{"id":306,"date":"2023-08-02T19:28:35","date_gmt":"2023-08-02T19:28:35","guid":{"rendered":"https:\/\/statorials.org\/tr\/en-kucuk-kareler\/"},"modified":"2023-08-02T19:28:35","modified_gmt":"2023-08-02T19:28:35","slug":"en-kucuk-kareler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/en-kucuk-kareler\/","title":{"rendered":"Alt kareler"},"content":{"rendered":"<p>Bu makale istatistikte en k\u00fc\u00e7\u00fck karelerin ne oldu\u011funu, en k\u00fc\u00e7\u00fck kareler y\u00f6nteminin ne oldu\u011funu ve bir regresyon modelinin en k\u00fc\u00e7\u00fck kareler kriterine nas\u0131l uydu\u011funu a\u00e7\u0131klamaktad\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-metodo-de-los-minimos-cuadrados\"><\/span> En k\u00fc\u00e7\u00fck kareler y\u00f6ntemi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>En k\u00fc\u00e7\u00fck kareler y\u00f6ntemi,<\/strong> bir regresyonun denklemini belirlemek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir. Ba\u015fka bir deyi\u015fle en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, regresyon denklemi hesaplan\u0131rken elde edilen hatay\u0131 en aza indirmek i\u00e7in regresyon modelinde kullan\u0131lan bir kriterdir.<\/p>\n<p> Somut olarak en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, art\u0131klar\u0131n kareleri toplam\u0131n\u0131n en aza indirilmesinden olu\u015fur, ba\u015fka bir deyi\u015fle regresyon modelinin \u00f6ng\u00f6rd\u00fc\u011f\u00fc de\u011ferler ile g\u00f6zlenen de\u011ferler aras\u0131ndaki farklar\u0131n kareleri toplam\u0131n\u0131n en aza indirilmesine dayan\u0131r. . . A\u015fa\u011f\u0131da bir regresyon modelinin en k\u00fc\u00e7\u00fck kareler kriterine nas\u0131l uydu\u011funu detayl\u0131 olarak g\u00f6rece\u011fiz.<\/p>\n<p> En k\u00fc\u00e7\u00fck kareler y\u00f6nteminin temel \u00f6zelli\u011fi, g\u00f6zlenen de\u011ferler ile regresyon fonksiyonu aras\u0131ndaki en uzun mesafelerin en aza indirilmesidir. Di\u011fer regresyon kriterlerinden farkl\u0131 olarak, en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, b\u00fcy\u00fck bir say\u0131n\u0131n karesi k\u00fc\u00e7\u00fck bir say\u0131n\u0131n karesinden \u00e7ok daha b\u00fcy\u00fck oldu\u011fundan, b\u00fcy\u00fck art\u0131klar\u0131 en aza indirmenin k\u00fc\u00e7\u00fck art\u0131klardan daha \u00f6nemli oldu\u011funu d\u00fc\u015f\u00fcnmektedir. say\u0131.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"error-de-estimacion\"><\/span> Tahmin hatas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> En k\u00fc\u00e7\u00fck kareler kavram\u0131n\u0131 tam olarak anlamak i\u00e7in \u00f6ncelikle bir regresyon modelinde art\u0131klar\u0131n ne oldu\u011fu konusunda net olmam\u0131z gerekir. Bu nedenle a\u015fa\u011f\u0131da tahmin hatas\u0131n\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<p> \u0130statistikte, <strong>art\u0131k<\/strong> olarak da adland\u0131r\u0131lan <strong>tahmin hatas\u0131<\/strong> , ger\u00e7ek de\u011fer ile regresyon modelinin uydurdu\u011fu de\u011fer aras\u0131ndaki farkt\u0131r. Dolay\u0131s\u0131yla istatistiksel art\u0131k \u015fu \u015fekilde hesaplan\u0131r:<\/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-2028e64ca2c0035860e93c4bf244e2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i=y_i-\\widehat{y}_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" 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-550848dfdd05b5c6464d4e22fbf52486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> i verisinin kal\u0131nt\u0131s\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-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 ger\u00e7ek 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-a990a8fe969bd365cba7899d3d1c4406_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{y}_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> i verileri i\u00e7in regresyon modeli taraf\u0131ndan sa\u011flanan de\u011ferdir.