{"id":85,"date":"2023-08-05T15:46:55","date_gmt":"2023-08-05T15:46:55","guid":{"rendered":"https:\/\/statorials.org\/tr\/korelasyon-matrisi\/"},"modified":"2023-08-05T15:46:55","modified_gmt":"2023-08-05T15:46:55","slug":"korelasyon-matrisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/korelasyon-matrisi\/","title":{"rendered":"Korelasyon matrisi"},"content":{"rendered":"

Bu makalede korelasyon matrisinin ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve korelasyon matrisinin nas\u0131l yorumlanaca\u011f\u0131n\u0131 ke\u015ffedeceksiniz. Ek olarak korelasyon matrisinin yorumlanmas\u0131na ili\u015fkin somut bir \u00f6rnek g\u00f6rebileceksiniz. <\/p>\n

<\/span> Korelasyon matrisi nedir?<\/span><\/h2>\n

Korelasyon matrisi, i,j<\/em> konumunda i<\/em> ve j<\/em> de\u011fi\u015fkenleri aras\u0131ndaki korelasyon katsay\u0131s\u0131n\u0131 i\u00e7eren bir matristir.<\/strong><\/p>\n

Dolay\u0131s\u0131yla korelasyon matrisi, ana k\u00f6\u015fegen \u00fczerindekilerle dolu bir kare matris olup, i<\/em> sat\u0131r\u0131 ve j<\/em> s\u00fctununun eleman\u0131, i<\/em> de\u011fi\u015fkeni ile j<\/em> de\u011fi\u015fkeni aras\u0131ndaki korelasyon katsay\u0131s\u0131n\u0131n de\u011ferinden olu\u015fur.<\/p>\n

Korelasyon matrisinin form\u00fcl\u00fc<\/strong> bu nedenle a\u015fa\u011f\u0131daki gibidir: <\/p>\n

\n
\"korelasyon<\/figure>\n<\/div>\n

Alt\u0131n<\/p>\n<\/p>\n

\"r_{ij}\"<\/p>\n

de\u011fi\u015fkenler aras\u0131ndaki korelasyon katsay\u0131s\u0131d\u0131r<\/p>\n

\"i\"<\/p>\n

Ve<\/p>\n

\"j.\"<\/p>\n<\/p>\n

Dolay\u0131s\u0131yla bir veri setinin korelasyon matrisini bulmak i\u00e7in korelasyon katsay\u0131s\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 bilmeniz \u00f6nemlidir. Hat\u0131rlam\u0131yorsan\u0131z, a\u015fa\u011f\u0131daki ba\u011flant\u0131da bunu \u00e7evrimi\u00e7i hesap makinesiyle nas\u0131l yapaca\u011f\u0131n\u0131z\u0131 \u00f6\u011freneceksiniz: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> korelasyon katsay\u0131s\u0131 hesaplay\u0131c\u0131s\u0131<\/a><\/div>\n

Korelasyon katsay\u0131s\u0131n\u0131n bir \u00f6zelli\u011fi, de\u011fi\u015fkenlerin s\u0131ras\u0131n\u0131n hesaplanmas\u0131nda \u00f6nemli olmamas\u0131d\u0131r, yani korelasyon katsay\u0131s\u0131<\/p>\n<\/p>\n

\"r_{ij}\"<\/p>\n

e\u015fde\u011ferdir<\/p>\n

\"r_{ji}.\"<\/p>\n

Bu nedenle korelasyon matrisi simetriktir.<\/p>\n<\/p>\n

\"\\displaystyle<\/p>\n<\/p>\n

Bir korelasyon matrisinin anlaml\u0131 olabilmesi i\u00e7in istatistiksel veri setinin ikiden fazla de\u011fi\u015fkene sahip olmas\u0131 gerekir. Aksi takdirde tek bir korelasyon katsay\u0131s\u0131n\u0131n belirlenmesi yeterli olacakt\u0131r ve korelasyon matrisi anlaml\u0131 olacakt\u0131r. <\/p>\n

