{"id":1533,"date":"2023-07-25T23:59:19","date_gmt":"2023-07-25T23:59:19","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%94%e1%80%be%e1%80%af%e1%80%90%e1%80%ba%e1%80%92%e1%80%bd%e1%80%ad%e1%80%80%e1%80%ad%e1%80%94%e1%80%ba%e1%80%b8%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-%e1%80%84%e1%80%ab%e1%80%b8\/"},"modified":"2023-07-25T23:59:19","modified_gmt":"2023-07-25T23:59:19","slug":"%e1%80%a1%e1%80%94%e1%80%be%e1%80%af%e1%80%90%e1%80%ba%e1%80%92%e1%80%bd%e1%80%ad%e1%80%80%e1%80%ad%e1%80%94%e1%80%ba%e1%80%b8%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-%e1%80%84%e1%80%ab%e1%80%b8","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%94%e1%80%be%e1%80%af%e1%80%90%e1%80%ba%e1%80%92%e1%80%bd%e1%80%ad%e1%80%80%e1%80%ad%e1%80%94%e1%80%ba%e1%80%b8%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-%e1%80%84%e1%80%ab%e1%80%b8\/","title":{"rendered":"\u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial \u1014\u103e\u1004\u1037\u103a poisson- \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Negative binomial regression<\/strong> \u1014\u103e\u1004\u1037\u103a <strong>Poisson regression \u101e\u100a\u103a<\/strong> discrete count outcomes \u1016\u103c\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 variable \u1000\u102d\u102f<\/a> \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1005\u103a\u1019\u103b\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u101b\u1031\u1010\u103d\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1001\u103b\u102d\u102f\u1037\u104f \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1019\u103e \u1018\u103d\u1032\u1037\u101b\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u101c\u1019\u103a\u1038\u1006\u102f\u1036\u1019\u103e\u102c \u101a\u102c\u1009\u103a\u1019\u1010\u1031\u102c\u103a\u1010\u1006\u1019\u103e\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1019\u102c\u101b\u101e\u103d\u1014\u103a\u1015\u103c\u102d\u102f\u1004\u103a\u1015\u103d\u1032\u1015\u103c\u102e\u1038\u1019\u103c\u1031\u102c\u1000\u103a\u101e\u1030\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u101c\u1000\u103a\u101c\u102e\u1005\u1010\u102d\u102f\u1038\u1006\u102d\u102f\u1004\u103a\u1010\u103d\u1004\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u101c\u1010\u1005\u103a\u101c\u1021\u1010\u103d\u1004\u103a\u1038 \u1015\u103c\u1014\u103a\u101b\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1015\u102b\u1000\u104a Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\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;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u1000\u103c\u102e\u1038\u1014\u1031\u1015\u102b\u1000\u104a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1014\u102d\u102f\u1004\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poisson regression \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a negative binomial regression \u101e\u100a\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c data set \u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1015\u102d\u102f\u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1019\u103e\u102f \u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1014\u103e\u1005\u103a\u1001\u102f \u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u101c\u1000\u103a\u1000\u103b\u1014\u103a\u1019\u103c\u1031\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1010\u1005\u103a\u1001\u102f\u1019\u103e \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1005\u1036\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u104f\u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\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;\">\u1005\u1036\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u103b\u1014\u103a\u1014\u1031\u101e\u1031\u1038\u101e\u1031\u102c\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u101e\u100a\u103a -2 \u1014\u103e\u1004\u1037\u103a 2 \u1000\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u1000 Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u101e\u100a\u103a \u1024\u1018\u1031\u102c\u1004\u103a\u1021\u1015\u103c\u1004\u103a\u1018\u1000\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u101b\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u104a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u101e\u1031\u102c \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1005\u1031\u1014\u102d\u102f\u1004\u103a\u1016\u103d\u101a\u103a\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Poisson regression model \u1014\u103e\u1004\u1037\u103a negative binomial regression model \u1000\u102d\u102f \u1010\u1030\u100a\u102e\u101e\u1031\u102c data set \u1010\u103d\u1004\u103a \u1010\u1015\u103a\u1006\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u103c\u102e\u1038 \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031 \u1021\u1001\u103b\u102d\u102f\u1038\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\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u101a\u103a\u104d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\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 \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u101e\u1031\u102c \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \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;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u101e\u100a\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1036\u1021\u1010\u103d\u1000\u103a Poisson regression \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a negative