{"id":1098,"date":"2023-07-27T16:32:06","date_gmt":"2023-07-27T16:32:06","guid":{"rendered":"https:\/\/statorials.org\/tr\/rye-box-cox-donusumu\/"},"modified":"2023-07-27T16:32:06","modified_gmt":"2023-07-27T16:32:06","slug":"rye-box-cox-donusumu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rye-box-cox-donusumu\/","title":{"rendered":"R&#39;de box-cox d\u00f6n\u00fc\u015f\u00fcm\u00fc nas\u0131l ger\u00e7ekle\u015ftirilir (\u00f6rneklerle)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Box-cox d\u00f6n\u00fc\u015f\u00fcm\u00fc,<\/strong> normal olarak da\u011f\u0131t\u0131lmayan bir veri k\u00fcmesini daha normal olarak da\u011f\u0131t\u0131lan bir k\u00fcmeye d\u00f6n\u00fc\u015ft\u00fcrmek i\u00e7in yayg\u0131n olarak kullan\u0131lan bir y\u00f6ntemdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu y\u00f6ntemin arkas\u0131ndaki temel fikir, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak d\u00f6n\u00fc\u015ft\u00fcr\u00fclen verinin normal da\u011f\u0131l\u0131ma m\u00fcmk\u00fcn oldu\u011fu kadar yak\u0131n olmas\u0131n\u0131 sa\u011flayacak bir \u03bb de\u011feri bulmakt\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">y(\u03bb) = (y <sup>\u03bb<\/sup> \u2013 1) \/ \u03bb e\u011fer y \u2260 0 ise<\/span><\/li>\n<li> <span style=\"color: #000000;\">y(\u03bb) = log(y) e\u011fer y = 0 ise<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>MASS()<\/strong> k\u00fct\u00fcphanesindeki <strong>boxcox()<\/strong> fonksiyonunu kullanarak R&#8217;de box-cox d\u00f6n\u00fc\u015f\u00fcm\u00fc ger\u00e7ekle\u015ftirebiliriz.<\/span> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekte bu fonksiyonun pratikte nas\u0131l kullan\u0131laca\u011f\u0131 g\u00f6sterilmektedir.<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">Box-Cox d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fcn geli\u015fiminin g\u00fczel bir \u00f6zeti i\u00e7in Connecticut \u00dcniversitesi&#8217;nin <a href=\"https:\/\/www.ime.usp.br\/~abe\/lista\/pdfm9cJKUmFZp.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">bu makalesine<\/a> bak\u0131n.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek: R&#8217;de Box-Cox D\u00f6n\u00fc\u015f\u00fcm\u00fc<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, do\u011frusal bir regresyon modelinin bir veri k\u00fcmesine nas\u0131l s\u0131\u011fd\u0131r\u0131laca\u011f\u0131n\u0131, ard\u0131ndan <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkenini<\/a> d\u00f6n\u00fc\u015ft\u00fcrmek ve yeni bir modele uyacak en uygun lambday\u0131 bulmak i\u00e7in <strong>boxcox()<\/strong> i\u015flevinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (MASS)\n\n<span style=\"color: #008080;\">#create data<\/span>\ny=c(1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 6, 7, 8)\nx=c(7, 7, 8, 3, 2, 4, 4, 6, 6, 7, 5, 3, 3, 5, 8)\n\n<span style=\"color: #008080;\">#fit linear regression model<\/span>\nmodel &lt;- lm(y~x)\n\n<span style=\"color: #008080;\">#find optimal lambda for Box-Cox transformation<\/span> \nbc &lt;- boxcox(y ~ x)\n(lambda &lt;- bc$x[which.max(bc$y)])\n\n[1] -0.4242424\n\n<span style=\"color: #008080;\">#fit new linear regression model using the Box-Cox transformation<\/span>\nnew_model &lt;- lm(((y^lambda-1)\/lambda) ~ x)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Optimum lambdan\u0131n <strong>-0,4242424<\/strong> oldu\u011fu ortaya \u00e7\u0131kt\u0131. B\u00f6ylece yeni regresyon modeli orijinal yan\u0131t de\u011fi\u015fkeni y&#8217;yi y = (y <sup>-0,4242424<\/sup> \u2013 1) \/ -0,4242424 de\u011fi\u015fkeniyle de\u011fi\u015ftirdi.