{"id":3469,"date":"2023-07-17T07:59:02","date_gmt":"2023-07-17T07:59:02","guid":{"rendered":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-ols-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/"},"modified":"2023-07-17T07:59:02","modified_gmt":"2023-07-17T07:59:02","slug":"r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-ols-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-ols-%e1%80%86%e1%80%af%e1%80%90%e1%80%ba%e1%80%9a%e1%80%af%e1%80%90%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/","title":{"rendered":"R \u1010\u103d\u1004\u103a ols regression \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 (\u1025\u1015\u1019\u102c\u1016\u103c\u1004\u1037\u103a)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u101e\u102c\u1019\u1014\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1019\u103b\u102c\u1038 (OLS) \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \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\u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a <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> \u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a \u1019\u103b\u1009\u103a\u1038\u1010\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101e\u100a\u1037\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u101b\u103e\u102c\u1016\u103d\u1031\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0177 = b <sub>0<\/sub> + b <sub>1<\/sub> x<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0177<\/strong> : \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>0<\/sub><\/strong> : \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u104f \u1019\u1030\u101c\u1021\u1005<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>1<\/sub><\/strong> : \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u104f \u101c\u103b\u103e\u1031\u102c\u1005\u1031\u102c\u1000\u103a<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\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\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \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\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101b\u1014\u103a \u104e\u1004\u103a\u1038\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 R \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\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><b>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/b><\/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 \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 15 \u1026\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b variable \u1014\u103e\u1005\u103a\u1001\u102f\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\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1001\u1032\u1037\u101e\u100a\u1037\u103a \u1014\u102c\u101b\u102e\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a<\/span><\/li>\n<\/ul>\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\u1021\u1016\u103c\u1005\u103a \u1014\u102c\u101b\u102e\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1015\u1031\u1038\u101e\u100a\u1037\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\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;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1024\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1021\u1010\u102f\u1000\u102d\u102f R \u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1016\u1014\u103a\u1010\u102e\u1038\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create dataset<\/span>\ndf &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (hours=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14),\n                 score=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89))\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(df)\n\n  hours score\n1 1 64\n2 2 66\n3 4 76\n4 5 73\n5 5 74\n6 6 81\n<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><b>\u1021\u1006\u1004\u1037\u103a 2- \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\">OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u102e \u1014\u102c\u101b\u102e\u1014\u103e\u1004\u1037\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1021\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u1005\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: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (ggplot2)\n\n<span style=\"color: #008080;\">#create scatterplot\n<\/span>ggplot(df, aes(x=hours, y=score)) +\n  geom_point(size= <span style=\"color: #008000;\">2<\/span> )\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28969 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/vieux1.jpg\" alt=\"\" width=\"486\" height=\"410\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">linear regression \u104f <a href=\"https:\/\/statorials.org\/my\/linear-regression-\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u101c\u1031\u1038\u1001\u102f<\/a> \u1021\u1014\u1000\u103a\u1019\u103e \u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1014\u103e\u1004\u1037\u103a response variable \u1021\u1000\u103c\u102c\u1038 linear \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f \u101b\u103e\u102d\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1002\u101b\u1015\u103a\u1019\u103e \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103b\u1009\u103a\u1038\u101e\u102c\u1038\u1015\u102f\u1036\u1015\u1031\u102b\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1014\u102c\u101b\u102e\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u101c\u102c\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1021\u1019\u103b\u103e \u101b\u1019\u103e\u1010\u103a\u101e\u100a\u103a\u101c\u100a\u103a\u1038 \u1019\u103b\u1009\u103a\u1038\u1016\u103c\u1031\u102c\u1004\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u102d\u102f\u1038\u101c\u102c\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u102c\u101f\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a boxplot \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a<\/strong> &#8211; R \u101e\u100a\u103a \u1010\u1010\u102d\u101a quartile \u1011\u1000\u103a 1.5 \u1006 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1015\u1011\u1019 quartile \u1021\u1031\u102c\u1000\u103a\u101b\u103e\u102d interquartile \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u1001\u103c\u102c\u1038 