{"id":86,"date":"2023-08-05T15:31:11","date_gmt":"2023-08-05T15:31:11","guid":{"rendered":"https:\/\/statorials.org\/tr\/korelasyon\/"},"modified":"2023-08-05T15:31:11","modified_gmt":"2023-08-05T15:31:11","slug":"korelasyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/korelasyon\/","title":{"rendered":"Korelasyon"},"content":{"rendered":"<p>Bu makale, iki de\u011fi\u015fken aras\u0131ndaki korelasyonun anlam\u0131n\u0131, korelasyon katsay\u0131s\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve mevcut farkl\u0131 korelasyon t\u00fcrlerini a\u00e7\u0131klamaktad\u0131r. Ayr\u0131ca iki de\u011fi\u015fken aras\u0131ndaki korelasyonun de\u011ferinin nas\u0131l yorumlanaca\u011f\u0131 g\u00f6sterilmektedir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-correlacion\"><\/span> Korelasyon nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Korelasyon<\/strong> , iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin derecesini g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Daha spesifik olarak <strong>do\u011frusal korelasyon<\/strong> , iki farkl\u0131 de\u011fi\u015fken aras\u0131ndaki do\u011frusal korelasyonun derecesini belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> \u0130ki de\u011fi\u015fken birbirine ba\u011fl\u0131d\u0131r, bir de\u011fi\u015fkenin de\u011ferlerini de\u011fi\u015ftirirken di\u011fer de\u011fi\u015fkenin de\u011ferleri de de\u011fi\u015fir. \u00d6rne\u011fin A de\u011fi\u015fkeninin artmas\u0131 B de\u011fi\u015fkenini de art\u0131r\u0131yorsa A ve B de\u011fi\u015fkenleri aras\u0131nda bir korelasyon vard\u0131r.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-correlacion\"><\/span> Korelasyon t\u00fcrleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130ki rastgele de\u011fi\u015fken aras\u0131ndaki ili\u015fkiye ba\u011fl\u0131 olarak a\u015fa\u011f\u0131daki <strong>do\u011frusal korelasyon t\u00fcrleri<\/strong> ay\u0131rt edilir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Do\u011frudan korelasyon (veya pozitif korelasyon)<\/strong> : Bir de\u011fi\u015fken artt\u0131\u011f\u0131nda di\u011feri de artar.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ters korelasyon (veya negatif korelasyon)<\/strong> : Bir de\u011fi\u015fken artt\u0131\u011f\u0131nda di\u011feri azal\u0131r ve bunun tersi de ge\u00e7erlidir; bir de\u011fi\u015fken azald\u0131\u011f\u0131nda di\u011feri artar.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>S\u0131f\u0131r korelasyon (korelasyon yok)<\/strong> : \u0130ki de\u011fi\u015fken aras\u0131nda herhangi bir ili\u015fki yoktur.<\/span><\/li>\n<\/ul>\n<p> Bunlar\u0131n mevcut farkl\u0131 do\u011frusal korelasyon t\u00fcrleri oldu\u011funu unutmay\u0131n; ancak iki de\u011fi\u015fken aras\u0131ndaki matematiksel ili\u015fki d\u00fcz bir \u00e7izgiyle temsil edilemeyebilir, bunun yerine bir benzetme gibi daha karma\u015f\u0131k bir fonksiyonun kullan\u0131lmas\u0131 gerekebilir. veya bir logaritma. Bu durumda <strong>do\u011frusal olmayan bir korelasyon<\/strong> olacakt\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"coeficiente-de-correlacion\"><\/span> Korelasyon katsay\u0131s\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Korelasyonun tan\u0131m\u0131n\u0131 ve mevcut farkl\u0131 korelasyon t\u00fcrlerini g\u00f6z \u00f6n\u00fcnde bulundurarak bu istatistiksel de\u011ferin nas\u0131l hesapland\u0131\u011f\u0131na bakal\u0131m.