{"id":83,"date":"2023-08-05T16:23:19","date_gmt":"2023-08-05T16:23:19","guid":{"rendered":"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi-1\/"},"modified":"2023-08-05T16:23:19","modified_gmt":"2023-08-05T16:23:19","slug":"pearson-korelasyon-katsayisi-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/pearson-korelasyon-katsayisi-1\/","title":{"rendered":"Pearson korelasyon katsay\u0131s\u0131"},"content":{"rendered":"

Bu makalede Pearson korelasyon katsay\u0131s\u0131n\u0131n (veya do\u011frusal korelasyon katsay\u0131s\u0131n\u0131n) ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Pearson korelasyon katsay\u0131s\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rmayla ke\u015ffedeceksiniz. Ek olarak, herhangi bir veri setinin Pearson Korelasyon Katsay\u0131s\u0131 de\u011ferini, sondaki \u00e7evrimi\u00e7i hesaplay\u0131c\u0131y\u0131 kullanarak bulabilirsiniz. <\/p>\n

<\/span> Pearson korelasyon katsay\u0131s\u0131 nedir?<\/span><\/h2>\n

Do\u011frusal<\/strong> korelasyon katsay\u0131s\u0131 veya basit\u00e7e korelasyon katsay\u0131s\u0131<\/strong> olarak da adland\u0131r\u0131lan Pearson<\/strong> korelasyon katsay\u0131s\u0131, iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr.<\/p>\n

\u0130ki de\u011fi\u015fken aras\u0131ndaki Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in, s\u00f6z konusu de\u011fi\u015fkenlerin kovaryans\u0131n\u0131, varyanslar\u0131n\u0131n \u00e7arp\u0131m\u0131n\u0131n karek\u00f6k\u00fcne b\u00f6lmeniz gerekir.<\/p>\n

B\u00f6ylece Pearson korelasyon katsay\u0131s\u0131, iki niceliksel rastgele de\u011fi\u015fken aras\u0131ndaki do\u011frusal ba\u011f\u0131ml\u0131l\u0131\u011f\u0131 \u00f6l\u00e7meye \u00e7al\u0131\u015f\u0131r. \u00d6ncelikle, de\u011fi\u015fkenler aras\u0131ndaki korelasyonu say\u0131sal olarak de\u011ferlendirmek karma\u015f\u0131kt\u0131r \u00e7\u00fcnk\u00fc de\u011fi\u015fken \u00e7iftlerinin aras\u0131nda daha fazla korelasyon oldu\u011funu belirlemek zordur, e\u011fer pues’ta oldu\u011fu gibi Pearson korelasyon katsay\u0131s\u0131n\u0131n amac\u0131 de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi de\u011ferlendirebilmek i\u00e7in de\u011fi\u015fkenler aras\u0131ndaki ili\u015fkiyi de\u011ferlendirmekse aralar\u0131nda kar\u015f\u0131la\u015ft\u0131r\u0131n.<\/p>\n

Pearson korelasyon indeksinin de\u011feri -1 ile +1 aras\u0131ndad\u0131r. A\u015fa\u011f\u0131da Pearson korelasyon katsay\u0131s\u0131 de\u011ferinin nas\u0131l yorumland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz. <\/p>\n

<\/span> Pearson Korelasyon Katsay\u0131s\u0131 Form\u00fcl\u00fc<\/span><\/h2>\n

\u0130ki istatistiksel de\u011fi\u015fkenin Pearson 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.<\/strong><\/p>\n

Bu nedenle Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir: <\/p>\n

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

\ud83d\udc49Herhangi bir veri seti i\u00e7in Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u><\/p>\n

Pearson korelasyon katsay\u0131s\u0131 bir pop\u00fclasyon \u00fczerinde hesaplan\u0131rken genellikle Yunanca \u03c1 harfiyle ifade edilir. Ancak katsay\u0131 bir \u00f6rne\u011fe g\u00f6re hesaplan\u0131rken sembol olarak genellikle r harfi kullan\u0131l\u0131r.<\/p>\n

Pearson korelasyon katsay\u0131s\u0131n\u0131 belirlemek i\u00e7in iki de\u011fi\u015fken aras\u0131ndaki kovaryans\u0131 ve bir de\u011fi\u015fkenin varyans\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 bilmeniz gerekti\u011fini unutmay\u0131n. Ayr\u0131ca bu istatistiksel \u00f6l\u00e7\u00fcmlerin ne anlama geldi\u011fini de anlamal\u0131s\u0131n\u0131z. Bu nedenle a\u00e7\u0131klamaya devam etmeden \u00f6nce a\u015fa\u011f\u0131daki iki makalenin okunmas\u0131 tavsiye edilir: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> kovaryans nas\u0131l hesaplan\u0131r<\/a>
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> bo\u015fluk nas\u0131l hesaplan\u0131r<\/a> <\/div>\n

<\/span> Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplama \u00f6rne\u011fi<\/span><\/h2>\n