<\/span> Korelasyon matrisi nas\u0131l yap\u0131l\u0131r<\/span><\/h2>\n

Korelasyon matrisinin tan\u0131m\u0131 g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, bu t\u00fcr istatistiksel matrisin nas\u0131l olu\u015fturuldu\u011funu g\u00f6relim:<\/p>\n

    \n
  1. Her de\u011fi\u015fken \u00e7iftinin korelasyon katsay\u0131s\u0131n\u0131 hesaplay\u0131n. De\u011fi\u015fkenlerin s\u0131ras\u0131n\u0131n sonucu de\u011fi\u015ftirmedi\u011fini, dolay\u0131s\u0131yla her de\u011fi\u015fken \u00e7ifti i\u00e7in yaln\u0131zca bir kez hesaplanmas\u0131 gerekti\u011fini unutmay\u0131n.<\/span><\/li>\n
  2. Veri serisindeki de\u011fi\u015fken say\u0131s\u0131yla ayn\u0131 boyutta bir kare matris olu\u015fturun. Bu matris korelasyon matrisi olacakt\u0131r.<\/span><\/li>\n
  3. Korelasyon matrisinin ana k\u00f6\u015fegeninin her bir eleman\u0131na 1 koyun.<\/span><\/li>\n
  4. i<\/em> , j<\/em> de\u011fi\u015fkenlerinin korelasyon katsay\u0131s\u0131n\u0131 i<\/em> , j<\/em> ve j<\/em> , i<\/em> konumlar\u0131na yerle\u015ftirin.<\/span><\/li>\n
  5. Korelasyon matrisi olu\u015fturulduktan sonra geriye kalan tek \u015fey de\u011ferlerinin yorumlanmas\u0131d\u0131r.<\/span><\/li>\n<\/ol>\n

    Korelasyon matrisini \u00e7al\u0131\u015ft\u0131rman\u0131n yeterli olmad\u0131\u011f\u0131n\u0131, daha sonra de\u011ferlerini yorumlay\u0131p ne anlama geldi\u011fini anlaman\u0131z gerekti\u011fini unutmay\u0131n. A\u015fa\u011f\u0131daki b\u00f6l\u00fcmde bir korelasyon matrisinin nas\u0131l yorumlanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. <\/p>\n

    <\/span> Korelasyon matrisinin yorumlanmas\u0131<\/span><\/h2>\n

    Korelasyon matrisini do\u011fru bir \u015fekilde yorumlamak i\u00e7in korelasyon katsay\u0131s\u0131n\u0131n de\u011ferinin -1 ile +1 aras\u0131nda de\u011fi\u015febilece\u011fini dikkate almak gerekir:<\/p>\n

      \n
    • 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
    • -1<r<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’e ne kadar yak\u0131nsa de\u011fi\u015fkenler o kadar negatif ili\u015fkilidir.<\/span><\/li>\n
    • 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
    • 0<r<1<\/strong> : \u0130ki de\u011fi\u015fken aras\u0131ndaki korelasyon pozitiftir, de\u011fer +1’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
    • r=1<\/strong> : iki de\u011fi\u015fken m\u00fckemmel pozitif korelasyona sahiptir, yani pozitif do\u011frusal ili\u015fkiye sahiptirler.<\/span><\/li>\n<\/ul>\n

      Bu nedenle korelasyon matrisini yorumlamak i\u00e7in her bir korelasyon katsay\u0131s\u0131n\u0131n yorumlanmas\u0131 ve farkl\u0131 sonu\u00e7lar\u0131n kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131 gerekir.<\/strong><\/p>\n

      Bu \u015fekilde hangi de\u011fi\u015fkenlerin birbiriyle en \u00e7ok ili\u015fkili oldu\u011funu, hangi de\u011fi\u015fkenlerin en \u00f6nemli oldu\u011funu, hangi de\u011fi\u015fkenlerin birbiriyle neredeyse hi\u00e7 ili\u015fkisi olmad\u0131\u011f\u0131n\u0131 vb. g\u00f6rebileceksiniz. <\/p>\n