<\/p>\n<p> <strong>Do\u011frusal<\/strong> <strong>korelasyon katsay\u0131s\u0131<\/strong> veya <strong>Pearson korelasyon katsay\u0131s\u0131<\/strong> olarak da adland\u0131r\u0131lan korelasyon katsay\u0131s\u0131, iki de\u011fi\u015fken aras\u0131ndaki korelasyonun de\u011feridir.<\/p>\n<p> \u0130ki istatistiksel de\u011fi\u015fkenin korelasyon katsay\u0131s\u0131, de\u011fi\u015fkenlerin kovaryans\u0131 ile her de\u011fi\u015fkenin varyans\u0131n\u0131n \u00e7arp\u0131m\u0131n\u0131n karek\u00f6k\u00fc aras\u0131ndaki b\u00f6l\u00fcme e\u015fittir. Bu nedenle korelasyon katsay\u0131s\u0131n\u0131 hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1a64ef5b8eb2f144d29ded978b0e1282_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\rho_{XY}=\\cfrac{Cov(X,Y)}{\\sqrt{Var(X)\\cdot Var(Y)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"212\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Bir pop\u00fclasyondaki korelasyon katsay\u0131s\u0131 hesaplan\u0131rken korelasyon sembol\u00fc Yunanca \u03c1 harfidir. Ancak katsay\u0131 bir \u00f6rne\u011fe g\u00f6re hesaplan\u0131rken sembol olarak genellikle r harfi kullan\u0131l\u0131r.<\/p>\n<p> Korelasyon indeksinin de\u011feri -1 ile +1 aras\u0131nda olabilir. A\u015fa\u011f\u0131da korelasyon katsay\u0131s\u0131 de\u011ferinin nas\u0131l yorumland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<p> A\u015fa\u011f\u0131daki ba\u011flant\u0131da korelasyon katsay\u0131s\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair somut bir \u00f6rnek g\u00f6rebilirsiniz: <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi-1\/\">korelasyon katsay\u0131s\u0131n\u0131n hesaplanmas\u0131na ili\u015fkin \u00f6rnek<\/a><\/div>\n<p> Spearman&#8217;\u0131n veya Kendall&#8217;\u0131n korelasyon katsay\u0131s\u0131 gibi ba\u015fka t\u00fcrde korelasyon katsay\u0131lar\u0131n\u0131n da oldu\u011funu unutmay\u0131n. Ancak en yayg\u0131n olan\u0131 \u015f\u00fcphesiz Pearson korelasyon katsay\u0131s\u0131d\u0131r.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-de-la-correlacion\"><\/span> Korelasyonun yorumlanmas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Korelasyon katsay\u0131s\u0131n\u0131n de\u011feri -1&#8217;den +1&#8217;e kadar de\u011fi\u015febilir. Yani korelasyon katsay\u0131s\u0131n\u0131n de\u011ferine ba\u011fl\u0131 olarak iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin bir y\u00f6nde veya di\u011fer y\u00f6nde oldu\u011fu anlam\u0131na gelir. <strong>Korelasyon de\u011ferinin nas\u0131l yorumlanaca\u011f\u0131<\/strong> a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>r=-1<\/strong> : iki de\u011fi\u015fken m\u00fckemmel bir negatif korelasyona sahiptir, dolay\u0131s\u0131yla t\u00fcm noktalar\u0131n birbirine ba\u011fland\u0131\u011f\u0131 negatif e\u011fimli bir \u00e7izgi \u00e7izebiliriz.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>-1&lt;r&lt;0<\/strong> : iki de\u011fi\u015fken aras\u0131ndaki korelasyon negatiftir, yani bir de\u011fi\u015fken artt\u0131\u011f\u0131nda di\u011feri azal\u0131r. De\u011fer -1&#8217;e ne kadar yak\u0131nsa de\u011fi\u015fkenler o kadar negatif ili\u015fkilidir.