/strong> \u1014\u103e\u1004\u1037\u103a <strong>\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1015\u102b\u1019\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define predictor and response variables\n<\/span>y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[[' <span style=\"color: #ff0000;\">hours<\/span> ', ' <span style=\"color: #ff0000;\">exams<\/span> ']]\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n\n<span style=\"color: #008080;\">#view model summary\n<\/span><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.718\nModel: OLS Adj. R-squared: 0.661\nMethod: Least Squares F-statistic: 12.70\nDate: Mon, 31 Oct 2022 Prob (F-statistic): 0.00180\nTime: 09:22:56 Log-Likelihood: -38.618\nNo. Observations: 13 AIC: 83.24\nDf Residuals: 10 BIC: 84.93\nModel: 2                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 71.4048 4.001 17.847 0.000 62.490 80.319\nhours 5.1275 1.018 5.038 0.001 2.860 7.395\nexams -1.2121 1.147 -1.057 0.315 -3.768 1.344\n==================================================== ============================\nOmnibus: 1,103 Durbin-Watson: 1,248\nProb(Omnibus): 0.576 Jarque-Bera (JB): 0.803\nSkew: -0.289 Prob(JB): 0.669\nKurtosis: 1.928 Cond. No. 11.7\n==================================================== ============================\n<\/strong><\/span><\/pre>\n<h2> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3: Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a <strong>statsmodels<\/strong> <strong>het_goldfeldquandt()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a<\/strong> &#8211; Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u104f \u1021\u101c\u101a\u103a\u1017\u101f\u102d\u102f\u1010\u103d\u1004\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1030\u1038\u1005\u1019\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1021\u1015\u103c\u102c\u1038\u1000\u102d\u102f \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1015\u103c\u102e\u1038 \u1000\u103b\u1014\u103a\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u1000\u103b\u1000\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1017\u101f\u102d\u102f\u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u104f \u1018\u1031\u1038\u1010\u1005\u103a\u1016\u1000\u103a\u1005\u102e\u1010\u103d\u1004\u103a \u1001\u103b\u102d\u1010\u103a\u1006\u1000\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u101b\u101c\u1012\u103a\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1014\u103e\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1016\u103c\u1004\u1037\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u104f 20% \u1001\u1014\u1037\u103a\u1000\u102d\u102f \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u101b\u1014\u103a \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u104f 20% \u1000\u102d\u102f \u1016\u101a\u103a\u101b\u103e\u102c\u1038\u101c\u102d\u102f\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a <strong>drop<\/strong> argument \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Goldfeld-Quandt test\n<\/span>sm. <span style=\"color: #3366ff;\">stats<\/span> . <span style=\"color: #3366ff;\">diagnosis<\/span> . <span style=\"color: #3366ff;\">het_goldfeldquandt<\/span> (y, x, drop= <span style=\"color: #008000;\">0.2<\/span> )\n\n(1.7574505407790355, 0.38270288684680076, 'increasing')<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a <b>1,757<\/b> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-value \u101e\u100a\u103a <strong>0.383<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\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 \u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Null (H <sub>0<\/sub> )<\/strong> : Homoskedasticity \u101b\u103e\u102d\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038 ( <sub>HA<\/sub> ):<\/strong> Heteroskedasticity \u101b\u103e\u102d\u1014\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">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<\/span><\/p>\n<p> <span style=\"color: #000000;\">heteroskedasticity \u101e\u100a\u103a regression model \u1010\u103d\u1004\u103a \u1015\u103c\u103f\u1014\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1031\u102c\u1012\u1000\u1010\u1000\u103a\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> <strong>\u1018\u102c\u1006\u1000\u103a\u101c\u102f\u1015\u103a\u101b\u1019\u101c\u1032<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f null hypothesis \u1000\u102d\u102f \u101e\u1004\u103a \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u1000\u104a heteroscedasticity \u101e\u100a\u103a \u1019\u101b\u103e\u102d\u1014\u102d\u102f\u1004\u103a\u1018\u1032 \u1019\u1030\u101c\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u104f \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u101e\u1004\u103a \u1006\u1000\u103a\u101c\u1000\u103a \u1021\u1014\u1000\u103a\u1016\u103d\u1004\u1037\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u102b\u1000\u104a heteroskedasticity \u101e\u100a\u103a data \u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a regression output table \u1010\u103d\u1004\u103a\u1015\u103c\u101e\u1011\u102c\u1038\u101e\u1031\u102c standard errors \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1005\u102d\u1010\u103a\u1001\u103b\u101b\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1015\u103c\u103f\u1014\u102c\u1000\u102d\u102f \u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u101b\u1014\u103a \u1018\u102f\u1036\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1005\u103d\u102c \u1021\u1015\u102b\u1021\u101d\u1004\u103a\u104a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\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><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u103d\u1004\u103a\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104a \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a <a href=\"https:\/\/statorials.org\/my\/python-\u1010\u103d\u1004\u103a-data-\u1000\u102d\u102f\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u104b\/\" target=\"_blank\" rel=\"noopener\">\u104f \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u104a \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u101b\u1010\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a cube \u1021\u1019\u103c\u1005\u103a\u1000\u102d\u102f<\/a> \u101b\u101a\u1030\u1015\u102b\u104b \u101a\u1031\u1018\u1030\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101c\u102d\u102f\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u1015\u103b\u1031\u102c\u1000\u103a\u1005\u1031\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \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><\/span><\/p>\n<p> <span style=\"color: #000000;\">Weighted regression \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\u1000\u102d\u102f \u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1012\u1031\u1010\u102c\u1021\u1019\u103e\u1010\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u102d\u102f\u1037 \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b \u1021\u1001\u103c\u1031\u1001\u1036\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1015\u103c\u102e\u1038 \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u102d\u1019\u1037\u103a\u1005\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u101e\u1031\u102c\u1021\u101c\u1031\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1015\u103c\u1014\u103a\u1006\u102f\u1010\u103a\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a heteroskedasticity \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<h2> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a Python \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1018\u102f\u1036\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/ols-regression-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/python-\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1002\u101b\u1015\u103a\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a Residual Plot \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/python-\u1010\u103d\u1004\u103a-\u1021\u1016\u103c\u1030\u101b\u1031\u102c\u1004\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\">Python \u1010\u103d\u1004\u103a White&#8217;s Test \u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/breusch-\u1021\u101a\u1030\u1019\u103e\u102c\u1038\u1005\u1019\u103a\u1038\u101e\u1015\u103a-python\/\" target=\"_blank\" rel=\"noopener\">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<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Goldfeld-Quandt \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u103d\u1004\u103a heteroskedasticity \u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b Heteroscedasticity \u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f \u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u104f \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1019\u100a\u102e\u1019\u103b\u103e\u1005\u103d\u102c \u1015\u103b\u1036\u1037\u1014\u103e\u1036\u1037\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 heteroskedasticity \u101b\u103e\u102d\u1014\u1031\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1021\u100a\u102e\u1021\u1019\u103b\u103e 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