{"id":305,"date":"2023-08-02T19:59:18","date_gmt":"2023-08-02T19:59:18","guid":{"rendered":"https:\/\/statorials.org\/tr\/basit-dogrusal-regresyon\/"},"modified":"2023-08-02T19:59:18","modified_gmt":"2023-08-02T19:59:18","slug":"basit-dogrusal-regresyon","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/basit-dogrusal-regresyon\/","title":{"rendered":"Basit do\u011frusal regresyon"},"content":{"rendered":"

Bu makalede istatistikte basit do\u011frusal regresyonun ne oldu\u011fu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Benzer \u015fekilde, \u00e7\u00f6z\u00fclm\u00fc\u015f basit bir do\u011frusal regresyon al\u0131\u015ft\u0131rmas\u0131 ve buna ek olarak \u00e7evrimi\u00e7i olarak basit bir do\u011frusal regresyon hesaplay\u0131c\u0131s\u0131 bulacaks\u0131n\u0131z. <\/p>\n

<\/span> Basit do\u011frusal regresyon nedir?<\/span><\/h2>\n

Basit do\u011frusal regresyon,<\/strong> ba\u011f\u0131ms\u0131z bir de\u011fi\u015fkeni ili\u015fkilendirmek i\u00e7in kullan\u0131lan istatistiksel bir modeldir ve iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi yakla\u015f\u0131k olarak tahmin etmeye \u00e7al\u0131\u015f\u0131r\u0131z.<\/p>\n

Bu nedenle, iki de\u011fi\u015fkeni do\u011frusal olarak ili\u015fkilendiren bir denklem bulmak i\u00e7in basit do\u011frusal regresyon kullan\u0131l\u0131r. Mant\u0131ksal olarak iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkinin do\u011frusal olmas\u0131 gerekir, aksi halde ba\u015fka t\u00fcr bir regresyon modelinin kullan\u0131lmas\u0131 gerekir.<\/p>\n

Basit bir do\u011frusal regresyon modelinin denklemi iki katsay\u0131dan olu\u015fur: denklemin sabiti (b 0<\/sub> ) ve iki de\u011fi\u015fken aras\u0131ndaki korelasyon katsay\u0131s\u0131 (b 1<\/sub> ). Bu nedenle, basit bir do\u011frusal regresyon modelinin denklemi y=b 0<\/sub> +b 1<\/sub> x’tir.<\/p>\n<\/p>\n

\"y=b_0+b_1x\"<\/p>\n<\/p>\n

Basit bir do\u011frusal regresyon denklemi d\u00fcz bir \u00e7izgi olarak grafi\u011fe ge\u00e7irilmi\u015ftir, dolay\u0131s\u0131yla b 0<\/sub> katsay\u0131s\u0131 kesim noktas\u0131d\u0131r ve b 1<\/sub> katsay\u0131s\u0131 da \u00e7izginin e\u011fimidir. <\/p>\n

<\/span> Basit do\u011frusal regresyon form\u00fclleri<\/span><\/h2>\n

Basit bir do\u011frusal regresyonun katsay\u0131lar\u0131n\u0131 hesaplamak i\u00e7in form\u00fcller<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n

\"basit<\/figure>\n

\ud83d\udc49Herhangi bir veri seti i\u00e7in basit do\u011frusal regresyonun katsay\u0131lar\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesini kullanabilirsiniz.<\/u><\/p>\n

A\u00e7\u0131k\u00e7as\u0131, basit do\u011frusal regresyon modelinden elde edilen denklem t\u00fcm g\u00f6zlemlerin kesin de\u011ferini tahmin edemeyecek \u00e7\u00fcnk\u00fc bu model sadece iki de\u011fi\u015fken aras\u0131ndaki ili\u015fkiye yakla\u015fan bir denklem bulmaya \u00e7al\u0131\u015f\u0131yor. B\u00f6ylece art\u0131k, ger\u00e7ek de\u011fer ile do\u011frusal regresyon modeliyle tahmin edilen de\u011fer aras\u0131ndaki fark olarak tan\u0131mlan\u0131r.<\/p>\n<\/p>\n

\"e_i=y_i-\\widehat{y}_i\"<\/p>\n<\/p>\n

Basit bir do\u011frusal regresyon modelinin amac\u0131n\u0131n art\u0131klar\u0131n karelerini en aza indirmek oldu\u011funu, yani basit do\u011frusal regresyonun en k\u00fc\u00e7\u00fck kareler<\/a> kriterine dayand\u0131\u011f\u0131n\u0131 unutmay\u0131n. <\/p>\n

<\/span> Basit do\u011frusal regresyonun somut \u00f6rne\u011fi<\/span><\/h2>\n

Basit do\u011frusal regresyon y\u00f6ntemini anlamay\u0131 tamamlamak i\u00e7in, burada basit bir do\u011frusal regresyon modelinin denkleminin bir dizi istatistiksel veriden hesapland\u0131\u011f\u0131 pratik, ad\u0131m ad\u0131m bir \u00f6rnek verilmi\u015ftir.<\/p>\n

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  • \u0130statistik s\u0131nav\u0131na girdikten sonra be\u015f \u00f6\u011frenciye s\u0131nava ka\u00e7 saat \u00e7al\u0131\u015ft\u0131klar\u0131 soruldu. Veriler a\u015fa\u011f\u0131daki tabloda sunulmaktad\u0131r. \u00c7al\u0131\u015fma saatlerini al\u0131nan notla do\u011frusal olarak ili\u015fkilendirmek i\u00e7in toplanan istatistiksel verilerin basit bir do\u011frusal regresyon modelini ger\u00e7ekle\u015ftirin. <\/li>\n<\/ul>\n
    \"\"<\/figure>\n