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>r=0<\/strong> : \u0130ki de\u011fi\u015fken aras\u0131ndaki korelasyon \u00e7ok zay\u0131ft\u0131r, asl\u0131nda aralar\u0131ndaki do\u011frusal ili\u015fki s\u0131f\u0131rd\u0131r. Bu, de\u011fi\u015fkenlerin ba\u011f\u0131ms\u0131z oldu\u011fu anlam\u0131na gelmez \u00e7\u00fcnk\u00fc do\u011frusal olmayan bir ili\u015fkiye sahip olabilirler.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>0&lt;r&lt;1<\/strong> : \u0130ki de\u011fi\u015fken aras\u0131ndaki korelasyon pozitiftir, de\u011fer +1&#8217;e ne kadar yak\u0131nsa de\u011fi\u015fkenler aras\u0131ndaki ili\u015fki o kadar g\u00fc\u00e7l\u00fcd\u00fcr. Bu durumda de\u011fi\u015fkenlerden biri artarken di\u011feri de de\u011ferini art\u0131rma e\u011filimindedir.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>r=1<\/strong> : iki de\u011fi\u015fken m\u00fckemmel pozitif korelasyona sahiptir, yani pozitif do\u011frusal ili\u015fkiye sahiptirler.<\/span> <\/li>\n<\/ul>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/types-de-correlation.png\" alt=\"korelasyon t\u00fcrleri\" class=\"wp-image-1848\" width=\"686\" height=\"440\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Yukar\u0131daki da\u011f\u0131l\u0131m grafiklerinde g\u00f6rebilece\u011finiz gibi, iki de\u011fi\u015fken aras\u0131ndaki korelasyon ne kadar g\u00fc\u00e7l\u00fc olursa, grafikteki noktalar birbirine o kadar yak\u0131n olur. \u00d6te yandan noktalar\u0131n birbirinden \u00e7ok uzak olmas\u0131 korelasyonun zay\u0131f oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> Unutmay\u0131n ki iki de\u011fi\u015fken aras\u0131nda korelasyon olsa bile bu, aralar\u0131nda nedensellik oldu\u011fu anlam\u0131na gelmez; yani <strong>iki de\u011fi\u015fken aras\u0131ndaki korelasyon, bir de\u011fi\u015fkendeki de\u011fi\u015fimin di\u011ferindeki de\u011fi\u015fimin nedeni oldu\u011fu anlam\u0131na gelmez. de\u011fi\u015fken.<\/strong><\/p>\n<p> \u00d6rne\u011fin, v\u00fccudun iki farkl\u0131 hormon \u00fcretmesi aras\u0131nda pozitif bir ili\u015fki oldu\u011funu bulursak, bu, bir hormondaki art\u0131\u015f\u0131n di\u011fer hormonda da art\u0131\u015fa yol a\u00e7aca\u011f\u0131 anlam\u0131na gelmez. V\u00fccudun her iki hormonu da \u00fcretmesi, \u00e7\u00fcnk\u00fc bir hastal\u0131kla m\u00fccadele etmek i\u00e7in her ikisine de ihtiya\u00e7 duymas\u0131 ve bu nedenle her ikisinin de d\u00fczeylerini ayn\u0131 anda art\u0131rmas\u0131 m\u00fcmk\u00fcnd\u00fcr; bu durumda nedeni hastal\u0131k olabilir. \u0130ki hormon aras\u0131nda nedensel bir ba\u011flant\u0131 olup olmad\u0131\u011f\u0131n\u0131n tespiti i\u00e7in daha detayl\u0131 bir \u00e7al\u0131\u015fma yap\u0131lmas\u0131 gerekmektedir.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"correlacion-y-regresion\"><\/span> Korelasyon ve regresyon<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Korelasyon ve regresyon<\/strong> genel olarak birbiriyle ili\u015fkili iki kavramd\u0131r \u00e7\u00fcnk\u00fc her ikisi de iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Korelasyon, iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7en istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr; ancak regresyon, iki de\u011fi\u015fkenin ili\u015fkilendirilmesine olanak tan\u0131yan bir denklem (do\u011frusal bir regresyon ise d\u00fcz bir \u00e7izgi olacakt\u0131r) olu\u015fturmay\u0131 i\u00e7erir.