binomial regression model \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1015\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a R \u1010\u103d\u1004\u103a \u1024\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- \u1021\u1014\u103e\u102f\u1010\u103a\u1014\u103e\u1005\u103a\u1021\u1019\u100a\u103a\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1011\u1000\u103a\u1010\u1014\u103a\u1038\u1000\u103b\u1031\u102c\u1004\u103a\u1038 \u1018\u1031\u1037\u1005\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1010\u1005\u103a\u1026\u1038\u101e\u100a\u103a \u104e\u1004\u103a\u1038\u104f\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u100c\u102c\u1014\u1001\u103d\u1032 (&#8220; A&#8221; , &#8220; B&#8221;  \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a &#8220; C&#8221; ) \u1014\u103e\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u104f\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u1021\u1006\u1004\u1037\u103a\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1001\u101b\u102d\u102f\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1015\u100a\u102c\u101e\u1004\u103a\u1006\u102f\u1019\u100a\u103a\u1019\u103b\u103e\u101b\u101b\u103e\u102d\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u102d\u1001\u103b\u1004\u103a\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1010\u1000\u1039\u1000\u101e\u102d\u102f\u101c\u103a\u101d\u1004\u103a\u1001\u103d\u1004\u1037\u103a\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032 (0 \u1019\u103e 100)\u104b )<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression model \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a Poisson regression model \u101e\u100a\u103a data \u1014\u103e\u1004\u1037\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/span><\/p>\n<p> <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><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1018\u1031\u1037\u1005\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 1,000 \u104f \u1012\u1031\u1010\u102c\u1019\u103b\u102c\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\u1031\u102c \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1014\u103e\u1004\u1037\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set. <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#create dataset\n<\/span>data &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (offers = c(rep(0, 700), rep(1, 100), rep(2, 100),\n                              rep(3, 70), rep(4, 30)),\n                   division = sample(c(' <span style=\"color: #008000;\">A<\/span> ', ' <span style=\"color: #008000;\">B<\/span> ', ' <span style=\"color: #008000;\">C<\/span> '), 100, replace = <span style=\"color: #008000;\">TRUE<\/span> ),\n                   exam = c(runif(700, 60, 90), runif(100, 65, 95),\n                            runif(200, 75, 95)))\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(data)\n\n  offers division exam\n1 0 A 66.22635\n2 0 C 66.85974\n3 0 A 77.87136\n4 0 B 77.24617\n5 0 A 62.31193\n6 0 C 61.06622<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1014\u103e\u1004\u1037\u103a Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037 \u1000\u102d\u102f\u1000\u103a\u100a\u102e\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;\">#fit Poisson regression model\n<\/span>p_model &lt;- glm(offers ~ division + exam, family = ' <span style=\"color: #008000;\">fish<\/span> ', data = data)\n\n<span style=\"color: #008080;\">#fit negative binomial regression model\n<\/span><span style=\"color: #993300;\">library<\/span> (MASS)\n\nnb_model &lt;- glm. <span style=\"color: #3366ff;\">nb<\/span> (offers ~ division + exam, data = data)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- \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><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1005\u103a\u1019\u103b\u102d\u102f\u1038\u101c\u102f\u1036\u1038\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u1014\u103a\u101b\u103e\u102d\u101e\u1031\u102c \u1019\u103c\u1031\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1011\u102f\u1010\u103a\u101c\u102f\u1015\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#Residual plot for Poisson regression\n<\/span>p_res &lt;- <span style=\"color: #3366ff;\">resid<\/span> (p_model)\nplot(fitted(p_model), p_res, col=' <span style=\"color: #008000;\">steelblue<\/span> ', pch=16,\n     xlab=' <span style=\"color: #008000;\">Predicted Offers<\/span> ', ylab=' <span style=\"color: #008000;\">Standardized Residuals<\/span> ', main=' <span style=\"color: #008000;\">Poisson<\/span> ')\nabline(0,0)\n\n<span style=\"color: #008080;\">#Residual plot for negative binomial regression<\/span>\nnb_res &lt;- <span style=\"color: #3366ff;\">resid<\/span> (nb_model)\nplot(fitted(nb_model), nb_res, col=' <span style=\"color: #008000;\">steelblue<\/span> ', pch=16,\n     xlab=' <span style=\"color: #008000;\">Predicted Offers<\/span> ', ylab=' <span style=\"color: #008000;\">Standardized Residuals<\/span> ', main=' <span style=\"color: #008000;\">Negative Binomial<\/span> ')\nabline(0,0)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-15231 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/negatifbinom1.png\" alt=\"Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c\u1014\u103e\u1005\u103a\u1001\u102f\" width=\"679\" height=\"327\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1002\u101b\u1015\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u104a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1021\u1010\u103d\u1000\u103a (\u1021\u1001\u103b\u102d\u102f\u1037\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a 3 \u1011\u1000\u103a\u1000\u103b\u1031\u102c\u103a\u101c\u103d\u1014\u103a\u1014\u1031\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b) \u1021\u1014\u102f\u1010\u103a binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u1015\u102d\u102f\u1019\u102d\u102f\u1015\u103b\u1036\u1037\u1014\u103e\u1036\u1037\u1014\u1031\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104f \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression model \u101e\u100a\u103a \u1015\u102d\u102f\u104d\u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101c\u1000\u1039\u1001\u100f\u102c\u1010\u1005\u103a\u101b\u1015\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 4- \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1021\u1001\u103b\u102d\u102f\u1038\u1000\u102d\u102f \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1021\u1001\u103b\u102d\u102f\u1038\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-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>pchisq(2 * ( <span style=\"color: #3366ff;\">logLik<\/span> (nb_model) - <span style=\"color: #3366ff;\">logLik<\/span> (p_model)), df = 1, lower. <span style=\"color: #3366ff;\">tail<\/span> = <span style=\"color: #008000;\">FALSE<\/span> )\n\n'log Lik.' 3.508072e-29 (df=5)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u104f p-value \u101e\u100a\u103a <strong>3.508072e-29<\/strong> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 0.05 \u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1014\u100a\u103a\u1038\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\u104a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression model \u101e\u100a\u103a Poisson regression model \u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 data \u1014\u103e\u1004\u1037\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\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\/\u1021\u1014\u103e\u102f\u1010\u103a-1-\u101e\u100a\u103a-binomial-\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1004\u102b\u1038\u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u101b\u1031\u1038\/\" target=\"_blank\" rel=\"noopener\">Poisson \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Negative binomial regression \u1014\u103e\u1004\u1037\u103a Poisson regression \u101e\u100a\u103a discrete count outcomes \u1016\u103c\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f variable \u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u1031\u102c \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1014\u103e\u1005\u103a\u1019\u103b\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u101b\u1031\u1010\u103d\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1001\u103b\u102d\u102f\u1037\u104f \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a- \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1019\u103e \u1018\u103d\u1032\u1037\u101b\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u101c\u1019\u103a\u1038\u1006\u102f\u1036\u1019\u103e\u102c \u101a\u102c\u1009\u103a\u1019\u1010\u1031\u102c\u103a\u1010\u1006\u1019\u103e\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u1019\u102c\u101b\u101e\u103d\u1014\u103a\u1015\u103c\u102d\u102f\u1004\u103a\u1015\u103d\u1032\u1015\u103c\u102e\u1038\u1019\u103c\u1031\u102c\u1000\u103a\u101e\u1030\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u101c\u1000\u103a\u101c\u102e\u1005\u1010\u102d\u102f\u1038\u1006\u102d\u102f\u1004\u103a\u1010\u103d\u1004\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c \u101c\u1010\u1005\u103a\u101c\u1021\u1010\u103d\u1004\u103a\u1038 \u1015\u103c\u1014\u103a\u101b\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1015\u102b\u1000\u104a Poisson \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u101e\u100a\u103a \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u1000\u103c\u102e\u1038\u1014\u1031\u1015\u102b\u1000\u104a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101e\u100a\u103a \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1014\u102d\u102f\u1004\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b Poisson [&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>\u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial \u1014\u103e\u1004\u1037\u103a Poisson- \u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1000\u102d\u102f \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u100a\u103a\u1038<\/title>\n<meta name=\"description\" content=\"\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial \u1014\u103e\u1004\u1037\u103a Poisson regression \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \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 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content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%94%e1%80%be%e1%80%af%e1%80%90%e1%80%ba%e1%80%92%e1%80%bd%e1%80%ad%e1%80%80%e1%80%ad%e1%80%94%e1%80%ba%e1%80%b8%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-%e1%80%84%e1%80%ab%e1%80%b8\/\",\"url\":\"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%94%e1%80%be%e1%80%af%e1%80%90%e1%80%ba%e1%80%92%e1%80%bd%e1%80%ad%e1%80%80%e1%80%ad%e1%80%94%e1%80%ba%e1%80%b8%e1%80%94%e1%80%be%e1%80%84%e1%80%b7%e1%80%ba-%e1%80%84%e1%80%ab%e1%80%b8\/\",\"name\":\"\u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c binomial 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