    Basit bir do\u011frusal regresyon modeli ger\u00e7ekle\u015ftirmek i\u00e7in denklemin b 0<\/sub> ve b 1<\/sub> katsay\u0131lar\u0131n\u0131 belirlemeli ve bunun i\u00e7in yukar\u0131daki b\u00f6l\u00fcmde g\u00f6r\u00fclen form\u00fclleri kullanmal\u0131y\u0131z.<\/p>\n

    Ancak basit do\u011frusal regresyon form\u00fcllerini uygulamak i\u00e7in \u00f6ncelikle ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin ortalamas\u0131n\u0131 ve ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin ortalamas\u0131n\u0131 hesaplamam\u0131z gerekir:<\/p>\n<\/p>\n

    \"\\begin{array}{c}\\overline{x}=\\cfrac{11+5+10+12+7}{5}=9\\\\[4ex]\\overline{y}=\\cfrac{7+4+5+8+6}{5}=6\\end{array}\"<\/p>\n<\/p>\n

    Art\u0131k de\u011fi\u015fkenlerin ortalamas\u0131n\u0131 bildi\u011fimize g\u00f6re, ilgili form\u00fcl\u00fc kullanarak modelin b 1<\/sub> katsay\u0131s\u0131n\u0131 hesapl\u0131yoruz:<\/p>\n<\/p>\n

    \"\\begin{array}{c}b_1=\\cfrac{\\displaystyle<\/p>\n<\/p>\n

    Son olarak, ilgili form\u00fcl\u00fc kullanarak modelin b 0<\/sub> katsay\u0131s\u0131n\u0131 hesapl\u0131yoruz:<\/p>\n<\/p>\n

    \"\\begin{array}{l}b_0=\\overline{y}-b_1\\overline{x}\\\\[3ex]b_0=6-0,4412\\cdot<\/p>\n<\/p>\n

    K\u0131sacas\u0131 problemin basit do\u011frusal regresyon modelinin denklemi \u015f\u00f6yledir:<\/p>\n<\/p>\n

    \"y=2,0294+0,4412x\"<\/p>\n<\/p>\n

    A\u015fa\u011f\u0131da \u00f6rnek verilerin grafiksel g\u00f6sterimini ve basit do\u011frusal regresyon modelinin d\u00fcz \u00e7izgisini g\u00f6rebilirsiniz: <\/p>\n

    \"basit<\/figure>\n

    Son olarak basit do\u011frusal regresyon modelinin denklemini hesaplad\u0131ktan sonra geriye kalan tek \u015fey elde edilen sonucu yorumlamakt\u0131r. Bunun i\u00e7in regresyon modelinin belirleme katsay\u0131s\u0131n\u0131n hesaplanmas\u0131 \u015fartt\u0131r, bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 sitemizde ilgili makaleyi arayarak g\u00f6rebilirsiniz. <\/p>\n

    <\/span> Basit Do\u011frusal Regresyon Varsay\u0131mlar\u0131<\/span><\/h2>\n

    Basit bir do\u011frusal regresyon ger\u00e7ekle\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131n kar\u015f\u0131lanmas\u0131 gerekir:<\/p>\n

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    • Ba\u011f\u0131ms\u0131zl\u0131k<\/strong> : G\u00f6zlenen kal\u0131nt\u0131lar birbirinden ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r. Model ba\u011f\u0131ms\u0131zl\u0131\u011f\u0131n\u0131 sa\u011flaman\u0131n yayg\u0131n bir yolu \u00f6rnekleme s\u00fcrecine rastgelelik eklemektir.<\/span><\/li>\n
    • Homoskedastisite<\/strong> : Art\u0131klar\u0131n varyanslar\u0131nda homojenlik olmal\u0131, yani art\u0131klar\u0131n de\u011fi\u015fkenli\u011fi sabit olmal\u0131d\u0131r.<\/span><\/li>\n
    • Normallik<\/strong> : Art\u0131klar\u0131n normal da\u011f\u0131lmas\u0131 veya ba\u015fka bir deyi\u015fle ortalamas\u0131 0 olan normal da\u011f\u0131l\u0131ma uymas\u0131 gerekir.<\/span><\/li>\n
    • Do\u011frusall\u0131k<\/strong> \u2013 Ba\u011f\u0131ms\u0131z de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fki do\u011frusal olmal\u0131d\u0131r.<\/span> <\/li>\n<\/ul>\n

      <\/span> Basit Do\u011frusal Regresyon Hesaplay\u0131c\u0131s\u0131<\/span><\/h2>\n

      \u0130ki de\u011fi\u015fken aras\u0131nda basit bir do\u011frusal regresyon modeli olu\u015fturmak i\u00e7in a\u015fa\u011f\u0131daki hesap makinesine \u00f6rnek bir veri ekleyin. Veri \u00e7iftlerini ay\u0131rman\u0131z gerekir, b\u00f6ylece ilk kutuda yaln\u0131zca ba\u011f\u0131ms\u0131z de\u011fi\u015fken X’in de\u011ferleri bulunur ve ikinci kutuda yaln\u0131zca ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y’nin de\u011ferleri bulunur.<\/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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      • Ba\u011f\u0131ms\u0131z de\u011fi\u015fken <\/li>\n<\/ul>\n