<\/p>\n<p> Bu nedenle korelasyon, de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiye basit\u00e7e say\u0131sal bir de\u011fer sa\u011flarken regresyon, bir de\u011fi\u015fkenin di\u011ferine g\u00f6re de\u011ferini tahmin etmeye \u00e7al\u0131\u015fmak i\u00e7in kullan\u0131labilir.<\/p>\n<p> Genel olarak \u00f6ncelikle korelasyon katsay\u0131s\u0131n\u0131 hesaplayarak de\u011fi\u015fkenlerin korelasyonlu olup olmad\u0131\u011f\u0131n\u0131 analiz ederiz. Korelasyon anlaml\u0131ysa veri setinde bir regresyon ger\u00e7ekle\u015ftiririz.<\/p>\n<p> Korelasyon katsay\u0131s\u0131n\u0131 do\u011frusal regresyonda elde edilen do\u011frunun e\u011fimi de\u011feriyle kar\u0131\u015ft\u0131rmak yayg\u0131nd\u0131r ancak bunlar e\u015fde\u011fer de\u011fildir.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"matriz-de-correlacion\"><\/span> Korelasyon matrisi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Korelasyon matrisi,<\/strong> <em>i,j<\/em> konumunda <em>i<\/em> ve <em>j<\/em> de\u011fi\u015fkenleri aras\u0131ndaki korelasyon katsay\u0131s\u0131n\u0131 i\u00e7eren bir matristir.<\/p>\n<p> Dolay\u0131s\u0131yla korelasyon matrisi, ana k\u00f6\u015fegen \u00fczerindekilerle dolu bir kare matris olup, <em>i<\/em> sat\u0131r\u0131 ve <em>j<\/em> s\u00fctununun eleman\u0131, <em>i<\/em> de\u011fi\u015fkeni ile <em>j<\/em> de\u011fi\u015fkeni aras\u0131ndaki korelasyon katsay\u0131s\u0131n\u0131n de\u011ferinden olu\u015fur.<\/p>\n<p> Dolay\u0131s\u0131yla korelasyon matrisinin form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/matrice-de-correlation.png\" alt=\"korelasyon matrisi\" class=\"wp-image-1862\" width=\"383\" height=\"245\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-247f749babdab47d38e25ff82f7e2706_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r_{ij}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"19\" style=\"vertical-align: -6px;\"><\/p>\n<p> de\u011fi\u015fkenler aras\u0131ndaki korelasyon katsay\u0131s\u0131d\u0131r<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-31318c5dcb226c69e0818e5f7d2422b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6af8b344893b41828947991fc4242ed3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"j.\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Korelasyon matrisi, sonu\u00e7lar\u0131 \u00f6zetlemek ve birden fazla de\u011fi\u015fken aras\u0131ndaki korelasyonu ayn\u0131 anda kar\u015f\u0131la\u015ft\u0131rmak i\u00e7in \u00e7ok kullan\u0131\u015fl\u0131d\u0131r \u00e7\u00fcnk\u00fc hangi ili\u015fkilerin g\u00fc\u00e7l\u00fc oldu\u011funu h\u0131zl\u0131 bir \u015fekilde g\u00f6rebilirsiniz.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale, iki de\u011fi\u015fken aras\u0131ndaki korelasyonun anlam\u0131n\u0131, korelasyon katsay\u0131s\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve mevcut farkl\u0131 korelasyon t\u00fcrlerini a\u00e7\u0131klamaktad\u0131r. Ayr\u0131ca iki de\u011fi\u015fken aras\u0131ndaki korelasyonun de\u011ferinin nas\u0131l yorumlanaca\u011f\u0131 g\u00f6sterilmektedir. Korelasyon nedir? Korelasyon , iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin derecesini g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Daha spesifik olarak do\u011frusal korelasyon , iki farkl\u0131 de\u011fi\u015fken aras\u0131ndaki do\u011frusal korelasyonun derecesini belirlemek i\u00e7in kullan\u0131l\u0131r. 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