{"id":1244,"date":"2023-07-27T03:48:40","date_gmt":"2023-07-27T03:48:40","guid":{"rendered":"https:\/\/statorials.org\/ru\/%d0%be%d1%81%d1%82%d0%b0%d1%82%d0%ba%d0%b8-%d0%b2-%d0%b3-%d1%81%d1%82%d1%8c%d1%8e%d0%b4%d0%b5%d0%bd%d1%82%d0%b8%d0%b7%d0%b8%d1%80%d0%be%d0%b2%d0%b0%d0%bd%d0%bd%d0%be%d0%bc\/"},"modified":"2023-07-27T03:48:40","modified_gmt":"2023-07-27T03:48:40","slug":"%d0%be%d1%81%d1%82%d0%b0%d1%82%d0%ba%d0%b8-%d0%b2-%d0%b3-%d1%81%d1%82%d1%8c%d1%8e%d0%b4%d0%b5%d0%bd%d1%82%d0%b8%d0%b7%d0%b8%d1%80%d0%be%d0%b2%d0%b0%d0%bd%d0%bd%d0%be%d0%bc","status":"publish","type":"post","link":"https:\/\/statorials.org\/ru\/%d0%be%d1%81%d1%82%d0%b0%d1%82%d0%ba%d0%b8-%d0%b2-%d0%b3-%d1%81%d1%82%d1%8c%d1%8e%d0%b4%d0%b5%d0%bd%d1%82%d0%b8%d0%b7%d0%b8%d1%80%d0%be%d0%b2%d0%b0%d0%bd%d0%bd%d0%be%d0%bc\/","title":{"rendered":"\u041a\u0430\u043a \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043e\u0441\u0442\u0430\u0442\u043a\u0438 \u0432 r"},"content":{"rendered":"

<\/p>\n

\n

\u041e\u0441\u0442\u0430\u0442\u043e\u043a \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430<\/strong> \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u043e \u043e\u0441\u0442\u0430\u0442\u043e\u043a, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 \u0435\u0433\u043e \u0440\u0430\u0441\u0447\u0435\u0442\u043d\u043e\u0435 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435.<\/span><\/p>\n

\u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043c\u044b \u043e\u0431\u044b\u0447\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u043b\u044e\u0431\u043e\u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435<\/a> \u0432 \u043d\u0430\u0431\u043e\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043e\u0441\u0442\u0430\u0442\u043e\u043a \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430 \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 3, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u044b\u0431\u0440\u043e\u0441\u043e\u043c.<\/span><\/p>\n

\u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0431\u044b\u0441\u0442\u0440\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043e\u0441\u0442\u0430\u0442\u043a\u0438 \u043b\u044e\u0431\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0432 R, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044e studres()<\/strong> \u0438\u0437 \u043f\u0430\u043a\u0435\u0442\u0430 MASS, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u0441\u0438\u043d\u0442\u0430\u043a\u0441\u0438\u0441:<\/span><\/p>\n

\u0448\u043f\u0438\u043b\u044c\u043a\u0438 (\u043c\u043e\u0434\u0435\u043b\u044c)<\/strong><\/span><\/p>\n

\u0433\u0434\u0435 \u043c\u043e\u0434\u0435\u043b\u044c<\/em> \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043b\u044e\u0431\u0443\u044e \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c.<\/span><\/p>\n

\u041f\u0440\u0438\u043c\u0435\u0440: \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u0432 R<\/strong><\/span><\/h3>\n

\u041f\u0440\u0435\u0434\u043f\u043e\u043b\u043e\u0436\u0438\u043c, \u043c\u044b \u0441\u043e\u0437\u0434\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u043f\u0440\u043e\u0441\u0442\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438<\/a> \u0432 R, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0432\u0441\u0442\u0440\u043e\u0435\u043d\u043d\u044b\u0439 \u043d\u0430\u0431\u043e\u0440 \u0434\u0430\u043d\u043d\u044b\u0445 mtcars<\/em> :<\/span><\/p>\n

