{"id":1239,"date":"2023-07-27T04:23:20","date_gmt":"2023-07-27T04:23:20","guid":{"rendered":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-%e1%80%a1%e1%80%93%e1%80%ad%e1%80%80%e1%80%a1%e1%80%85%e1%80%ad%e1%80%90%e1%80%ba%e1%80%a1%e1%80%95%e1%80%ad%e1%80%af%e1%80%84%e1%80%ba%e1%80%b8%e1%80%81\/"},"modified":"2023-07-27T04:23:20","modified_gmt":"2023-07-27T04:23:20","slug":"r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-%e1%80%a1%e1%80%93%e1%80%ad%e1%80%80%e1%80%a1%e1%80%85%e1%80%ad%e1%80%90%e1%80%ba%e1%80%a1%e1%80%95%e1%80%ad%e1%80%af%e1%80%84%e1%80%ba%e1%80%b8%e1%80%81","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/r-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-%e1%80%a1%e1%80%93%e1%80%ad%e1%80%80%e1%80%a1%e1%80%85%e1%80%ad%e1%80%90%e1%80%ba%e1%80%a1%e1%80%95%e1%80%ad%e1%80%af%e1%80%84%e1%80%ba%e1%80%b8%e1%80%81\/","title":{"rendered":"R- \u1010\u1005\u103a\u1006\u1004\u1037\u103a\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1006\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1010\u103d\u1004\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038 \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038\u104b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Principal components analysis, \u1019\u1000\u103c\u102c\u1001\u100f\u1021\u1010\u102d\u102f\u1000\u1031\u102c\u1000\u103a PCA, \u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/\u1000\u103c\u102e\u1038\u1000\u103c\u1015\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a-\u1000\u103c\u102e\u1038\u1000\u103c\u1015\u103a\u1019\u1011\u102c\u1038\u101e\u1031\u102c-\u101e\u1004\u103a\u101a\u1030\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1000\u103c\u102e\u1038\u1000\u103c\u1015\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101e\u1031\u102c<\/a> \u1005\u1000\u103a\u101e\u1004\u103a\u101a\u1030\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1004\u103a\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1021\u1015\u103c\u102c\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u1037\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u2014\u1019\u1030\u101b\u1004\u103a\u1038\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u101b\u103e\u102c\u1016\u103d\u1031\u101e\u100a\u1037\u103a- \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1021\u101d\u1031\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">PCA \u104f\u1015\u1014\u103a\u1038\u1010\u102d\u102f\u1004\u103a\u101e\u100a\u103a \u1019\u1030\u101c\u1012\u1031\u1010\u102c\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1019\u103e\u102f\u1011\u1000\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1015\u102b\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>p<\/em> variables \u1019\u103b\u102c\u1038\u1015\u102b\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 \u1021\u1010\u103d\u1032\u101c\u102d\u102f\u1000\u103a \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u1000\u103d\u1032\u101c\u103d\u1032\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1006\u1014\u103a\u1038\u1005\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u101c\u103b\u1004\u103a\u1019\u103c\u1014\u103a\u1005\u103d\u102c \u1000\u103c\u102e\u1038\u1019\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>p<\/em> \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a\u104a p(p-1)\/2 point cloud \u1019\u103b\u102c\u1038\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 p = 15 \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1010\u103d\u1000\u103a\u1006\u1011\u102c\u1038\u101e\u1031\u102c \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a\u104a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103d\u1032 \u1041\u1040\u1045 \u1001\u102f \u101b\u103e\u102d\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u1036\u1000\u1031\u102c\u1004\u103a\u1038\u1011\u1031\u102c\u1000\u103a\u1019\u1005\u103d\u102c\u104a PCA \u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u1010\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1019\u103b\u103e \u1016\u1019\u103a\u1038\u101a\u1030\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1036\u104f \u1021\u1014\u102d\u1019\u1037\u103a\u1015\u102d\u102f\u1004\u103a\u1038 \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u1000\u102d\u102f \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c\u1014\u103e\u1005\u103a\u101b\u1015\u103a\u1016\u103c\u1004\u1037\u103a \u1016\u1019\u103a\u1038\u101a\u1030\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u1030\u101c\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1019\u103e \u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1000\u102d\u102f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u1005\u1010\u1005\u103a\u1001\u102f\u1021\u1016\u103c\u1005\u103a \u1015\u102f\u1036\u1016\u1031\u102c\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u1014\u100a\u103a\u1038\u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>p<\/em> <sub>\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038<\/sub> <sub>\u1014\u103e\u1004\u1037\u103a\u1021\u1010\u1030<\/sub> <sub>\u1012\u1031\u1010\u102c<\/sub> <sub>\u1021\u1005\u102f\u1036\u1000\u102d\u102f<\/sub> <sub>\u1015\u1031\u1038\u101e\u100a\u103a<\/sub> <em>:<\/em> <em>_<\/em><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><sub>Z<\/sub> <sub>m<\/sub> <sub>=<\/sub> <sub>\u03a3\u03a6<\/sub> <sub>jm<\/sub> <sub>_<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\">Z <sub>1<\/sub> \u101e\u100a\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u1010\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1019\u103b\u103e \u1016\u1019\u103a\u1038\u101a\u1030\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u104f \u1019\u103b\u1009\u103a\u1038\u1016\u103c\u1031\u102c\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">Z <sub>2<\/sub> \u101e\u100a\u103a <em>\u1021\u1005\u102e\u1021\u1005\u1025\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038<\/em> (\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c Z <sub>1<\/sub> \u1019\u103e \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101e\u1031\u102c) \u1016\u103c\u1005\u103a\u1014\u1031\u1005\u1009\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1016\u1019\u103a\u1038\u101a\u1030\u1019\u100a\u1037\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1014\u1031\u102c\u1000\u103a\u1011\u1015\u103a\u1010\u1005\u103a\u1015\u103c\u1031\u1038\u100a\u102e\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a Z <sub>3<\/sub> \u101e\u100a\u103a Z <sub>2<\/sub> \u101e\u102d\u102f\u1037 \u1021\u1005\u102e\u1021\u1005\u1025\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1014\u1031\u1005\u1009\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u101b\u103e\u102d\u1006\u102f\u1036\u1038\u1000\u102d\u102f \u1016\u1019\u103a\u1038\u101a\u1030\u1019\u100a\u1037\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f\u1014\u1031\u102c\u1000\u103a\u1011\u1015\u103a\u1010\u1005\u103a\u1015\u103c\u1031\u1038\u100a\u102e\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a &#8230; \u1015\u103c\u102e\u1038\u1010\u1031\u102c\u1037\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u1030\u101b\u1004\u103a\u1038\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u104f \u1019\u103b\u1009\u103a\u1038\u1016\u103c\u1031\u102c\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\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\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u102c\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e 0 \u1014\u103e\u1004\u1037\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f 1 \u101b\u103e\u102d\u101b\u1014\u103a \u1005\u1000\u1031\u1038\u1001\u103b\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> \u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1021\u1010\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1019\u1000\u103a\u1011\u101b\u1005\u103a\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> covariance matrix \u104f eigenvalues \u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">linear \u1021\u1000\u1039\u1001\u101b\u102c\u101e\u1004\u103a\u1039\u1001\u103b\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038 eigenvalue \u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101e\u1031\u102c eigenvector \u101e\u100a\u103a \u1015\u1011\u1019\u1006\u102f\u1036\u1038 \u1021\u1013\u102d\u1000 \u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1015\u103c\u101e\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1010\u1005\u103a\u1014\u100a\u103a\u1038\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1024\u1021\u1011\u1030\u1038\u101f\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1011\u102f\u1010\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1010\u103d\u1004\u103a \u1021\u1000\u103c\u102e\u1038\u1019\u102c\u1038\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1012\u102f\u1010\u102d\u101a\u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038 eigenvalue \u1014\u103e\u1004\u1037\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101e\u1031\u102c eigenvector \u101e\u100a\u103a \u1012\u102f\u1010\u102d\u101a \u1021\u1013\u102d\u1000 \u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038 \u1016\u103c\u1005\u103a\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 \u1010\u103d\u1004\u103a \u1024\u101c\u102f\u1015\u103a\u1004\u1014\u103a\u1038\u1005\u1009\u103a\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102f\u1036\u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1010\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1015\u103c\u102e\u1038 \u1001\u103c\u101a\u103a\u101c\u103e\u101a\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u101e\u1031\u102c \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038 \u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c <strong>Tidyverse<\/strong> \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103b\u103a\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c \u1010\u1004\u103a\u1015\u1031\u1038\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (tidyverse)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1025\u1015\u1019\u102c\u1021\u1010\u103d\u1000\u103a\u104a <em>\u101c\u1030\u101e\u1010\u103a\u1019\u103e\u102f<\/em> \u104a <em>\u1001\u103b\u1031\u1019\u103e\u102f\u1014\u103a\u1038\u1019\u103e\u102f<\/em> \u104a \u1014\u103e\u1004\u1037\u103a <em>\u1019\u102f\u1012\u102d\u1019\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038<\/em> \u1021\u1010\u103d\u1000\u103a US \u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1014\u1031\u1011\u102d\u102f\u1004\u103a\u101e\u1030 100,000 \u1010\u1005\u103a\u1026\u1038\u101c\u103b\u103e\u1004\u103a \u1016\u1019\u103a\u1038\u1006\u102e\u1038\u1001\u1036\u101b\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c R \u1010\u103d\u1004\u103a\u1010\u100a\u103a\u1006\u1031\u102c\u1000\u103a\u1011\u102c\u1038\u101e\u1031\u102c <em>USArrests<\/em> dataset \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1019\u103c\u102d\u102f\u1037\u1015\u103c\u1012\u1031\u101e\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1014\u1031\u1011\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u101c\u1030\u1026\u1038\u101b\u1031 \u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u104a <em>UrbanPop<\/em> \u101c\u100a\u103a\u1038 \u1015\u102b\u101d\u1004\u103a\u101e\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 \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u104f \u1015\u1011\u1019\u1010\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1010\u1004\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1015\u103c\u101e\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: #993300;\"><span style=\"color: #008080;\">#load data<\/span>\n<span style=\"color: #000000;\">data<\/span><\/span> <span style=\"color: #000000;\">(\"USArrests\")<\/span>\n\n<span style=\"color: #008080;\">#view first six rows of data<\/span>\nhead(USArrests)\n\n           Murder Assault UrbanPop Rape\nAlabama 13.2 236 58 21.2\nAlaska 10.0 263 48 44.5\nArizona 8.1 294 80 31.0\nArkansas 8.8 190 50 19.5\nCalifornia 9.0 276 91 40.6\nColorado 7.9 204 78 38.7\n<\/strong><\/pre>\n<h3> <strong>\u1021\u1006\u1004\u1037\u103a 2- \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u102b\u104b<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1010\u1004\u103a\u1015\u103c\u102e\u1038\u1014\u1031\u102c\u1000\u103a\u104a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u104f \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a R \u104f built-in \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a <strong>prcomp() \u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u1000\u1031\u1038 = TRUE<\/strong> \u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a \u101e\u1031\u1001\u103b\u102c\u1015\u102b\u1005\u1031\u104b \u101e\u102d\u102f\u1037\u1019\u103e\u101e\u102c \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e 0 \u1014\u103e\u1004\u1037\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1019\u102e 1 \u104f \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1005\u1031\u101b\u1014\u103a \u1005\u1000\u1031\u1038\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">R \u101b\u103e\u102d eigenvectors \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1015\u102f\u1036\u101e\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1014\u102f\u1010\u103a\u101c\u1000\u1039\u1001\u100f\u102c\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u1037\u103a \u1026\u1038\u1010\u100a\u103a\u1001\u103b\u1000\u103a\u1010\u103d\u1004\u103a\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104a \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1019\u103e\u1010\u103a\u1021\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u103c\u1014\u103a\u101c\u103e\u1014\u103a\u101b\u1014\u103a -1 \u1016\u103c\u1004\u1037\u103a \u1019\u103c\u103e\u1031\u102c\u1000\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate main components\n<\/span>results &lt;- prcomp(USArrests, scale = <span style=\"color: #008000;\">TRUE<\/span> )\n\n<span style=\"color: #008080;\">#reverse the signs\n<\/span>results$rotation &lt;- -1*results$rotation\n\n<span style=\"color: #008080;\">#display main