{"id":312,"date":"2023-08-02T16:52:39","date_gmt":"2023-08-02T16:52:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/regresyon-katsayisi\/"},"modified":"2023-08-02T16:52:39","modified_gmt":"2023-08-02T16:52:39","slug":"regresyon-katsayisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/regresyon-katsayisi\/","title":{"rendered":"Regresyon katsay\u0131s\u0131"},"content":{"rendered":"<p>Bu makale istatistikte regresyon katsay\u0131lar\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Bu nedenle bir regresyon katsay\u0131s\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve de\u011ferinin nas\u0131l yorumlanaca\u011f\u0131n\u0131 ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-coeficiente-de-regresion\"><\/span> Regresyon katsay\u0131s\u0131 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Regresyon katsay\u0131s\u0131,<\/strong> bir regresyon modelindeki her a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenle ili\u015fkili de\u011ferdir. Yani regresyon katsay\u0131lar\u0131, bir regresyon denklemindeki a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenleri, her a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken bir regresyon katsay\u0131s\u0131na kar\u015f\u0131l\u0131k gelecek \u015fekilde \u00e7arpan de\u011ferlerdir.<\/p>\n<p> \u00d6rne\u011fin, bir regresyon modelinden elde edilen denklem y=3+2x <sub>1<\/sub> -7x <sub>2<\/sub> ise modelin regresyon katsay\u0131lar\u0131 3, 2 ve -7 olur. Denklem (3)&#8217;teki sabitin, herhangi bir de\u011fi\u015fkeni \u00e7arpmamas\u0131na ra\u011fmen, ayn\u0131 zamanda bir regresyon katsay\u0131s\u0131 olarak kabul edildi\u011fini unutmay\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-3e0b8b843c03868db62f87256174dd6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\color{blue}\\bm{3}\\color{black}+\\color{blue}\\bm{2}\\color{black}x_1\\color{blue}\\bm{-7}\\color{black}x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"345\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla, bir regresyon modelinde, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler (veya ba\u011f\u0131ms\u0131z de\u011fi\u015fkenler) art\u0131 model denklemindeki sabite kar\u015f\u0131l\u0131k gelen bir tane kadar regresyon katsay\u0131s\u0131 vard\u0131r.<\/p>\n<p> Ayr\u0131ca regresyon katsay\u0131s\u0131 ba\u011f\u0131ms\u0131z de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi g\u00f6sterir. \u00d6rne\u011fin bir regresyon katsay\u0131s\u0131n\u0131n pozitif olmas\u0131, ba\u011f\u0131ms\u0131z de\u011fi\u015fken artt\u0131k\u00e7a ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin de artaca\u011f\u0131 anlam\u0131na gelir. Ancak iki de\u011fi\u015fken aras\u0131ndaki ili\u015fki her zaman bu kadar do\u011frudan de\u011fildir. A\u015fa\u011f\u0131da bir regresyon katsay\u0131s\u0131n\u0131n nas\u0131l yorumlanaca\u011f\u0131n\u0131 g\u00f6rece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-coeficiente-de-regresion\"><\/span> Regresyon Katsay\u0131s\u0131 Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Basit bir do\u011frusal regresyon i\u00e7in denklemi \u015fu \u015fekildedir:<\/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-59539ee9a2d30ec4b1a2f75658c2123e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=b_0+b_1\\cdot x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"108\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Modelin iki regresyon katsay\u0131s\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan form\u00fcller 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-f4582a02500f36499fc60647a4dd5869_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b_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}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: -49px;\"><\/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-369b22bafb2489dc46579d38f5ac6917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b_0=\\overline{y}-b_1\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> A\u015fa\u011f\u0131daki ba\u011flant\u0131da regresyon katsay\u0131lar\u0131n\u0131n hesapland\u0131\u011f\u0131 \u00e7\u00f6z\u00fclm\u00fc\u015f bir problemi 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\/basit-dogrusal-regresyon\/\">Basit do\u011frusal regresyon al\u0131\u015ft\u0131rmas\u0131 \u00e7\u00f6z\u00fcld\u00fc<\/a><\/div>\n<p> \u00c7oklu do\u011frusal regresyon modelinin regresyon katsay\u0131lar\u0131n\u0131 hesaplamak istiyorsan\u0131z form\u00fcller \u00e7ok daha karma\u015f\u0131k oldu\u011fundan bilgisayar yaz\u0131l\u0131m\u0131n\u0131 kullanmak en iyisidir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-del-coeficiente-de-regresion\"><\/span> Regresyon katsay\u0131s\u0131n\u0131n yorumlanmas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k istatistikte regresyon katsay\u0131s\u0131n\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 bildi\u011fimize g\u00f6re, regresyon katsay\u0131s\u0131n\u0131n nas\u0131l yorumland\u0131\u011f\u0131na bakal\u0131m.