 #build simple linear regression model<\/span>\nmodel <- lm(mpg ~ disp, data=mtcars)\n<\/strong><\/pre>\n
 \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044e studres()<\/strong> \u0438\u0437 \u043f\u0430\u043a\u0435\u0442\u0430 MASS \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u0434\u043b\u044f \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u0432 \u043d\u0430\u0431\u043e\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445:<\/span><\/p>\n
 library<\/span> (MASS)<\/span>\n\n#calculate studentized residuals<\/span>\nstud_resids <- studres(model)\n\n#view first three studentized residuals<\/span>\nhead(stud_resids, 3)\n\n    Mazda RX4 Mazda RX4 Wag Datsun 710 \n   -0.6236250 -0.6236250 -0.7405315 \n<\/strong><\/pre>\n
 \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u0431\u044b\u0441\u0442\u0440\u044b\u0439 \u0433\u0440\u0430\u0444\u0438\u043a \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445-\u043f\u0440\u0435\u0434\u0438\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u0440\u043e\u0442\u0438\u0432 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u0445 \u0438\u0437\u0443\u0447\u0435\u043d\u043d\u044b\u0445 \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432:<\/span> <\/p>\n
 #plot predictor variable vs. studentized residuals\n<\/span>plot(mtcars$disp, stud_resids, ylab=' Studentized Residuals<\/span> ', xlab=' Displacement<\/span> ') \n\n#add horizontal line at 0\n<\/span>abline(0, 0)<\/strong> <\/pre>\n
\"\u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435<\/p>\n
 \u041d\u0430 \u0433\u0440\u0430\u0444\u0438\u043a\u0435 \u043c\u044b \u0432\u0438\u0434\u0438\u043c, \u0447\u0442\u043e \u043d\u0438 \u043e\u0434\u043d\u043e \u0438\u0437 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0439 \u043d\u0435 \u0438\u043c\u0435\u0435\u0442 \u043e\u0441\u0442\u0430\u0442\u043a\u0430 \u0421\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0430 \u0441 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u044b\u043c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435\u043c \u0431\u043e\u043b\u044c\u0448\u0435 3, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432 \u043d\u0430\u0431\u043e\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445 \u043d\u0435\u0442 \u044f\u0432\u043d\u044b\u0445 \u0432\u044b\u0431\u0440\u043e\u0441\u043e\u0432.<\/span><\/p>\n
 \u041c\u044b \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u0435\u043c \u0434\u043e\u0431\u0430\u0432\u0438\u0442\u044c \u043e\u0431\u0440\u0430\u0442\u043d\u043e \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043e\u0441\u0442\u0430\u0442\u043a\u0438 \u043a\u0430\u0436\u0434\u043e\u0433\u043e \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u0432 \u0438\u0441\u0445\u043e\u0434\u043d\u043e\u043c \u043d\u0430\u0431\u043e\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445, \u0435\u0441\u043b\u0438 \u0437\u0430\u0445\u043e\u0442\u0438\u043c:<\/span><\/p>\n
 #add studentized residuals to orignal dataset\n<\/span>final_data <- cbind<\/span> (mtcars[c(' mpg<\/span> ', ' disp<\/span> ')], stud_resids)\n\n#view final dataset\n<\/span>head(final_data)\n\n                   mpg disp stud_resids\nMazda RX4 21.0 160 -0.6236250\nMazda RX4 Wag 21.0 160 -0.6236250\nDatsun 710 22.8 108 -0.7405315\nHornet 4 Drive 21.4 258 0.7556078\nHornet Sportabout 18.7 360 1.2658336\nValiant 18.1 225 -0.6896297<\/strong><\/pre>\n
 \u0417\u0430\u0442\u0435\u043c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043e\u0442\u0441\u043e\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043a\u0430\u0436\u0434\u043e\u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 \u043e\u0442 \u0441\u0430\u043c\u043e\u0433\u043e \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e \u043a \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0435\u043c\u0443 \u043d\u0430 \u043e\u0441\u043d\u043e\u0432\u0435 \u043e\u0441\u0442\u0430\u0442\u043a\u0430 \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430, \u0447\u0442\u043e\u0431\u044b \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u043e \u0442\u043e\u043c, \u043a\u0430\u043a\u0438\u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u044f \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0431\u043b\u0438\u0437\u043a\u0438 \u043a \u0432\u044b\u0431\u0440\u043e\u0441\u0430\u043c:<\/span><\/p>\n
