{"id":321,"date":"2023-08-02T13:13:50","date_gmt":"2023-08-02T13:13:50","guid":{"rendered":"https:\/\/statorials.org\/tr\/regresyon-denklemi\/"},"modified":"2023-08-02T13:13:50","modified_gmt":"2023-08-02T13:13:50","slug":"regresyon-denklemi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/regresyon-denklemi\/","title":{"rendered":"Regresyon denklemi"},"content":{"rendered":"<p>Bu makalede regresyon denkleminin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, bir regresyon denklemini nas\u0131l bulaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve son olarak herhangi bir veri seti i\u00e7in regresyon denklemini hesaplamak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini nas\u0131l bulaca\u011f\u0131n\u0131z\u0131 \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-ecuacion-de-regresion\"><\/span> Regresyon denklemi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Regresyon denklemi<\/strong> nokta grafi\u011fine en iyi uyan denklemdir, yani regresyon denklemi bir veri k\u00fcmesinin en iyi yakla\u015f\u0131m\u0131d\u0131r.<\/p>\n<p> Regresyon denklemi y=\u03b2 <sub>0<\/sub> +\u03b2 <sub>1<\/sub> x formundad\u0131r; burada \u03b2 <sub>0<\/sub> denklemin sabiti ve \u03b2 <sub>1<\/sub> denklemin e\u011fimidir.<\/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-83e43f626a469e9de3d5ecfed9a216ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\beta_0+\\beta_1x\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"100\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Regresyon denklemine bakarsan\u0131z, bu bir do\u011frunun denklemidir. Bu, \u00e7izgi do\u011frusal bir ili\u015fkiyi temsil etti\u011finden ba\u011f\u0131ms\u0131z de\u011fi\u015fken X ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y aras\u0131ndaki ili\u015fkinin do\u011frusal bir ili\u015fki olarak modellendi\u011fi anlam\u0131na gelir.<\/p>\n<p> B\u00f6ylece regresyon denklemi, bir veri setinin ba\u011f\u0131ms\u0131z de\u011fi\u015fkeni ile ba\u011f\u0131ml\u0131 de\u011fi\u015fkenini matematiksel olarak ili\u015fkilendirmemize olanak tan\u0131r. Regresyon denklemi genellikle her g\u00f6zlemin de\u011ferini kesin olarak belirleme yetene\u011fine sahip olmasa da yine de de\u011ferinin yakla\u015f\u0131k bir de\u011ferini elde etmek i\u00e7in kullan\u0131l\u0131r. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne-de-regression.png\" alt=\"regresyon denklemi\" class=\"wp-image-6708\" width=\"235\" height=\"219\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6nceki grafikte g\u00f6rebilece\u011finiz gibi regresyon denklemi, bir veri setinin e\u011filimini ve ba\u011f\u0131ms\u0131z de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131nda ne t\u00fcr bir ili\u015fkinin bulundu\u011funu g\u00f6rmemize yard\u0131mc\u0131 olur. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-ecuacion-de-regresion\"><\/span> Regresyon denklemi nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Basit do\u011frusal regresyon denkleminin katsay\u0131lar\u0131n\u0131 hesaplamak i\u00e7in form\u00fcller<\/strong> 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-459281504d26f92756115054ef567021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\beta_1=\\cfrac{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})(y_i-\\overline{y})}{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})^2}\\\\[12ex]\\beta_0=\\overline{y}-\\beta_1\\overline{x}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"176\" width=\"192\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c5ba513cc7e504bc674f76afa70a3442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\beta_0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> regresyon denkleminin sabitidir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dff50ab66b848b910ea781069cba1094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\beta_1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> regresyon denkleminin e\u011fimidir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> i verisinin ba\u011f\u0131ms\u0131z de\u011fi\u015fkeni X&#8217;in de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-761333a1d61654bd1cb5c7224b0d1994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> i verisinin ba\u011f\u0131ml\u0131 de\u011fi\u015fkeni Y&#8217;nin de\u011feridir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin de\u011ferlerinin ortalamas\u0131d\u0131r<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y&#8217;nin de\u011ferlerinin ortalamas\u0131d\u0131r. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-ecuacion-de-regresion\"><\/span> Regresyon denklemini hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> \u0130statistik s\u0131nav\u0131na girdikten sonra be\u015f \u00f6\u011frenciye s\u0131nava ka\u00e7 saat ders \u00e7al\u0131\u015ft\u0131klar\u0131 soruldu, veriler a\u015fa\u011f\u0131daki tabloda g\u00f6sterildi. \u00c7al\u0131\u015fma saatlerini al\u0131nan notla do\u011frusal olarak ili\u015fkilendirmek i\u00e7in toplanan istatistiksel verilerden regresyon denklemini hesaplay\u0131n. Daha sonra 8 saat ders \u00e7al\u0131\u015fan \u00f6\u011frencinin hangi notu alaca\u011f\u0131n\u0131 belirleyin. <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/donnees-de-regression-lineaire-simple.png\" alt=\"\" class=\"wp-image-6503\" width=\"213\" height=\"220\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6rnek verilere ili\u015fkin regresyon denklemini bulmak i\u00e7in denklemin b <sub>0<\/sub> ve b <sub>1<\/sub> katsay\u0131lar\u0131n\u0131 belirlememiz ve bunun i\u00e7in yukar\u0131daki b\u00f6l\u00fcmde g\u00f6r\u00fclen form\u00fclleri kullanmam\u0131z gerekir.