Pearson korelasyon katsay\u0131s\u0131n\u0131n tan\u0131m\u0131 ve form\u00fcl\u00fc g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in a\u015fa\u011f\u0131da ad\u0131m ad\u0131m bir \u00f6rnek verilmi\u015ftir.<\/p>\n

    \n
  • A\u015fa\u011f\u0131daki iki s\u00fcrekli de\u011fi\u015fken aras\u0131ndaki Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplay\u0131n: <\/li>\n<\/ul>\n
    \n
    \"\u00f6rnek<\/figure>\n<\/div>\n

    Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplamadan \u00f6nce, iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in veri k\u00fcmesini bir da\u011f\u0131l\u0131m grafi\u011finde temsil edece\u011fiz: <\/p>\n

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

    Sa\u00e7\u0131l\u0131m grafi\u011finden verilerin pozitif bir trende sahip olabilece\u011fi, yani bir de\u011fi\u015fkenin de\u011feri artt\u0131\u011f\u0131nda di\u011fer de\u011fi\u015fkenin de artt\u0131\u011f\u0131 sonucu \u00e7\u0131kar\u0131labilir. Korelasyonu kontrol etmek i\u00e7in Pearson katsay\u0131s\u0131n\u0131 bulaca\u011f\u0131z.<\/p>\n

    Yap\u0131lacak ilk \u015fey, her de\u011fi\u015fkenin aritmetik ortalamas\u0131n\u0131 ayr\u0131 ayr\u0131 bulmakt\u0131r; bu, verilerin toplam toplam\u0131n\u0131n g\u00f6zlem say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fde\u011ferdir.<\/p>\n<\/p>\n

    \"\\overline{x}=\\cfrac{\\displaystyle<\/p>\n<\/p>\n

    \"\\overline{y}=\\cfrac{\\displaystyle<\/p>\n<\/p>\n

    Art\u0131k her de\u011fi\u015fkenin ortalamas\u0131n\u0131 bildi\u011fimize g\u00f6re, a\u015fa\u011f\u0131daki s\u00fctunlar\u0131 veri tablosuna eklememiz gerekiyor: <\/p>\n

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

    Tabloda hesaplanan verilerden kovaryans ve varyanslar\u0131n de\u011ferlerini belirliyoruz (e\u011fer bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 hat\u0131rlam\u0131yorsan\u0131z yukar\u0131da bunun ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131kland\u0131\u011f\u0131 iki ba\u011flant\u0131 vard\u0131r): <\/p>\n<\/p>\n

    \"Cov(X,Y)=\\cfrac{\\displaystyle<\/p>\n<\/p>\n

    \"Var(X)=\\cfrac{\\displaystyle\\sum_{i=1}^n\\left(x_i-\\overline{x}\\right)^2}{n}=\\cfrac{44,1}{10}=4,41\"<\/p>\n<\/p>\n

    \"Var(Y)=\\cfrac{\\displaystyle\\sum_{i=1}^n\\left(y_i-\\overline{y}\\right)^2}{n}=\\cfrac{122,9}{10}=12,29\"<\/p>\n<\/p>\n

    Son olarak, de\u011ferini elde etmek i\u00e7in Pearson korelasyon katsay\u0131s\u0131 form\u00fcl\u00fcn\u00fc uygulaman\u0131z yeterlidir:<\/p>\n<\/p>\n

    \"\\rho_{XY}=\\cfrac{Cov(X,Y)}{\\sqrt{Var(X)\\cdot<\/p>\n<\/p>\n

    Pearson korelasyon katsay\u0131s\u0131 1’e \u00e7ok yak\u0131n bir de\u011fere sahiptir, bu da bu iki de\u011fi\u015fkenin olduk\u00e7a g\u00fc\u00e7l\u00fc bir pozitif korelasyona sahip oldu\u011fu anlam\u0131na gelir.<\/p>\n

    G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi Pearson korelasyon katsay\u0131s\u0131n\u0131 belirlemek i\u00e7in Excel gibi s\u00fctun hesaplamalar\u0131n\u0131 daha h\u0131zl\u0131 yapabilecek programlar kullanmak olduk\u00e7a faydal\u0131d\u0131r. <\/p>\n

    <\/span> Pearson Korelasyon Katsay\u0131s\u0131 Hesaplay\u0131c\u0131s\u0131<\/span><\/h2>\n

    \u0130ki de\u011fi\u015fken aras\u0131ndaki Pearson korelasyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine bir dizi istatistiksel veri girin. Veri \u00e7iftlerini, ilk kutuda yaln\u0131zca bir de\u011fi\u015fkenin de\u011ferleri olacak ve ikinci kutuda yaln\u0131zca ikinci de\u011fi\u015fkenin de\u011ferleri olacak \u015fekilde ay\u0131rman\u0131z gerekir.<\/p>\n

    Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir.<\/p>\n

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    • Rastgele de\u011fi\u015fken <\/li>\n<\/ul>\n