 #sort studentized residuals descending\n<\/span>final_data[ order<\/span> (-stud_resids),]\n\n                     mpg disp stud_resids\nToyota Corolla 33.9 71.1 2.52397102\nPontiac Firebird 19.2 400.0 2.06825391\nFiat 128 32.4 78.7 2.03684699\nLotus Europa 30.4 95.1 1.53905536\nHonda Civic 30.4 75.7 1.27099586\nHornet Sportabout 18.7 360.0 1.26583364\nChrysler Imperial 14.7 440.0 1.06486066\nHornet 4 Drive 21.4 258.0 0.75560776\nPorsche 914-2 26.0 120.3 0.42424678\nFiat X1-9 27.3 79.0 0.30183728\nMerc 240D 24.4 146.7 0.26235893\nFord Pantera L 15.8 351.0 0.20825609\nCadillac Fleetwood 10.4 472.0 0.08338531\nLincoln Continental 10.4 460.0 -0.07863385\nDuster 360 14.3 360.0 -0.14476167\nMerc 450SL 17.3 275.8 -0.28759769\nDodge Challenger 15.5 318.0 -0.30826585\nMerc 230 22.8 140.8 -0.30945955\nMerc 450SE 16.4 275.8 -0.56742476\nAMC Javelin 15.2 304.0 -0.58138205\nCamaro Z28 13.3 350.0 -0.58848471\nMazda RX4 Wag 21.0 160.0 -0.62362497\nMazda RX4 21.0 160.0 -0.62362497\nMaserati Bora 15.0 301.0 -0.68315010\nValiant 18.1 225.0 -0.68962974\nDatsun 710 22.8 108.0 -0.74053152\nMerc 450SLC 15.2 275.8 -0.94814699\nToyota Corona 21.5 120.1 -0.99751166\nVolvo 142E 21.4 121.0 -1.01790487\nMerc 280 19.2 167.6 -1.09979261\nFerrari Dino 19.7 145.0 -1.24732999\nMerc 280C 17.8 167.6 -1.57258064\n<\/strong><\/pre>\n
 \u0414\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u0440\u0435\u0441\u0443\u0440\u0441\u044b<\/strong><\/span><\/h3>\n
 \u041a\u0430\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043f\u0440\u043e\u0441\u0442\u0443\u044e \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e \u0432 R<\/a>
 \u041a\u0430\u043a \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0443\u044e \u043b\u0438\u043d\u0435\u0439\u043d\u0443\u044e \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u044e \u0432 R<\/a>
 \u041a\u0430\u043a \u0441\u043e\u0437\u0434\u0430\u0442\u044c \u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u044b\u0439 \u0433\u0440\u0430\u0444\u0438\u043a \u0432 R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u041e\u0441\u0442\u0430\u0442\u043e\u043a \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430 \u2014 \u044d\u0442\u043e \u043f\u0440\u043e\u0441\u0442\u043e \u043e\u0441\u0442\u0430\u0442\u043e\u043a, \u0440\u0430\u0437\u0434\u0435\u043b\u0435\u043d\u043d\u044b\u0439 \u043d\u0430 \u0435\u0433\u043e \u0440\u0430\u0441\u0447\u0435\u0442\u043d\u043e\u0435 \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u043e\u0435 \u043e\u0442\u043a\u043b\u043e\u043d\u0435\u043d\u0438\u0435. \u041d\u0430 \u043f\u0440\u0430\u043a\u0442\u0438\u043a\u0435 \u043c\u044b \u043e\u0431\u044b\u0447\u043d\u043e \u0433\u043e\u0432\u043e\u0440\u0438\u043c, \u0447\u0442\u043e \u043b\u044e\u0431\u043e\u0435 \u043d\u0430\u0431\u043b\u044e\u0434\u0435\u043d\u0438\u0435 \u0432 \u043d\u0430\u0431\u043e\u0440\u0435 \u0434\u0430\u043d\u043d\u044b\u0445, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043e\u0441\u0442\u0430\u0442\u043e\u043a \u0441\u0442\u0443\u0434\u0435\u043d\u0442\u0430 \u043f\u0440\u0435\u0432\u044b\u0448\u0430\u0435\u0442 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 3, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u044b\u0431\u0440\u043e\u0441\u043e\u043c. \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u0431\u044b\u0441\u0442\u0440\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u0442\u044c\u044e\u0434\u0435\u043d\u0442\u0438\u0437\u0438\u0440\u043e\u0432\u0430\u043d\u043d\u044b\u0435 \u043e\u0441\u0442\u0430\u0442\u043a\u0438 \u043b\u044e\u0431\u043e\u0439 \u043c\u043e\u0434\u0435\u043b\u0438 \u0440\u0435\u0433\u0440\u0435\u0441\u0441\u0438\u0438 \u0432 R, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044e studres() \u0438\u0437 \u043f\u0430\u043a\u0435\u0442\u0430 MASS, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442 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