<\/p>\n<p> Ancak do\u011frusal regresyon denkleminin 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<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7a7aa6f1f20fa4ff0d61a2ad0dd2ea1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\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}\" title=\"Rendered by QuickLaTeX.com\" height=\"105\" width=\"226\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Art\u0131k de\u011fi\u015fkenlerin ortalamas\u0131n\u0131 bildi\u011fimize g\u00f6re, ilgili form\u00fcl\u00fc kullanarak modelin \u03b2 <sub>1<\/sub> katsay\u0131s\u0131n\u0131 hesapl\u0131yoruz:<\/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-d9407478d6d590c0d970ac41963f6fbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\beta_1=\\cfrac{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})(y_i-\\overline{y})}{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})^2}\\\\[10ex] \\beta_1=\\cfrac{\\begin{array}{c}(11-9)(7-6)+(5-9)(4-6)+(10-9)(5-6)+\\\\+(12-9)(8-6)+(7-9)(6-6)\\end{array}}{(11-9)^2+(5-9)^2+(10-9)^2+(12-9)^2+(7-9)^2}\\\\[6ex]\\beta_1=0,4412\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"264\" width=\"461\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Son olarak, ilgili form\u00fcl\u00fc kullanarak modelin \u03b2 <sub>0<\/sub> katsay\u0131s\u0131n\u0131 hesapl\u0131yoruz:<\/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-a8872fb5b9904b106d02b504ae36bb92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\beta_0=\\overline{y}-\\beta_1\\overline{x}\\\\[3ex]\\beta_0=6-0,4412\\cdot 9 \\\\[3ex]\\beta_0=2,0294\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"146\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> K\u0131saca problemin do\u011frusal regresyon \u00e7izgisinin denklemi 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-7097952b105295743a390d0332e7a2b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2,0294+0,4412x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> A\u015fa\u011f\u0131da basit do\u011frusal regresyon modeli denklemiyle birlikte \u00f6rnek verilerin grafiksel g\u00f6sterimini g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-regression-lineaire-simple.png\" alt=\"do\u011frusal regresyon \u00e7izgisi \u00f6rne\u011fi\" class=\"wp-image-6517\" width=\"454\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Regresyon denklemini hesaplad\u0131ktan sonra, 8 saat ders \u00e7al\u0131\u015fan bir \u00f6\u011frencinin alaca\u011f\u0131 notu tahmin etmek i\u00e7in bu de\u011feri elde edilen regresyon denkleminde yerine koyman\u0131z yeterlidir:<\/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-d1ef36c064448262d7c58b7f51b215c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2,0294+0,4412\\cdot 8=5,56\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"239\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece ger\u00e7ekle\u015ftirilen do\u011frusal regresyon modeline g\u00f6re bir \u00f6\u011frenci sekiz saat ders \u00e7al\u0131\u015f\u0131rsa s\u0131navdan 5,56 puan alacakt\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-ecuacion-de-regresion\"><\/span> Regresyon denklemi hesaplay\u0131c\u0131s\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Regresyon denkleminizi hesaplamak 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&#8217;in de\u011ferleri bulunur ve ikinci kutuda yaln\u0131zca ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y&#8217;nin de\u011ferleri bulunur.<\/p>\n<p> Veriler bir bo\u015flukla ayr\u0131lmal\u0131 ve ondal\u0131k ay\u0131r\u0131c\u0131 olarak nokta kullan\u0131larak girilmelidir.<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li> Ba\u011f\u0131ms\u0131z de\u011fi\u015fken <\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"1 4 8 5 7.2 9 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la variable explicativa aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li> Ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y: <\/li>\n<\/ul>\n<p><textarea name=\"datosY\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"2 5 7 3 2 1 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la variable respuesta aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Hesaplamak\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ecuacion-de-regresion-lineal-multiple\"><\/span> \u00c7oklu do\u011frusal regresyon denklemi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Basit do\u011frusal regresyon denkleminin ne oldu\u011funu az \u00f6nce g\u00f6rd\u00fck, ancak regresyon modeli ayn\u0131 zamanda iki veya daha fazla ba\u011f\u0131ms\u0131z de\u011fi\u015fken i\u00e7eren \u00e7oklu do\u011frusal regresyon modeli de olabilir. B\u00f6ylece \u00e7oklu do\u011frusal regresyon, bir\u00e7ok a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenin bir yan\u0131t de\u011fi\u015fkenine do\u011frusal olarak ba\u011flanmas\u0131n\u0131 m\u00fcmk\u00fcn k\u0131lar.