1.5 \u1006 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1000\u103d\u102c\u1010\u102c\u1038\u1021\u1000\u103d\u102c\u1021\u101d\u1031\u1038\u104f 1.5 \u1006 \u1016\u103c\u1005\u103a\u1015\u102b\u1000 \u1005\u1031\u102c\u1004\u1037\u103a\u1000\u103c\u100a\u1037\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u1000\u103c\u1019\u103a\u1038\u1016\u103b\u1004\u103a\u1038\u1021\u1016\u103c\u1005\u103a \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u1010\u102d\u1015\u103c\u102f\u1005\u101b\u102c\u1010\u1005\u103a\u1001\u102f\u1000 \u1015\u102d\u102f\u101e\u102c\u101c\u103d\u1014\u103a\u1015\u102b\u1000\u104a \u1000\u103d\u1000\u103a\u101c\u1015\u103a\u1010\u103d\u1004\u103a \u1005\u1000\u103a\u101d\u102d\u102f\u1004\u103a\u1038\u1004\u101a\u103a\u1010\u1005\u103a\u1001\u102f \u1015\u1031\u102b\u103a\u101c\u102c\u1015\u102b\u1019\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (ggplot2)\n\n<span style=\"color: #008080;\">#create scatterplot\n<\/span>ggplot(df, aes(y=score)) +\n  geom_boxplot()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28970 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/vieux2.jpg\" alt=\"\" width=\"333\" height=\"384\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">boxplot \u1010\u103d\u1004\u103a \u1005\u1000\u103a\u101d\u102d\u102f\u1004\u103a\u1038\u1004\u101a\u103a\u1019\u103b\u102c\u1038\u1019\u101b\u103e\u102d\u1015\u102b\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u1021\u1005\u103d\u1014\u103a\u1038\u1011\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><b>\u1021\u1006\u1004\u1037\u103a 3- OLS Regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><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 R \u1010\u103d\u1004\u103a <strong>lm()<\/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\u103c\u102e\u1038 OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \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\u1021\u1016\u103c\u1005\u103a \u1014\u102c\u101b\u102e\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\u1021\u1016\u103c\u1005\u103a \u101b\u1019\u103e\u1010\u103a\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit simple linear regression model\n<\/span>model &lt;- lm(score~hours, data=df)\n\n<span style=\"color: #008080;\">#view model summary<\/span>\nsummary(model)\n\nCall:\nlm(formula = score ~ hours)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-5,140 -3,219 -1,193 2,816 5,772 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 65,334 2,106 31,023 1.41e-13 ***\nhours 1.982 0.248 7.995 2.25e-06 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.641 on 13 degrees of freedom\nMultiple R-squared: 0.831, Adjusted R-squared: 0.818 \nF-statistic: 63.91 on 1 and 13 DF, p-value: 2.253e-06\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1019\u103e\u104a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1019\u103e\u102c-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101b\u1019\u103e\u1010\u103a = 65.334 + 1.982*(\u1014\u102c\u101b\u102e)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u101e\u1031\u102c \u1014\u102c\u101b\u102e\u1010\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a <strong>1,982<\/strong> \u1019\u103e\u1010\u103a \u1010\u102d\u102f\u1038\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>65,334<\/strong> \u104f\u1019\u1030\u101b\u1004\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1014\u102c\u101b\u102e\u1005\u102c\u101c\u1031\u1037\u101c\u102c\u1014\u1031\u101e\u100a\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1019\u103b\u103e\u1031\u102c\u103a\u1019\u103e\u1014\u103a\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1010\u1005\u103a\u1026\u1038\u104f\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u102c\u101b\u102e\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d\u1019\u103b\u103e\u1031\u102c\u103a\u101c\u1004\u1037\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038\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;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a 10 \u1014\u102c\u101b\u102e\u1000\u103c\u102c\u101c\u1031\u1037\u101c\u102c\u101e\u1031\u102c \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a <strong>85.15<\/strong> \u101b\u101b\u103e\u102d\u101e\u1004\u1037\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101b\u1019\u103e\u1010\u103a = 65.334 + 1.982*(10) = 85.15<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u1014\u103a\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1000\u102d\u102f \u1024\u1021\u101b\u102c\u1000 \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;\"><strong>Pr(&gt;|t|) :<\/strong> \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1016\u1031\u102c\u103a\u1000\u102d\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1006\u1000\u103a\u1005\u1015\u103a\u1014\u1031\u101e\u100a\u1037\u103a p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b <em>\u1014\u102c\u101b\u102e<\/em> \u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a p-value (2.25e-06) \u101e\u100a\u103a 0.05 \u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1014\u100a\u103a\u1038\u1014\u1031\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a <em>\u1014\u102c\u101b\u102e<\/em> \u1014\u103e\u1004\u1037\u103a <em>\u101b\u1019\u103e\u1010\u103a<\/em> \u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1015\u103c\u1031\u102c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Multiple R-squared-<\/strong> \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1000\u102d\u102f \u101c\u1031\u1037\u101c\u102c\u101e\u100a\u1037\u103a\u1014\u102c\u101b\u102e\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u101f\u102f \u1024\u1014\u1036\u1015\u102b\u1010\u103a\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1015\u103c\u1031\u102c\u1015\u103c\u101e\u100a\u103a\u104b \u101a\u1031\u1018\u1030\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a regression model \u1010\u1005\u103a\u1001\u102f\u104f R-squared \u1010\u1014\u103a\u1016\u102d\u102f\u1038 \u1015\u102d\u102f\u1000\u103c\u102e\u1038\u101c\u1031\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030 variable \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f variable \u104f \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101b\u102c\u1010\u103d\u1004\u103a \u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u101c\u1031\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f <strong>83.1%<\/strong> \u1000\u102d\u102f \u1014\u102c\u101b\u102e\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1000\u103b\u1014\u103a\u1014\u1031\u101e\u1031\u102c\u1005\u1036\u101c\u103d\u1032\u1001\u103b\u1031\u102c\u103a\u1019\u103e\u102f-<\/strong> \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101e\u1010\u102d\u1015\u103c\u102f\u1019\u102d\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1000\u103d\u102c\u1021\u101d\u1031\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1014\u102d\u1019\u1037\u103a\u101c\u1031\u104a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u101e\u100a\u103a \u1005\u1031\u102c\u1004\u1037\u103a\u1000\u103c\u100a\u1037\u103a\u101c\u1031\u1037\u101c\u102c\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1014\u102d\u102f\u1004\u103a\u101c\u1031\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1010\u103d\u1004\u103a\u1010\u103d\u1031\u1037\u101b\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u101b\u1019\u103e\u1010\u103a\u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u1019\u103e \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101b\u1019\u103e\u1010\u103a\u1019\u103e <strong>3,641<\/strong> \u1019\u103e\u1010\u103a\u1016\u103c\u1004\u1037\u103a \u101e\u103d\u1031\u1016\u100a\u103a\u101e\u103d\u102c\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F-statistic \u1014\u103e\u1004\u1037\u103a p-value-<\/strong> F-statistic ( <strong>63.91<\/strong> ) \u1014\u103e\u1004\u1037\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101e\u1031\u102c p-value ( <strong>2.253e-06<\/strong> ) \u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u104f \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1015\u103c\u101e\u100a\u103a\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101b\u103e\u102d \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\u101e\u100a\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u101e\u101c\u102c\u1038\u104a . \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f variable \u1010\u103d\u1004\u103a\u104b \u1024\u1025\u1015\u1019\u102c\u101b\u103e\u102d 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\u104f\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038 <em>\u1015\u103c\u102e\u1038<\/em> <em>\u101b\u1019\u103e\u1010\u103a<\/em> \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101b\u102c\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 4- \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1019\u103c\u1031\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/heteroscedasticity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1019\u103b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u1017\u102e\u1007<\/a> \u1014\u103e\u1004\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1005\u103a\u1010\u100a\u103a\u1019\u103e\u102f<\/a> \u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u1000\u103b\u1014\u103a\u1014\u1031\u101e\u1031\u102c\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Homoscedasticity<\/strong> \u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103e\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u104f <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\u101e\u100a\u103a<\/a> \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\u1010\u1005\u103a\u1001\u102f\u104f \u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\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\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a\u104a <strong>\u1000\u103b\u1014\u103a\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u1031\u102c \u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a<\/strong> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">x-axis \u101e\u100a\u103a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1015\u103c\u101e\u1015\u103c\u102e\u1038 y-axis \u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1015\u103c\u101e\u101e\u100a\u103a\u104b \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101d\u1014\u103a\u1038\u1000\u103b\u1004\u103a\u101b\u103e\u102d \u1002\u101b\u1015\u103a\u1010\u1005\u103a\u101c\u103b\u103e\u1031\u102c\u1000\u103a\u101c\u102f\u1036\u1038 \u1000\u103b\u1015\u1014\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1005\u103a\u1015\u103c\u1031\u1038\u100a\u102e \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1014\u1031\u101e\u101b\u103d\u1031\u1037\u104a \u1019\u103b\u102d\u102f\u1038\u1010\u1030\u101b\u102d\u102f\u1038\u1000\u103b\u1016\u103c\u1005\u103a\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u1001\u103b\u102d\u102f\u1038\u1016\u1031\u102c\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u101f\u102f\u1010\u103a\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101a\u1030\u1006\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define residuals\n<\/span>res &lt;- resid(model)\n\n<span style=\"color: #008080;\">#produce residual vs. fitted plot\n<\/span>plot(fitted(model), res)\n\n<span style=\"color: #008080;\">#add a horizontal line at 0 \n<\/span>abline(0,0)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28971 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ols3.jpg\" alt=\"\" width=\"501\" height=\"364\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102f\u100a\u101d\u1014\u103a\u1038\u1000\u103b\u1004\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u1015\u1014\u103a\u1038\u1000\u103b\u1015\u1014\u103a\u1038 \u1015\u103c\u1014\u1037\u103a\u1000\u103b\u1032\u1014\u1031\u1015\u102f\u1036\u101b\u1015\u103c\u102e\u1038 \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u100a\u1037\u103a\u1015\u102f\u1036\u1005\u1036\u1019\u1015\u103c\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\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\u1015\u102f\u1036\u1005\u1036\u104f <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\u101e\u100a\u103a<\/a> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 <b>\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1005\u103a\u101b\u102d\u102f\u1038<\/b> \u1016\u103c\u1005\u103a\u1005\u1009\u103a \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1010\u103d\u1004\u103a \u1016\u1031\u102c\u103a\u1015\u103c\u1011\u102c\u1038\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\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <strong>QQ \u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u1000\u102d\u102f<\/strong> \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u1021\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a 45 \u1012\u102e\u1002\u101b\u102e\u1011\u1031\u102c\u1004\u1037\u103a\u1000\u102d\u102f \u1016\u103d\u1032\u1037\u1005\u100a\u103a\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1000\u103c\u1019\u103a\u1038\u1016\u103b\u1004\u103a\u1038\u1016\u103c\u1031\u102c\u1004\u1037\u103a\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1010\u1005\u103a\u101c\u103b\u103e\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u1015\u102b\u1000\u104a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create QQ plot for residuals\n<\/span>qqnorm(res)\n\n<span style=\"color: #008080;\">#add a straight diagonal line to the plot\n<\/span>qqline(res) \n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28972 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ols4.jpg\" alt=\"\" width=\"416\" height=\"394\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a 45 \u1012\u102e\u1002\u101b\u102e\u1019\u103b\u1009\u103a\u1038\u1019\u103e \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u101e\u103d\u1031\u1016\u100a\u103a\u101e\u103d\u102c\u1038\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1015\u103c\u1004\u103a\u1038\u1011\u1014\u103a\u101e\u1031\u102c\u1005\u102d\u102f\u1038\u101b\u102d\u1019\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1005\u1031\u101b\u1014\u103a \u1019\u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u1015\u102b\u104b \u101e\u102c\u1019\u1014\u103a\u1016\u103c\u1005\u103a\u101b\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u1005\u1009\u103a \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101e\u100a\u103a\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101a\u1030\u1006\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1015\u103c\u102e\u1038 homoskeastic \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a OLS \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1005\u103a\u1006\u1031\u1038\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104f\u1011\u103d\u1000\u103a\u101b\u103e\u102d\u1019\u103e\u102f\u101e\u100a\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1005\u102d\u1010\u103a\u1001\u103b\u101b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a<\/strong> &#8211; \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u104d \u1019\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1012\u1031\u1010\u102c\u1000\u102d\u102f <a href=\"https:\/\/statorials.org\/my\/\u1012\u1031\u1010\u102c\u1000\u102d\u102f-r-\u1021\u1016\u103c\u1005\u103a\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1015\u102b\u104b\/\" target=\"_blank\" rel=\"noopener\">\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u101b\u1014\u103a<\/a> \u1000\u103c\u102d\u102f\u1038\u1005\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\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 R \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u1018\u102f\u1036\u1021\u101c\u102f\u1015\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\/multiple-linear-regression-r\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a linear regression \u1021\u1019\u103b\u102c\u1038\u1021\u1015\u103c\u102c\u1038\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-exponential-regression\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a exponential regression \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-\u101c\u1031\u1038\u1011\u1031\u102c\u1004\u1037\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038-\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038 \u1005\u1010\u102f\u101b\u1014\u103a\u1038 \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><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u101e\u102c\u1019\u1014\u103a\u1021\u1014\u100a\u103a\u1038\u1006\u102f\u1036\u1038\u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1019\u103b\u102c\u1038 (OLS) \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \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\u1010\u1005\u103a\u1001\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1010\u1005\u103a\u1001\u102f\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\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 \u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a \u1019\u103b\u1009\u103a\u1038\u1010\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101e\u100a\u1037\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u1021\u102c\u1038 \u101b\u103e\u102c\u1016\u103d\u1031\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101e\u100a\u103a- \u0177 = b 0 + b 1 x \u101b\u103d\u103e\u1031- \u0177 : \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1010\u1014\u103a\u1016\u102d\u102f\u1038 b 0 : \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u104f \u1019\u1030\u101c\u1021\u1005 b 1 : \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u1009\u103a\u1038\u104f \u101c\u103b\u103e\u1031\u102c\u1005\u1031\u102c\u1000\u103a \u1024\u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\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\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1000\u1030\u100a\u102e\u1015\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \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\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101b\u1014\u103a \u104e\u1004\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a [&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>R \u1010\u103d\u1004\u103a OLS Regression \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 (\u1025\u1015\u1019\u102c\u1014\u103e\u1004\u1037\u103a\u1021\u1010\u1030) - Statology<\/title>\n<meta name=\"description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \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\u1000\u102d\u102f \u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036 \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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