components\n<\/span>results$rotation\n\n               PC1 PC2 PC3 PC4\nMurder 0.5358995 -0.4181809 0.3412327 -0.64922780\nAssault 0.5831836 -0.1879856 0.2681484 0.74340748\nUrbanPop 0.2781909 0.8728062 0.3780158 -0.13387773\nRape 0.5434321 0.1673186 -0.8177779 -0.08902432<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038 (PC1) \u101e\u100a\u103a \u101c\u1030\u101e\u1010\u103a\u1019\u103e\u102f\u104a \u1001\u103b\u1031\u1019\u103e\u102f\u1014\u103a\u1038\u101b\u1031\u1038\u1014\u103e\u1004\u1037\u103a \u1019\u102f\u1012\u102d\u1019\u103a\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \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\u101e\u100a\u103a\u104a \u1024\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1024\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1000\u103c\u102e\u1038\u1000\u103b\u101a\u103a\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1012\u102f\u1010\u102d\u101a\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038 (PC2) \u101e\u100a\u103a UrbanPop \u1021\u1010\u103d\u1000\u103a \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u104a \u1024\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103c\u102d\u102f\u1037\u1015\u103c\u101c\u1030\u1026\u1038\u101b\u1031\u1000\u102d\u102f \u1021\u101c\u1031\u1038\u1015\u1031\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1014\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f <strong>\u101b\u101c\u1012\u103a $x<\/strong> \u1010\u103d\u1004\u103a \u101e\u102d\u1019\u103a\u1038\u1006\u100a\u103a\u1038\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104b \u101c\u1000\u1039\u1001\u100f\u102c\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u103c\u1014\u103a\u101c\u103e\u1014\u103a\u101b\u1014\u103a \u1024\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f -1 \u1016\u103c\u1004\u1037\u103a \u1019\u103c\u103e\u1031\u102c\u1000\u103a\u1015\u1031\u1038\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#reverse the signs of the scores\n<\/span>results$x &lt;- -1*results$x\n\n<span style=\"color: #008080;\">#display the first six scores\n<span style=\"color: #000000;\">head(results$x)<\/span>\n<\/span><span style=\"color: #000000;\">\n                  PC1 PC2 PC3 PC4\nAlabama 0.9756604 -1.1220012 0.43980366 -0.154696581\nAlaska 1.9305379 -1.0624269 -2.01950027 0.434175454\nArizona 1.7454429 0.7384595 -0.05423025 0.826264240\nArkansas -0.1399989 -1.1085423 -0.11342217 0.180973554\nCalifornia 2.4986128 1.5274267 -0.59254100 0.338559240\nColorado 1.4993407 0.9776297 -1.08400162 -0.001450164\n<\/span><\/strong><\/pre>\n<h3> <strong>\u1021\u1006\u1004\u1037\u103a 3- \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f biplot \u1016\u103c\u1004\u1037\u103a\u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u1011\u1019\u1014\u103e\u1004\u1037\u103a \u1012\u102f\u1010\u102d\u101a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f axes \u1021\u1016\u103c\u1005\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u1005\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1015\u102f\u1036\u1016\u1031\u102c\u103a\u1011\u102c\u1038\u101e\u100a\u1037\u103a <strong>biplot<\/strong> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u1000\u1031\u1038 = 0<\/strong> \u101e\u100a\u103a \u1000\u103d\u1000\u103a\u101c\u1015\u103a\u101b\u103e\u102d \u1019\u103c\u103e\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f loadings \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1005\u1000\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1031\u1001\u103b\u102c\u1005\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>biplot(results, scale = <span style=\"color: #008000;\">0<\/span> )\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12281 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pca1.png\" alt=\"R in Principal Component Analysis \u1021\u1010\u103d\u1000\u103a Biplot\" width=\"465\" height=\"464\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u1019\u103e \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u1014\u103e\u1005\u103a\u1018\u1000\u103a\u1019\u103c\u1004\u103a \u1021\u102c\u1000\u102c\u101e\u1021\u1010\u103d\u1004\u103a\u1038 \u1000\u102d\u102f\u101a\u103a\u1005\u102c\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1015\u103c\u100a\u103a\u1014\u101a\u103a 50 \u1001\u102f\u1005\u102e\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1002\u101b\u1015\u103a\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u1014\u102e\u1038\u1000\u1015\u103a\u1014\u1031\u101e\u1031\u102c \u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1019\u1030\u101b\u1004\u103a\u1038\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1005\u1015\u103a\u101c\u103b\u1009\u103a\u1038\u101e\u100a\u1037\u103a \u1021\u101c\u102c\u1038\u1010\u1030\u1012\u1031\u1010\u102c\u1015\u102f\u1036\u1005\u1036\u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u1001\u103c\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u1004\u1036\u1019\u103b\u102c\u1038\u1011\u1000\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u101b\u102c\u1007\u1040\u1010\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1015\u103c\u1004\u103a\u1038\u1011\u1014\u103a\u1005\u103d\u102c \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1014\u1031\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \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\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1002\u103b\u1031\u102c\u103a\u1002\u103b\u102e\u101a\u102c\u101e\u100a\u103a \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u101b\u103e\u102d <em>\u101c\u1030\u101e\u1010\u103a<\/em> \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u102e\u1038\u1006\u102f\u1036\u1038\u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1019\u1030\u101b\u1004\u103a\u1038\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u101c\u1030\u101e\u1010\u103a\u1019\u103e\u102f\u1014\u103e\u102f\u1014\u103a\u1038\u1021\u1019\u103c\u1004\u1037\u103a\u1006\u102f\u1036\u1038\u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103c\u100a\u1037\u103a\u1015\u102b\u1000\u104a \u1002\u103b\u1031\u102c\u103a\u1002\u103b\u102e\u101a\u102c\u1005\u102c\u101b\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1021\u1019\u103e\u1014\u103a\u1010\u1000\u101a\u103a \u1011\u102d\u1015\u103a\u1006\u102f\u1036\u1038\u101b\u1031\u102c\u1000\u103a\u1014\u1031\u101e\u100a\u103a\u1000\u102d\u102f \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#display states with highest murder rates in original dataset<\/span>\nhead(USArrests[ <span style=\"color: #3366ff;\">order<\/span> (-USArrests$Murder),])\n\n               Murder Assault UrbanPop Rape\nGeorgia 17.4 211 60 25.8\nMississippi 16.1 259 44 17.1\nFlorida 15.4 335 80 31.9\nLouisiana 15.4 249 66 22.2\nSouth Carolina 14.4 279 48 22.5\nAlabama 13.2 236 58 21.2<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 4- \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1019\u103e \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1019\u103e \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u1031\u102c \u1019\u1030\u101b\u1004\u103a\u1038\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u104f \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate total variance explained by each principal component\n<\/span>results$sdev^2 \/ <span style=\"color: #3366ff;\">sum<\/span> (results$sdev^2)\n\n[1] 0.62006039 0.24744129 0.08914080 0.04335752\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f <strong>62%<\/strong> \u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1012\u102f\u1010\u102d\u101a\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f <strong>24.7%<\/strong> \u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1010\u1010\u102d\u101a\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f <strong>8.9%<\/strong> \u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1005\u1010\u102f\u1010\u1039\u1011\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u101b\u103e\u102d \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f <strong>4.3%<\/strong> \u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1015\u1011\u1019\u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u101b\u103e\u102d \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1018\u101a\u103a\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u1006\u102d\u102f\u101e\u1031\u102c\u103a \u101a\u1001\u1004\u103a biplot \u101e\u100a\u103a \u101c\u1031\u1037\u101c\u102c\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f \u1019\u1030\u101c\u1012\u1031\u1010\u102c\u1019\u103e \u1015\u1011\u1019\u1021\u1013\u102d\u1000 \u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f\u101e\u102c \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u101e\u100a\u1037\u103a \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u1005\u102e\u1005\u1025\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u1031\u102c\u1004\u103a\u1038\u101e\u1031\u102c\u101c\u1000\u1039\u1001\u100f\u102c\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1015\u103c\u100a\u103a\u1014\u101a\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1001\u103d\u1032\u1001\u103c\u102c\u1038\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u101b\u1014\u103a biplot \u1019\u103e\u1015\u102f\u1036\u1005\u1036\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a\u1010\u101b\u102c\u1038\u101d\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">PCA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1019\u103e \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f\u1015\u103c\u101e\u101e\u100a\u1037\u103a \u1002\u101b\u1015\u103a\u1010\u1005\u103a\u1001\u102f &#8211; <strong>scree plot \u1000\u102d\u102f<\/strong> \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate total variance explained by each principal component\n<\/span>var_explained = results$sdev^2 \/ <span style=\"color: #3366ff;\">sum<\/span> (results$sdev^2)\n\n<span style=\"color: #008080;\">#create scree plot\n<\/span>qplot(c(1:4), var_explained) + \n  geom_line() + \n  xlab(\" <span style=\"color: #008000;\">Principal Component<\/span> \") + \n  ylab(\" <span style=\"color: #008000;\">Variance Explained<\/span> \") +\n  ggtitle(\" <span style=\"color: #008000;\">Scree Plot<\/span> \") +\n  ylim(0, 1)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12282 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pca2.png\" alt=\"R \u1015\u102f\u1036\u101e\u100f\u1039\u100c\u102c\u1014\u103a \u1019\u103b\u1000\u103a\u1014\u103e\u102c\u1015\u103c\u1004\u103a \u1021\u1014\u1031\u1021\u1011\u102c\u1038\" width=\"427\" height=\"428\" srcset=\"\" sizes=\"\"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a\u104a PCA \u1000\u102d\u102f \u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038 \u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Exploratory Data Analysis<\/strong> \u2013 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u101b\u103e\u102c\u1016\u103d\u1031\u1014\u1031\u1015\u103c\u102e\u1038 \u1012\u1031\u1010\u102c\u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1021\u101c\u102c\u1038\u101e\u100f\u1039\u100d\u102c\u1014\u103a\u1021\u101c\u102c\u1038\u1010\u1030\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1014\u102c\u1038\u101c\u100a\u103a\u101c\u102d\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a PCA \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Principal Component Regression<\/strong> &#8211; \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a <a href=\"https:\/\/statorials.org\/my\/r-\u1010\u103d\u1004\u103a-\u1021\u1013\u102d\u1000-\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">Principal Component Regression<\/a> \u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a PCA \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a <a href=\"https:\/\/statorials.org\/my\/multicollinearity-\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103b\u1025\u103a\u1038\u100a\u102e\u1011\u103d\u1031<\/a> \u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1024\u1006\u102f\u1010\u103a\u101a\u102f\u1010\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1000\u102d\u102f \u1019\u1000\u103c\u102c\u1001\u100f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<hr>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a R \u1000\u102f\u1012\u103a\u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036\u1000\u102d\u102f <a href=\"https:\/\/github.com\/Statorials\/R-Guides\/blob\/main\/pca.R\" target=\"_blank\" rel=\"noopener noreferrer\">\u1024\u1014\u1031\u101b\u102c\u1010\u103d\u1004\u103a<\/a> \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Principal components analysis, \u1019\u1000\u103c\u102c\u1001\u100f\u1021\u1010\u102d\u102f\u1000\u1031\u102c\u1000\u103a PCA, \u101e\u100a\u103a \u1000\u103c\u102e\u1038\u1000\u103c\u1015\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101e\u1031\u102c \u1005\u1000\u103a\u101e\u1004\u103a\u101a\u1030\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1004\u103a\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1021\u1015\u103c\u102c\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u1037\u103a \u1021\u1013\u102d\u1000\u1021\u1005\u102d\u1010\u103a\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u2014\u1019\u1030\u101b\u1004\u103a\u1038\u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1019\u103b\u1009\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u101b\u103e\u102c\u1016\u103d\u1031\u101e\u100a\u1037\u103a- \u1012\u1031\u1010\u102c\u1021\u1005\u102f\u1021\u101d\u1031\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b PCA \u104f\u1015\u1014\u103a\u1038\u1010\u102d\u102f\u1004\u103a\u101e\u100a\u103a \u1019\u1030\u101c\u1012\u1031\u1010\u102c\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1019\u103e\u102f\u1011\u1000\u103a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1015\u102b\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b p variables \u1019\u103b\u102c\u1038\u1015\u102b\u101e\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 \u1021\u1010\u103d\u1032\u101c\u102d\u102f\u1000\u103a \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f 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