<\/p>\n<p> Bir de\u011fi\u015fkenin <strong>regresyon katsay\u0131s\u0131n\u0131n yorumu<\/strong> basittir: A\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenlerin geri kalan\u0131 sabit kal\u0131rsa, a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkendeki bir art\u0131\u015f, katsay\u0131s\u0131n\u0131n i\u015faretinin pozitif veya pozitif olmas\u0131na ba\u011fl\u0131 olarak ba\u011f\u0131ml\u0131 de\u011fi\u015fkende bir art\u0131\u015fa veya azalmaya yol a\u00e7acakt\u0131r. pozitif. s\u0131ras\u0131yla negatif. .<\/p>\n<p> Dolay\u0131s\u0131yla a\u00e7\u0131klay\u0131c\u0131 bir de\u011fi\u015fkenin regresyon katsay\u0131s\u0131n\u0131n pozitif olmas\u0131, s\u00f6z konusu de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin pozitif bir korelasyona sahip oldu\u011fu anlam\u0131na gelir. \u00d6te yandan katsay\u0131n\u0131n negatif olmas\u0131 ba\u011f\u0131ms\u0131z de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fkenin negatif korelasyona sahip oldu\u011fu anlam\u0131na gelir.<\/p>\n<p> Ancak a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenler aras\u0131nda etkile\u015fim yoksa, yani a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenlerden biri de\u011fi\u015fti\u011finde di\u011fer de\u011fi\u015fkenler sabit kal\u0131yorsa t\u00fcm bunlar do\u011frudur. Aksi takdirde a\u00e7\u0131klay\u0131c\u0131 bir de\u011fi\u015fken ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkinin daha ayr\u0131nt\u0131l\u0131 olarak analiz edilmesi gerekir.<\/p>\n<p> Daha fazlas\u0131n\u0131 \u00f6\u011frenmek i\u00e7in a\u015fa\u011f\u0131daki makalemize g\u00f6z atabilirsiniz: <\/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\/korelasyon-turleri\/\">Korelasyon t\u00fcrleri<\/a><\/div>\n<p> Ek olarak, bir regresyon katsay\u0131s\u0131n\u0131 analiz ederken, kar\u015f\u0131l\u0131k gelen de\u011fi\u015fkenin do\u011frusal olup olmad\u0131\u011f\u0131n\u0131n dikkate al\u0131nmas\u0131 da \u00f6nemlidir. De\u011fi\u015fken do\u011frusal olmad\u0131\u011f\u0131 i\u00e7in de\u011fi\u015fkenin de\u011ferindeki bir de\u011fi\u015fiklik yan\u0131t de\u011fi\u015fkenini farkl\u0131 \u015fekilde etkileyecektir. \u00d6rne\u011fin, ikinci dereceden de\u011fi\u015fkenler, negatif de\u011ferleri pozitif de\u011ferlere d\u00f6n\u00fc\u015ft\u00fcr\u00fcr, dolay\u0131s\u0131yla ikinci dereceden bir de\u011fi\u015fken ne kadar negatif olursa, yan\u0131t de\u011fi\u015fkeni de o kadar b\u00fcy\u00fck olur. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"coeficiente-de-regresion-y-coeficiente-de-determinacion\"><\/span> Regresyon katsay\u0131s\u0131 ve belirleme katsay\u0131s\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak regresyon katsay\u0131s\u0131 ile belirleme katsay\u0131s\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rece\u011fiz \u00e7\u00fcnk\u00fc bunlar regresyon modellerinde \u00e7ok \u00f6nemli iki katsay\u0131d\u0131r ve anlamlar\u0131n\u0131n a\u00e7\u0131k olmas\u0131 gerekir.<\/p>\n<p> <strong>Belirleme katsay\u0131s\u0131 ( <sup>R2<\/sup> ),<\/strong> bir regresyon modelinin uyum iyili\u011fini \u00f6l\u00e7en bir istatistiktir. Basit\u00e7e ifade etmek gerekirse, belirleme katsay\u0131s\u0131 bir regresyon modelinin bir veri setine ne kadar iyi uydu\u011funu g\u00f6sterir.<\/p>\n<p> Dolay\u0131s\u0131yla <strong>regresyon katsay\u0131s\u0131 ile belirleme katsay\u0131s\u0131 aras\u0131ndaki fark,<\/strong> regresyon katsay\u0131s\u0131n\u0131n ba\u011f\u0131ms\u0131z bir de\u011fi\u015fken ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi g\u00f6stermesi, belirleme katsay\u0131s\u0131n\u0131n ise regresyon modelinin uyum iyili\u011fini g\u00f6stermesidir. . <\/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\/belirleme-katsayisi-r-kare\/\">Belirleme katsay\u0131s\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte regresyon katsay\u0131lar\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. Bu nedenle bir regresyon katsay\u0131s\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve de\u011ferinin nas\u0131l yorumlanaca\u011f\u0131n\u0131 ke\u015ffedeceksiniz. Regresyon katsay\u0131s\u0131 nedir? Regresyon katsay\u0131s\u0131, bir regresyon modelindeki her a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenle ili\u015fkili de\u011ferdir. Yani regresyon katsay\u0131lar\u0131, bir regresyon denklemindeki a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fkenleri, her a\u00e7\u0131klay\u0131c\u0131 de\u011fi\u015fken bir regresyon katsay\u0131s\u0131na kar\u015f\u0131l\u0131k gelecek \u015fekilde \u00e7arpan de\u011ferlerdir. \u00d6rne\u011fin, bir regresyon [&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-312","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 katsay\u0131s\u0131<\/title>\n<meta name=\"description\" content=\"Burada istatistikte regresyon katsay\u0131s\u0131n\u0131n ne oldu\u011funu, nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) 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