      <\/span> Korelasyon Matrisi \u00d6rne\u011fi<\/span><\/h2>\n

      Korelasyon matrisinin nelerden olu\u015ftu\u011funu ve nas\u0131l yorumland\u0131\u011f\u0131n\u0131 tam olarak anlamak i\u00e7in bu b\u00f6l\u00fcmde bir korelasyon matrisi \u00f6rne\u011fini analiz edece\u011fiz: <\/p>\n

      \n
      \"korelasyon<\/figure>\n<\/div>\n

      Korelasyon matrisinin yorumlanmas\u0131 katsay\u0131lar\u0131n de\u011ferlerine dayanmaktad\u0131r. B\u00f6ylece, en g\u00fc\u00e7l\u00fc korelasyonun, A de\u011fi\u015fkeni ile B de\u011fi\u015fkeni aras\u0131ndaki ili\u015fki oldu\u011funu g\u00f6rebiliriz, \u00e7\u00fcnk\u00fc buna kar\u015f\u0131l\u0131k gelen katsay\u0131 en b\u00fcy\u00fckt\u00fcr (0,87).<\/p>\n

      \u00d6te yandan, C de\u011fi\u015fkeninin neredeyse hi\u00e7bir de\u011fi\u015fkenle korelasyonu yoktur, \u00e7\u00fcnk\u00fc t\u00fcm katsay\u0131lar\u0131 s\u0131f\u0131ra \u00e7ok yak\u0131nd\u0131r ve bu nedenle \u00e7ok d\u00fc\u015f\u00fckt\u00fcr. Dolay\u0131s\u0131yla analizi basitle\u015ftirmek i\u00e7in bu de\u011fi\u015fkeni istatistiksel \u00e7al\u0131\u015fmadan \u00e7\u0131karmay\u0131 bile d\u00fc\u015f\u00fcnebiliriz.<\/p>\n

      Benzer \u015fekilde D de\u011fi\u015fkeninin di\u011fer de\u011fi\u015fkenlerle olan t\u00fcm ili\u015fkileri negatiftir, yani D de\u011fi\u015fkeni ile di\u011fer de\u011fi\u015fkenler aras\u0131ndaki korelasyon terstir. Bu, de\u011fi\u015fkenin ortadan kald\u0131r\u0131lmas\u0131 gerekti\u011fi anlam\u0131na gelmez, sadece D de\u011fi\u015fkeninin negatif korelasyona sahip oldu\u011fu anlam\u0131na gelir.<\/p>\n

      G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi korelasyon matrisi, verileri \u00f6zetlemek ve veri k\u00fcmesindeki farkl\u0131 de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkinin genel analizini yapmak i\u00e7in olduk\u00e7a kullan\u0131\u015fl\u0131d\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"

      Bu makalede korelasyon matrisinin ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve korelasyon matrisinin nas\u0131l yorumlanaca\u011f\u0131n\u0131 ke\u015ffedeceksiniz. Ek olarak korelasyon matrisinin yorumlanmas\u0131na ili\u015fkin somut bir \u00f6rnek g\u00f6rebileceksiniz. Korelasyon matrisi nedir? Korelasyon matrisi, i,j konumunda i ve j de\u011fi\u015fkenleri aras\u0131ndaki korelasyon katsay\u0131s\u0131n\u0131 i\u00e7eren bir matristir. Dolay\u0131s\u0131yla korelasyon matrisi, ana k\u00f6\u015fegen \u00fczerindekilerle dolu bir kare matris olup, i sat\u0131r\u0131 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-85","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n\u25b7 Korelasyon matrisi: nedir, form\u00fcl, yorum,...<\/title>\n<meta name=\"description\" content=\"Burada korelasyon matrisinin ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve nas\u0131l yorumland\u0131\u011f\u0131n\u0131 \u00f6\u011freneceksiniz. Korelasyon matrisinin somut bir \u00f6rne\u011fiyle.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/korelasyon-matrisi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Korelasyon matrisi: nedir, form\u00fcl, yorum,...\" \/>\n<meta property=\"og:description\" content=\"Burada korelasyon matrisinin ne oldu\u011funu, form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve nas\u0131l yorumland\u0131\u011f\u0131n\u0131 \u00f6\u011freneceksiniz. 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Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/85","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=85"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/85\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=85"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=85"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=85"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}