{"id":666,"date":"2023-07-29T03:58:36","date_gmt":"2023-07-29T03:58:36","guid":{"rendered":"https:\/\/statorials.org\/my\/durbin-watson-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af-r\/"},"modified":"2023-07-29T03:58:36","modified_gmt":"2023-07-29T03:58:36","slug":"durbin-watson-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/durbin-watson-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af-r\/","title":{"rendered":"R \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"},"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;\">\u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \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 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u104f \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a autocorrelation \u101b\u103e\u102d\u1014\u1031\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u101e\u102d\u101b\u103e\u102d\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/durbin-watson-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\" 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\u101b\u1014\u103a \u1016\u103c\u1005\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\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> (null hypothesis):<\/strong> \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \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> \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1021\u101b\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\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 R \u1016\u103c\u1004\u1037\u103a Durbin-Watson \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>\u1025\u1015\u1019\u102c- R \u1010\u103d\u1004\u103a Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c linear regression model \u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1015\u102b\u1019\u100a\u103a\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <strong>mtcars<\/strong> \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1011\u102c\u1038\u101e\u1031\u102c R \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u103c\u102e\u1038 \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a <strong>mpg \u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036 <strong>\u1014\u103e\u1004\u1037\u103a<\/strong> <strong>\u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b<\/strong> \u1016\u103c\u1005\u103a\u1005\u1031\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load mtcars dataset\n<\/span>data(mtcars)\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(mtcars)\n\n                   mpg cyl disp hp drat wt qsec vs am gear carb\nMazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4\nMazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4\nDatsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1\nHornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1\nHornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2\nValiant 18.1 6 225 105 2.76 3,460 20.22 1 0 3 1\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg ~ disp+wt, data=mtcars)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103b\u103a\u1019\u103e <strong>durbinWatsonTest()<\/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\u104d 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\u1031\u102c <strong>\u1000\u103c\u1031\u102c\u1004\u1037\u103a<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load car package\n<\/span>library(car)\n\n<span style=\"color: #008080;\">#perform Durbin-Watson test\n<\/span>durbinWatsonTest(model)\n\nLoading required package: carData\n lag Autocorrelation DW Statistic p-value\n   1 0.341622 1.276569 0.034\n Alternative hypothesis: rho != 0<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103e\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a <strong>1.276569<\/strong> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-value \u101e\u100a\u103a <strong>0.034<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \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 \u1024 regression model \u104f \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1021\u101b\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a autocorrelated \u1016\u103c\u1005\u103a\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<h3> <span style=\"color: #000000;\"><strong>autocorrelation \u1000\u102d\u102f\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u1000 \u1018\u102c\u101c\u102f\u1015\u103a\u101b\u1019\u101c\u1032<\/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","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 \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \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 \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u104f \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a autocorrelation \u101b\u103e\u102d\u1014\u1031\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u101e\u102d\u101b\u103e\u102d\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\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\u101b\u1014\u103a \u1016\u103c\u1005\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\u101e\u100a\u103a- H 0 (null hypothesis): \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \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)- \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1021\u101b\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u101c\u102d\u102f\u1021\u101c\u103b\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\u101e\u100a\u103a\u104b \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a R \u1016\u103c\u1004\u1037\u103a Durbin-Watson \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f 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