{"id":80,"date":"2023-08-05T17:04:07","date_gmt":"2023-08-05T17:04:07","guid":{"rendered":"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/"},"modified":"2023-08-05T17:04:07","modified_gmt":"2023-08-05T17:04:07","slug":"kovaryans-matrisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/","title":{"rendered":"Kovaryans matrisi"},"content":{"rendered":"<p>Bu makalede kovaryans matrisinin ne oldu\u011fu ve form\u00fcl\u00fcn\u00fcn ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Somut bir \u00f6rnekle kovaryans matrisinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 ve kovaryans matrislerinin \u00f6zelliklerini ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-matriz-de-covarianza\"><\/span> Kovaryans matrisi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Kovaryans matrisi,<\/strong> elemanlar\u0131 incelenen de\u011fi\u015fkenlerin varyanslar\u0131 ve kovaryanslar\u0131 olan bir kare matristir. B\u00f6ylece kovaryans matrisinin ana k\u00f6\u015fegeninin elemanlar\u0131 her bir de\u011fi\u015fkenin varyans\u0131n\u0131, geri kalan elemanlar ise de\u011fi\u015fkenler aras\u0131ndaki kovaryanslar\u0131 olu\u015fturur.<\/p>\n<p> \u0130statistikte kovaryans matrisi, iki veya daha fazla rastgele de\u011fi\u015fken aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in kullan\u0131l\u0131r. Kovaryans matrisi \u00e7ok kullan\u0131\u015fl\u0131d\u0131r \u00e7\u00fcnk\u00fc de\u011fi\u015fkenlerin t\u00fcm kovaryanslar\u0131n\u0131n de\u011ferlerini ayn\u0131 anda g\u00f6rebildi\u011finiz i\u00e7in bir\u00e7ok de\u011fi\u015fken aras\u0131ndaki korelasyonu h\u0131zl\u0131 bir \u015fekilde yorumlaman\u0131za olanak tan\u0131r.<\/p>\n<p> Kovaryans matrisinin sembol\u00fc, b\u00fcy\u00fck Yunan harfi sigma&#8217;d\u0131r (\u03a3). <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-matriz-de-covarianza\"><\/span> Kovaryans matrisi nas\u0131l hesaplan\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u00c7e\u015fitli istatistiksel de\u011fi\u015fkenlerin <strong>kovaryans matrisini hesaplamak<\/strong> i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar ger\u00e7ekle\u015ftirilmelidir:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">T\u00fcm de\u011fi\u015fkenlerin varyanslar\u0131n\u0131 hesaplay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Her de\u011fi\u015fken \u00e7iftinin kovaryans\u0131n\u0131 hesaplay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\">Kovaryans matrisini olu\u015fturun:<\/span><\/li>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\"><em>i<\/em> de\u011fi\u015fkeninin varyans\u0131 matrisin ana k\u00f6\u015fegenine, daha do\u011frusu <em>i,i<\/em> konumuna yerle\u015ftirilmelidir.<\/span><\/li>\n<li style=\"margin-bottom:8px\"> <span style=\"color:#101010;font-weight: normal;\"><em>i<\/em> ve <em>j<\/em> de\u011fi\u015fkenleri aras\u0131ndaki kovaryans matrisin <em>i,j<\/em> konumuna yerle\u015ftirilmelidir.<\/span><\/li>\n<\/ul>\n<\/ol>\n<p> Dolay\u0131s\u0131yla <strong>kovaryans matrisinin form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/matrice-de-covariance.png\" alt=\"kovaryans matrisi\" class=\"wp-image-1714\" width=\"602\" height=\"219\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-matriz-de-covarianza\"><\/span> Kovaryans Matrisi \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kovaryans matrisinin tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra a\u015fa\u011f\u0131da ad\u0131m ad\u0131m bir al\u0131\u015ft\u0131rma bulacaks\u0131n\u0131z, b\u00f6ylece bu t\u00fcr matrislerin nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz.<\/p>\n<p> De\u011ferleri a\u015fa\u011f\u0131daki gibi olan X, Y ve Z de\u011fi\u015fkenlerinin kovaryans matrisini hesaplar:<\/p>\n<ul>\n<li> X: 4, 7, 12, 5, 7<\/li>\n<li> Ve: 9, 15, 19, 6, 8<\/li>\n<li> Z: 7, 2, 4, 6, 3<\/li>\n<\/ul>\n<p> Yapmam\u0131z gereken ilk \u015fey t\u00fcm de\u011fi\u015fkenlerin varyanslar\u0131n\u0131 belirlemektir: <\/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-246675afb851649ad3289cc9fdd86de8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=7,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\"><\/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-04c40f4402759ea0ba6b1507f0865564_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(Y)=23,44\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/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-3b9aa0b6c1af85b98c41d6e91c2d42ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(Z)=3,44\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/varyans\/\">bo\u015fluk hesaplay\u0131c\u0131<\/a><\/div>\n<p> \u0130kinci olarak, her bir de\u011fi\u015fken \u00e7ifti aras\u0131ndaki kovaryans\u0131 buluyoruz: <\/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-997ada9147a8e29f8e808795aebb7c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)=11,2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -5px;\"><\/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-e7c4b2aa6cd24dabf9c4538030f30b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Z)=-2,6\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" style=\"vertical-align: -5px;\"><\/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-3f9c1dab7f4691d9a35e56e3e166d919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(Y,Z)=-4,36\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/kovaryans\/\">kovaryans