<\/p>\n<p> <strong>\u00c7oklu do\u011frusal regresyon modelinin denklemi<\/strong> \u015f\u00f6yledir:<\/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-fd3ba8386b5954b654ca555774108ac0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\beta_0+\\beta_1 x_1+\\beta_2 x_2+\\dots+\\beta_m x_m+\\varepsilon\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"305\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> ba\u011f\u0131ml\u0131 de\u011fi\u015fkendir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> ba\u011f\u0131ms\u0131z de\u011fi\u015fken i&#8217;dir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c5ba513cc7e504bc674f76afa70a3442_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\beta_0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e7oklu do\u011frusal regresyon denkleminin sabitidir.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ff540c55c6ee8f10a1dab8e2422947ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\beta_i\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> de\u011fi\u015fkenle ili\u015fkili regresyon 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-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-29b8f7fac5f2df4b101dff63e95516c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\varepsilon}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> hata veya art\u0131kt\u0131r, yani g\u00f6zlemlenen de\u011fer ile model taraf\u0131ndan tahmin edilen de\u011fer aras\u0131ndaki farkt\u0131r.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> modeldeki de\u011fi\u015fkenlerin toplam say\u0131s\u0131d\u0131r.<\/li>\n<\/ul>\n<p> Toplamda bir \u00f6rne\u011fimiz varsa<\/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-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> g\u00f6zlemlere dayanarak \u00e7oklu do\u011frusal regresyon modelini matris bi\u00e7iminde ortaya koyabiliriz:<\/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-5848686c8ed0857f16e7e24e2a31024e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix}y_1\\\\y_2\\\\\\vdots\\\\y_n\\end{pmatrix}=\\begin{pmatrix}1&amp;x_{11}&amp;\\dots&amp;x_{1m}\\\\1&amp;x_{21}&amp;\\dots&amp;x_{2m}\\\\ \\vdots&amp;\\vdots&amp;\\ddots&amp;\\vdots\\\\1&amp;x_{n1}&amp;\\dots&amp;x_{nm}\\end{pmatrix}\\cdot\\begin{pmatrix}\\beta_0\\\\\\beta_1\\\\\\vdots\\\\\\beta_m\\end{pmatrix}+\\begin{pmatrix}\\varepsilon_1\\\\\\varepsilon_2\\\\\\vdots\\\\\\varepsilon_n\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"96\" width=\"370\" style=\"vertical-align: -43px;\"><\/p>\n<\/p>\n<p> Yukar\u0131daki matris ifadesi, her matrise bir harf atanarak yeniden yaz\u0131labilir:<\/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-7614ddbb78ced2e2b8b6c7642d9969c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Y=X\\beta+\\varepsilon\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece, en k\u00fc\u00e7\u00fck kareler kriterini uygulayarak <strong>\u00e7oklu do\u011frusal regresyon denkleminin katsay\u0131lar\u0131n\u0131 tahmin etmek i\u00e7in form\u00fcle<\/strong> ula\u015fabiliriz:<\/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-b6ef097cee722e7355fa4eb77b7ea3e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{\\beta}=\\left(X^tX\\right)^{-1}X^tY\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"146\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Ancak bu form\u00fcl\u00fcn uygulanmas\u0131 \u00e7ok zahmetli ve zaman al\u0131c\u0131d\u0131r, bu nedenle pratikte \u00e7oklu regresyon modelinin \u00e7ok daha h\u0131zl\u0131 olu\u015fturulmas\u0131na olanak tan\u0131yan bilgisayar yaz\u0131l\u0131mlar\u0131n\u0131n (Minitab veya Excel gibi) kullan\u0131lmas\u0131 tavsiye edilir. <\/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\/coklu-dogrusal-regresyon-1\/\">\u00c7oklu do\u011frusal regresyon nedir?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede regresyon denkleminin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. Benzer \u015fekilde, bir regresyon denklemini nas\u0131l bulaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve son olarak herhangi bir veri seti i\u00e7in regresyon denklemini hesaplamak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini nas\u0131l bulaca\u011f\u0131n\u0131z\u0131 \u00f6\u011freneceksiniz. Regresyon denklemi nedir? Regresyon denklemi nokta grafi\u011fine en iyi uyan denklemdir, yani regresyon denklemi bir [&hellip;]<\/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-321","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Regresyon denklemi<\/title>\n<meta name=\"description\" content=\"Burada regresyon denkleminin ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl), \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ve regresyon denklemi hesaplay\u0131c\u0131s\u0131n\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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