<\/li>\n<\/ul>\n<p> Dolay\u0131s\u0131yla, bir veri par\u00e7as\u0131n\u0131n kal\u0131nt\u0131s\u0131 ne kadar b\u00fcy\u00fck olursa, regresyon modelinin bu veri par\u00e7as\u0131na uyarlanmas\u0131 o kadar zay\u0131f olur. Dolay\u0131s\u0131yla art\u0131k ne kadar k\u00fc\u00e7\u00fck olursa, ger\u00e7ek de\u011feri ile tahmin edilen de\u011feri aras\u0131ndaki mesafe de o kadar k\u00fc\u00e7\u00fck olur.<\/p>\n<p> Benzer \u015fekilde, bir verinin kal\u0131nt\u0131s\u0131 pozitifse bu, regresyon modelinin ger\u00e7ek de\u011ferden daha d\u00fc\u015f\u00fck bir de\u011fer \u00f6ng\u00f6rd\u00fc\u011f\u00fc anlam\u0131na gelir. Kal\u0131nt\u0131n\u0131n negatif olmas\u0131 ise tahmin edilen de\u011ferin ger\u00e7ek de\u011ferden b\u00fcy\u00fck oldu\u011fu anlam\u0131na gelir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"minimizar-los-cuadrados-de-los-errores\"><\/span> Hata karelerini en aza indirin<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k istatistikte kal\u0131nt\u0131n\u0131n ne oldu\u011funu bildi\u011fimize g\u00f6re hata karelerinin nas\u0131l en aza indirildi\u011fini anlamak daha kolay olacakt\u0131r.<\/p>\n<p> <strong>Bir hatan\u0131n karesi,<\/strong> bir art\u0131\u011f\u0131n karesidir, dolay\u0131s\u0131yla bir hatan\u0131n karesi, ger\u00e7ek de\u011fer ile ikinin kuvvetine y\u00fckseltilmi\u015f regresyon modelinin uydurdu\u011fu de\u011fer aras\u0131ndaki farka e\u015fittir.<\/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-f16302b9c06981bd49aad51ca8924592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i^2=(y_i-\\widehat{y}_i)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" style=\"vertical-align: -5px;\"><\/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-56f396eccc309c513ef34dc82f6fcd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> i verisinin kal\u0131nt\u0131s\u0131n\u0131n karesidir.<\/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 ger\u00e7ek 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-a990a8fe969bd365cba7899d3d1c4406_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{y}_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> i verileri i\u00e7in regresyon modeli taraf\u0131ndan sa\u011flanan de\u011ferdir.<\/li>\n<\/ul>\n<p> B\u00f6ylece en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, <strong>hatalar\u0131n karelerinin toplam\u0131n\u0131 en aza indirerek<\/strong> bir regresyon modeli olu\u015fturmaktan ibarettir. Bu nedenle en k\u00fc\u00e7\u00fck kareler kriteri a\u015fa\u011f\u0131daki ifadenin minimizasyonuna dayanmaktad\u0131r:<\/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-0a82d4d723b77093b4d584609f372cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\begin{array}{l} [MIN] \\ \\displaystyle \\sum_{i=1}^ne_i^2\\\\[4ex][MIN] \\ \\displaystyle \\sum_{i=1}^n(y_i-\\widehat{y}_i)^2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"116\" width=\"158\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bu nedenle en k\u00fc\u00e7\u00fck kareler kriterine en k\u00fc\u00e7\u00fck kareler kriteri de denilmektedir.