hesaplay\u0131c\u0131s\u0131<\/a><\/div>\n<p> Ve t\u00fcm varyanslar\u0131 ve kovaryanslar\u0131 hesaplad\u0131ktan sonra geriye kalan tek \u015fey kovaryans matrisini olu\u015fturmakt\u0131r. Bunu yapmak i\u00e7in varyans de\u011ferlerini matrisin ana k\u00f6\u015fegenine ve kovaryans de\u011ferlerini kar\u015f\u0131l\u0131k gelen konumlar\u0131na yerle\u015ftiririz:<\/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-3a423b40ad6d25b57327b1f3dccd5df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Sigma=\\begin{pmatrix}Var(X)&amp;Cov(X,Y)&amp;Cov(X,Z)\\\\[1.5ex]Cov(Y,X)&amp;Var(Y)&amp;Cov(Y,Z)\\\\[1.5ex]Cov(Z,X)&amp;Cov(Z,Y)&amp;Var(Z)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"342\" style=\"vertical-align: 0px;\"><\/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-d90c58cc3c8ecef6a85c88196e1dd08d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Sigma=\\begin{pmatrix}7,6&amp;11,2&amp;-2,6\\\\[1.5ex]11,2&amp;23,44&amp;-4,36\\\\[1.5ex]-2,6&amp;-4,36&amp;3,44\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"231\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi varyanslar\u0131 ve kovaryanslar\u0131 bir matriste temsil ederek de\u011fi\u015fkenleri yorumlamak \u00e7ok kolayd\u0131r. En b\u00fcy\u00fck da\u011f\u0131l\u0131ma sahip de\u011fi\u015fken Y&#8217;dir (23.44), di\u011fer taraftan X ve Y de\u011fi\u015fkenleri aras\u0131nda do\u011frudan ili\u015fki bulunurken, X ve Z (dolay\u0131s\u0131yla Y ve Z) de\u011fi\u015fkenleri aras\u0131nda ters ili\u015fki bulunmaktad\u0131r.<\/p>\n<p> \u0130ki de\u011fi\u015fken aras\u0131ndaki kovaryans de\u011fi\u015fkenlerin s\u0131ras\u0131na ba\u011fl\u0131 olmad\u0131\u011f\u0131ndan kovaryans matrisinin her zaman simetrik oldu\u011funu unutmay\u0131n. \u00d6rne\u011fin,<\/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-eba027bd1998d2c1dbe59f1b512ab953_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(X,Y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<p> e\u015fittir<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-def16a63c06994394f83cdc040bea555_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Cov(Y,X).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ayr\u0131ca kovaryans matrisi her zaman kare bir matris olacak ve boyutu de\u011fi\u015fken say\u0131s\u0131na e\u015fit olacakt\u0131r. Bu durumda \u00fc\u00e7 de\u011fi\u015fkenimiz vard\u0131 ve bu y\u00fczden bu 3&#215;3&#8217;l\u00fck bir matris, ancak yaln\u0131zca iki de\u011fi\u015fkenimiz olsayd\u0131 kovaryans matrisi 2&#215;2 olurdu. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-matriz-de-covarianza\"><\/span> Kovaryans matrisinin \u00f6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kovaryans matrisi a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul>\n<li> Kovaryans matrisi, de\u011fi\u015fken say\u0131s\u0131 mertebesinde bir kare matristir.<\/li>\n<li> Kovaryans matrisi simetriktir, yani matrisin ana k\u00f6\u015fegeni bir simetri eksenidir.<\/li>\n<li> Kovaryans matrisi her zaman pozitif yar\u0131 tan\u0131ml\u0131d\u0131r.<\/li>\n<li> Kovaryans matrisinin determinant\u0131 s\u0131f\u0131ra e\u015fit veya s\u0131f\u0131rdan b\u00fcy\u00fckt\u00fcr.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede kovaryans matrisinin ne oldu\u011fu ve form\u00fcl\u00fcn\u00fcn ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Somut bir \u00f6rnekle kovaryans matrisinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 ve kovaryans matrislerinin \u00f6zelliklerini ke\u015ffedeceksiniz. Kovaryans matrisi nedir? Kovaryans matrisi, elemanlar\u0131 incelenen de\u011fi\u015fkenlerin varyanslar\u0131 ve kovaryanslar\u0131 olan bir kare matristir. B\u00f6ylece kovaryans matrisinin ana k\u00f6\u015fegeninin elemanlar\u0131 her bir de\u011fi\u015fkenin varyans\u0131n\u0131, geri kalan elemanlar ise de\u011fi\u015fkenler aras\u0131ndaki kovaryanslar\u0131 [&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-80","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 Kovaryans matrisi nedir? (form\u00fcl ve \u00f6rnek)<\/title>\n<meta name=\"description\" content=\"Bu makalede kovaryans matrisinin ne oldu\u011fu ve form\u00fcl\u00fcn\u00fcn ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Somut bir \u00f6rnekle kovaryans matrisinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 ve kovaryans matrislerinin \u00f6zelliklerini ke\u015ffedeceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Kovaryans matrisi nedir? (form\u00fcl ve \u00f6rnek)\" \/>\n<meta property=\"og:description\" content=\"Bu makalede kovaryans matrisinin ne oldu\u011fu ve form\u00fcl\u00fcn\u00fcn ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. Somut bir \u00f6rnekle kovaryans matrisinin nas\u0131l olu\u015fturulaca\u011f\u0131n\u0131 ve kovaryans matrislerinin \u00f6zelliklerini ke\u015ffedeceksiniz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-05T17:04:07+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/matrice-de-covariance.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/\",\"url\":\"https:\/\/statorials.org\/tr\/kovaryans-matrisi\/\",\"name\":\"\u25b7 Kovaryans matrisi nedir? 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