{"id":1637,"date":"2023-07-25T13:50:04","date_gmt":"2023-07-25T13:50:04","guid":{"rendered":"https:\/\/statorials.org\/my\/breusch-godfrey-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba-python\/"},"modified":"2023-07-25T13:50:04","modified_gmt":"2023-07-25T13:50:04","slug":"breusch-godfrey-%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-godfrey-%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-godfrey \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;\"><a href=\"https:\/\/statorials.org\/my\/linear-regression-\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">linear regression \u104f \u1021\u1013\u102d\u1000 \u101a\u1030\u1006\u1001\u103b\u1000\u103a<\/a> \u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f \u1019\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1021\u1019\u103e\u102c\u1005\u102c autocorrelation \u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/durbin-watson-\u1005\u1019\u103a\u1038\u101e\u1015\u103a-python\/\" target=\"_blank\" rel=\"noopener\">Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/a> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c\u1021\u1019\u103e\u102c\u1005\u102c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a autocorrelation \u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101c\u102d\u102f\u1015\u102b\u1000 <strong>Breusch-Godfrey \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b <a href=\"https:\/\/statorials.org\/my\/\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038-\u1041\/\" target=\"_blank\" rel=\"noopener\">\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> (null hypothesis)-<\/strong> <em>p<\/em> \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c \u1021\u1019\u103e\u102c\u1005\u102c\u104f \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f \u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> (\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u101a\u1030\u1006\u1001\u103b\u1000\u103a)-<\/strong> <em>p<\/em> \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1021\u1019\u103e\u102c\u1005\u102c\u104f \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <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 \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f <em>p<\/em> \u1012\u102e\u1002\u101b\u102e\u1016\u103c\u1004\u1037\u103a Chi-square \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101e\u1031\u102c <a href=\"https:\/\/statorials.org\/my\/p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a-\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c-\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b\/\" target=\"_blank\" rel=\"noopener\">p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/a> \u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a (\u1025\u1015\u1019\u102c- 0.05) \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1014\u102d\u1019\u1037\u103a\u101e\u1031\u102c\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u1010\u103d\u1004\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a <em>p<\/em> \u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c autocorrelation \u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Python \u101b\u103e\u102d Breusch-Godfrey \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\u104a \u101e\u1004\u103a\u101e\u100a\u103a <b>statsmodels<\/b> \u1005\u102c\u1000\u103c\u100a\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1019\u103e <strong>acorr_breusch_godfrey()<\/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\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u101e\u100a\u103a Python \u101b\u103e\u102d Breusch-Godfrey \u1005\u1019\u103a\u1038\u101e\u1015\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\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1026\u1038\u1005\u103d\u102c\u104a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f (x1 \u1014\u103e\u1004\u1037\u103a x2) \u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a (y) \u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\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: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd<\/span>\n\n#create dataset<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">x1<\/span> ': [3, 4, 4, 5, 8, 9, 11, 13, 14, 16, 17, 20],\n                   ' <span style=\"color: #ff0000;\">x2<\/span> ': [7, 7, 8, 8, 12, 4, 5, 15, 9, 17, 19, 19],\n                    ' <span style=\"color: #ff0000;\">y<\/span> ': [24, 25, 25, 27, 29, 31, 34, 34, 39, 30, 40, 49]})\n\n<span style=\"color: #008080;\">#view first five rows of dataset\n<\/span>df. <span style=\"color: #3366ff;\">head<\/span> ()\n\n\tx1 x2 y\n0 3 7 24\n1 4 7 25\n2 4 8 25\n3 5 8 27\n4 8 12 29\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \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\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1000\u103c\u102d\u102f\u1010\u1004\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 y <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\">\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/a> \u1021\u1016\u103c\u1005\u103a x1 \u1014\u103e\u1004\u1037\u103a x2 \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d <a href=\"https:\/\/statorials.org\/my\/multiple-linear-regression\/\" target=\"_blank\" rel=\"noopener\">\u1019\u103b\u102c\u1038\u1005\u103d\u102c\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<\/a> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1005\u1031\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/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 response variable\n<\/span>y = df[' <span style=\"color: #ff0000;\">y<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variables\n<\/span>x = df[[' <span style=\"color: #ff0000;\">x1<\/span> ', ' <span style=\"color: #ff0000;\">x2<\/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<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- Breusch-Godfrey \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><\/h3>\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 \u1021\u1019\u103e\u102c\u1005\u102c <em>p<\/em> \u1010\u103d\u1004\u103a \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1021\u101b\u102c\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1031\u102c\u103a\u1010\u102d\u102f\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a Breusch-Godfrey \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 \u1012\u102e\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a <em>p<\/em> =3 \u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1015\u102b\u1019\u101a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">stats<\/span> . <span style=\"color: #3366ff;\">diagnosis<\/span> <span style=\"color: #008000;\">as<\/span> dg\n<\/span>\n#perform Breusch-Godfrey test at order <em>p<\/em> = 3\n<span style=\"color: #000000;\"><span style=\"color: #993300;\">print<\/span> (dg. <span style=\"color: #3366ff;\">acorr_breusch_godfrey<\/span> (model, nlags= <span style=\"color: #008000;\">3<\/span> ))\n\n(8.70314827, 0.0335094873, 5.27967224, 0.0403980576)\n<\/span><\/span><\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u1021\u1011\u103d\u1000\u103a\u104f \u1015\u1011\u1019\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u1015\u103c\u102e\u1038 \u1012\u102f\u1010\u102d\u101a\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103e \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1019\u103c\u1004\u103a\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\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038 X <sup>2<\/sup> = <strong>8.7031<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">P-value = <strong>0.0335<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024 p-value \u101e\u100a\u103a 0.05 \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 3 \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c \u1021\u1019\u103e\u102c\u1005\u102c\u104f\u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103b\u1014\u103a\u101b\u103e\u102d\u1015\u1005\u1039\u1005\u100a\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1014\u1031\u101e\u100a\u103a\u101f\u102f \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>autocorrelation \u1000\u102d\u102f \u1018\u101a\u103a\u101c\u102d\u102f\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1019\u101c\u1032\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u101a\u103a\u104d \u101e\u1004\u103a\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u103c\u102e\u1038 \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c autocorrelation \u1010\u103d\u1004\u103a autocorrelation \u101b\u103e\u102d\u1014\u1031\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u1000\u102d\u102f \u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u101e\u100a\u103a\u101f\u102f \u101e\u1004\u103a\u101a\u1030\u1006\u1015\u102b\u1000 \u1024\u1015\u103c\u103f\u1014\u102c\u1000\u102d\u102f \u1015\u103c\u1004\u103a\u101b\u1014\u103a \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1005\u101b\u102c\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul data-slot-rendered-dynamic=\"true\">\n<li> <span style=\"color: #000000;\">\u1021\u1015\u103c\u102f\u101e\u1018\u1031\u102c\u1006\u1031\u102c\u1004\u103a\u101e\u1031\u102c \u1021\u1019\u103e\u1010\u103a\u1005\u1009\u103a\u1006\u1000\u103a\u1014\u103d\u103e\u101a\u103a\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u102d\u102f\u1037 \u1019\u103e\u102e\u1001\u102d\u102f\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a\/\u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f \u1014\u1031\u102c\u1000\u103a\u1000\u103b\u1000\u103b\u1014\u103a\u1014\u1031\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u1015\u102b\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1021\u1014\u103e\u102f\u1010\u103a\u1021\u1019\u103e\u1010\u103a\u1005\u1009\u103a\u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a\u104a \u101e\u1004\u1037\u103a variable \u1019\u103b\u102c\u1038\u1011\u1032\u1019\u103e \u1010\u1005\u103a\u1001\u102f\u1019\u103b\u103e <em>\u1014\u103e\u1031\u102c\u1004\u1037\u103a\u1014\u103e\u1031\u1038\u1014\u1031\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038<\/em> \u101e\u1031\u1001\u103b\u102c\u1015\u102b\u1005\u1031\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u101b\u102c\u101e\u102e\u1021\u101c\u102d\u102f\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a\u104a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u102d\u102f\u1037 \u101b\u102c\u101e\u102e\u1021\u101c\u102d\u102f\u1000\u103a\u1021\u101b\u102f\u1015\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u100a\u1037\u103a\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u1015\u102b\u104b<\/span><\/li>\n<\/ul>\n<h3> <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><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/my\/linear-regression-python\/\" target=\"_blank\" rel=\"noopener\">Python \u101b\u103e\u102d Linear Regression \u1021\u1010\u103d\u1000\u103a \u1015\u103c\u102e\u1038\u1015\u103c\u100a\u1037\u103a\u1005\u102f\u1036\u101e\u1031\u102c \u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/durbin-watson-\u1005\u1019\u103a\u1038\u101e\u1015\u103a-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/ljung-box-\u1005\u1019\u103a\u1038\u101e\u1015\u103a-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a Ljung-Box \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>linear regression \u104f \u1021\u1013\u102d\u1000 \u101a\u1030\u1006\u1001\u103b\u1000\u103a \u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038 \u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f \u1019\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038 \u1016\u103c\u1005\u103a\u101e\u100a\u103a \u104b \u1015\u1011\u1019\u1021\u1019\u103e\u102c\u1005\u102c autocorrelation \u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c\u1021\u1019\u103e\u102c\u1005\u102c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a autocorrelation \u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101c\u102d\u102f\u1015\u102b\u1000 Breusch-Godfrey \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\u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104b \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b H 0 (null hypothesis)- p \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c \u1021\u1019\u103e\u102c\u1005\u102c\u104f \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f \u1019\u101b\u103e\u102d\u1015\u102b\u104b H A (\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u101a\u1030\u1006\u1001\u103b\u1000\u103a)- p \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1021\u1019\u103e\u102c\u1005\u102c\u104f [&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 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