<\/p>\n<p> \u00d6nceki form\u00fclde de g\u00f6rebilece\u011finiz gibi, en k\u00fc\u00e7\u00fck kareler kriteri, k\u00fc\u00e7\u00fck art\u0131klardan ziyade b\u00fcy\u00fck kal\u0131nt\u0131lar\u0131n minimizasyonuna daha fazla \u00f6nem vermektedir. \u00d6rne\u011fin, bir kal\u0131nt\u0131 3 ve di\u011fer bir kal\u0131nt\u0131 5 ise, bunlar\u0131n kareleri s\u0131ras\u0131yla 9 ve 25 olur, dolay\u0131s\u0131yla en k\u00fc\u00e7\u00fck kareler kriteri, birinci kal\u0131nt\u0131dan \u00f6nce ikinci kal\u0131nt\u0131n\u0131n en aza indirilmesine \u00f6ncelik verecektir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ajuste-por-minimos-cuadrados\"><\/span> En k\u00fc\u00e7\u00fck kareler ayar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>En k\u00fc\u00e7\u00fck kareler kriterini kullanarak bir regresyon modelinin yerle\u015ftirilmesi,<\/strong> art\u0131klar\u0131n karelerini en aza indiren bir regresyon modelinin bulunmas\u0131ndan olu\u015fur. Bu nedenle regresyon modelinden elde edilen denklem, g\u00f6zlenen de\u011ferler ile uydurulan de\u011ferler aras\u0131ndaki farklar\u0131n kareleri minimum olan bir denklem olacakt\u0131r.<\/p>\n<p> A\u015fa\u011f\u0131daki \u00f6rnekte, bir regresyon modeli olu\u015fturmak i\u00e7in daha fazla kriterin bulundu\u011funu ve se\u00e7ilen kritere ba\u011fl\u0131 olarak regresyon denkleminin farkl\u0131 oldu\u011funu unutmay\u0131n. <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"650\" height=\"355\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ajustement-par-les-moindres-carres.png\" alt=\"en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, en k\u00fc\u00e7\u00fck kareler ayarlamas\u0131\" class=\"wp-image-6548\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6nceki \u00f6rneklerde de g\u00f6r\u00fcld\u00fc\u011f\u00fc gibi ayn\u0131 veri seti i\u00e7in do\u011frusal regresyon modelinden elde edilen do\u011fru, se\u00e7ilen kritere ba\u011fl\u0131d\u0131r. Regresyon modellerinde genel olarak en k\u00fc\u00e7\u00fck kareler kriteri kullan\u0131lmaktad\u0131r.<\/p>\n<p> \u0130statistikte en yayg\u0131n kullan\u0131lan regresyon modeli, ba\u011f\u0131ms\u0131z de\u011fi\u015fken X ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y aras\u0131ndaki ili\u015fkiyi d\u00fcz bir \u00e7izgi kullanarak tahmin etmekten olu\u015fan basit do\u011frusal regresyon modelidir.<\/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-92da05e7be03363fecef8974393a84fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=b_0+b_1x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla, bir veri k\u00fcmesini basit bir do\u011frusal regresyon modeline s\u0131\u011fd\u0131rmaya y\u00f6nelik form\u00fcller \u015funlard\u0131r:<\/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> Basit bir do\u011frusal regresyon modelinin en k\u00fc\u00e7\u00fck kareler kriteri kullan\u0131larak nas\u0131l hesapland\u0131\u011f\u0131na dair bir \u00f6rne\u011fi a\u015fa\u011f\u0131daki ba\u011flant\u0131ya t\u0131klayarak 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 \u00f6rne\u011fi<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte en k\u00fc\u00e7\u00fck karelerin ne oldu\u011funu, en k\u00fc\u00e7\u00fck kareler y\u00f6nteminin ne oldu\u011funu ve bir regresyon modelinin en k\u00fc\u00e7\u00fck kareler kriterine nas\u0131l uydu\u011funu a\u00e7\u0131klamaktad\u0131r. En k\u00fc\u00e7\u00fck kareler y\u00f6ntemi nedir? En k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, bir regresyonun denklemini belirlemek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir. Ba\u015fka bir deyi\u015fle en k\u00fc\u00e7\u00fck kareler y\u00f6ntemi, regresyon denklemi hesaplan\u0131rken elde edilen [&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-306","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>\u25b7En k\u00fc\u00e7\u00fck kareler<\/title>\n<meta name=\"description\" content=\"Burada istatistikte en k\u00fc\u00e7\u00fck kareler y\u00f6nteminin ne oldu\u011funu ve en k\u00fc\u00e7\u00fck kareler kriterini kullanarak bir regresyon modelinin nas\u0131l uydurulaca\u011f\u0131n\u0131 ke\u015ffedeceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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