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, iki regresyon modeli aras\u0131ndaki art\u0131klardaki farklar\u0131 g\u00f6rselle\u015ftirmek i\u00e7in R&#8217;de iki <a href=\"https:\/\/statorials.org\/tr\/birisi-ilgisini-cekiyor\/\" target=\"_blank\" rel=\"noopener noreferrer\">QQ grafi\u011finin<\/a> nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define plotting area<\/span>\nop &lt;- par(pty = \"s\", mfrow = c(1, 2))\n\n<span style=\"color: #008080;\">#QQ plot for original model<\/span>\nqqnorm(model$residuals)\nqqline(model$residuals)\n\n<span style=\"color: #008080;\">#QQ plot for Box-Cox transformed model<\/span>\nqqnorm(new_model$residuals)\nqqline(new_model$residuals)\n\n<span style=\"color: #008080;\">#display both QQ plots<\/span>\nby(op)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11193 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/boitecoxr1.png\" alt=\"R'de Box-Cox taraf\u0131ndan d\u00f6n\u00fc\u015ft\u00fcr\u00fclen QQ arazisi\" width=\"501\" height=\"301\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Genel olarak, e\u011fer veri noktalar\u0131 bir QQ grafi\u011finde d\u00fcz bir \u00e7apraz \u00e7izgi boyunca uzan\u0131yorsa, veri seti muhtemelen normal bir da\u011f\u0131l\u0131m izlemektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Box-cox d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f modelinin, orijinal regresyon modelinden \u00e7ok daha d\u00fcz bir \u00e7izgiye sahip bir QQ grafi\u011fini nas\u0131l \u00fcretti\u011fine dikkat edin.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, box-cox d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f modelin art\u0131klar\u0131n\u0131n \u00e7ok daha normal da\u011f\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6sterir ve bu da <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener noreferrer\">do\u011frusal regresyonun varsay\u0131mlar\u0131ndan<\/a> birini kar\u015f\u0131lar.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/tr\/verileri-rye-donustur\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de Veri Nas\u0131l D\u00f6n\u00fc\u015ft\u00fcr\u00fcl\u00fcr (Log, Kare K\u00f6k, K\u00fcp K\u00f6k)<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/birisi-ilgisini-cekiyor\/\" target=\"_blank\" rel=\"noopener noreferrer\">R&#8217;de QQ grafi\u011fi nas\u0131l olu\u015fturulur ve yorumlan\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/shapiro-wilk-testi-r\/\">R&#8217;de normallik i\u00e7in Shapiro-Wilk testi nas\u0131l yap\u0131l\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Box-cox d\u00f6n\u00fc\u015f\u00fcm\u00fc, normal olarak da\u011f\u0131t\u0131lmayan bir veri k\u00fcmesini daha normal olarak da\u011f\u0131t\u0131lan bir k\u00fcmeye d\u00f6n\u00fc\u015ft\u00fcrmek i\u00e7in yayg\u0131n olarak kullan\u0131lan bir y\u00f6ntemdir. Bu y\u00f6ntemin arkas\u0131ndaki temel fikir, a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanarak d\u00f6n\u00fc\u015ft\u00fcr\u00fclen verinin normal da\u011f\u0131l\u0131ma m\u00fcmk\u00fcn oldu\u011fu kadar yak\u0131n olmas\u0131n\u0131 sa\u011flayacak bir \u03bb de\u011feri bulmakt\u0131r: y(\u03bb) = (y \u03bb \u2013 1) \/ \u03bb e\u011fer y \u2260 0 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1098","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R&#039;de Box-Cox D\u00f6n\u00fc\u015f\u00fcm\u00fc Nas\u0131l Ger\u00e7ekle\u015ftirilir (\u00d6rneklerle)<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde R&#039;de 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