{"id":1258,"date":"2023-07-27T02:51:27","date_gmt":"2023-07-27T02:51:27","guid":{"rendered":"https:\/\/statorials.org\/tr\/kalinti\/"},"modified":"2023-07-27T02:51:27","modified_gmt":"2023-07-27T02:51:27","slug":"kalinti","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kalinti\/","title":{"rendered":"I\u0307statistiklerde art\u0131klar nelerdir?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Art\u0131k<\/strong> ,<a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">regresyon analizinde<\/a> g\u00f6zlemlenen bir de\u011fer ile tahmin edilen bir de\u011fer aras\u0131ndaki farkt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Art\u0131k = G\u00f6zlemlenen de\u011fer \u2013 Tahmin edilen de\u011fer<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Do\u011frusal regresyonun amac\u0131n\u0131n, bir veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken ile bir <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener noreferrer\">yan\u0131t de\u011fi\u015fkeni<\/a> aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7mek oldu\u011funu hat\u0131rlay\u0131n. Bunu yapmak i\u00e7in do\u011frusal regresyon, <em>en k\u00fc\u00e7\u00fck kareler regresyon \u00e7izgisi<\/em> ad\u0131 verilen, verilere en iyi &#8220;uyan&#8221; \u00e7izgiyi bulur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00e7izgi, veri setindeki her <a href=\"https:\/\/statorials.org\/tr\/istatistikte-gozlem\/\" target=\"_blank\" rel=\"noopener noreferrer\">g\u00f6zlem<\/a> i\u00e7in bir tahmin \u00fcretir ancak regresyon \u00e7izgisi taraf\u0131ndan yap\u0131lan tahminin, g\u00f6zlemlenen de\u011ferle <em>tam olarak<\/em> e\u015fle\u015fmesi pek olas\u0131 de\u011fildir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tahmin ile g\u00f6zlemlenen de\u011fer aras\u0131ndaki fark art\u0131kt\u0131r. G\u00f6zlemlenen de\u011ferleri \u00e7izer ve uygun regresyon \u00e7izgisini \u00fcst \u00fcste koyarsak, her g\u00f6zlem i\u00e7in art\u0131klar, g\u00f6zlem ile regresyon \u00e7izgisi aras\u0131ndaki dikey mesafe olacakt\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12422 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus1-1.png\" alt=\"\u0130statistiklerde art\u0131k \u00f6rne\u011fi\" width=\"487\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bir g\u00f6zlemin de\u011feri, regresyon \u00e7izgisi taraf\u0131ndan tahmin edilen de\u011ferden b\u00fcy\u00fckse, <strong>pozitif bir art\u0131k de\u011feri<\/strong> vard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tersine, e\u011fer de\u011feri regresyon \u00e7izgisi taraf\u0131ndan tahmin edilen de\u011ferden k\u00fc\u00e7\u00fckse, bir g\u00f6zlemin <strong>negatif bir kal\u0131nt\u0131s\u0131<\/strong> vard\u0131r.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12423 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus2.png\" alt=\"Pozitif veya negatif kal\u0131nt\u0131lar\" width=\"481\" height=\"376\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Baz\u0131 g\u00f6zlemlerin pozitif art\u0131klar\u0131 olacak, baz\u0131lar\u0131n\u0131n ise negatif art\u0131klar\u0131 olacak, ancak t\u00fcm art\u0131klar\u0131n toplam\u0131 <strong>s\u0131f\u0131ra<\/strong> e\u015fit olacak.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Art\u0131klar\u0131n hesaplanmas\u0131na \u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Toplamda 12 g\u00f6zlem i\u00e7eren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12424 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus3.png\" alt=\"\" width=\"153\" height=\"269\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu veri setine do\u011frusal bir regresyon \u00e7izgisi s\u0131\u011fd\u0131rmak i\u00e7in istatistiksel yaz\u0131l\u0131m ( R , Excel , Python , Stata vb. gibi) kullan\u0131rsak, en uygun \u00e7izginin \u015fu \u015fekilde ortaya \u00e7\u0131kt\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = 29,63 + 0,7553x<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu sat\u0131r\u0131 kullanarak X de\u011ferine g\u00f6re her Y de\u011feri i\u00e7in tahmin edilen de\u011feri hesaplayabiliriz. \u00d6rne\u011fin ilk g\u00f6zlemin tahmin edilen de\u011feri \u015f\u00f6yle olacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 29,63 + 0,7553*(8) = <strong>35,67<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra bu g\u00f6zlemin art\u0131\u011f\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Art\u0131k = G\u00f6zlemlenen de\u011fer \u2013 Tahmin edilen de\u011fer = 41 \u2013 35,67 = <strong>5,33<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Her g\u00f6zlem i\u00e7in art\u0131k de\u011feri bulmak amac\u0131yla bu i\u015flemi tekrarlayabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12425 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus4.png\" alt=\"Art\u0131klar nas\u0131l hesaplan\u0131r\" width=\"334\" height=\"267\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">G\u00f6zlemleri uygun regresyon \u00e7izgisiyle g\u00f6rselle\u015ftirmek i\u00e7in bir da\u011f\u0131l\u0131m grafi\u011fi olu\u015fturursak, baz\u0131 g\u00f6zlemlerin \u00e7izginin \u00fcst\u00fcnde, di\u011ferlerinin ise \u00e7izginin alt\u0131nda oldu\u011funu g\u00f6rece\u011fiz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12426 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus5.png\" alt=\"Art\u0131k grafi\u011fi olan regresyon \u00e7izgisi\" width=\"481\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Kal\u0131nt\u0131lar\u0131n \u00f6zellikleri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Kal\u0131nt\u0131lar a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir veri setindeki her g\u00f6zlemin kar\u015f\u0131l\u0131k gelen bir kal\u0131nt\u0131s\u0131 vard\u0131r. Yani, e\u011fer bir veri seti toplamda 100 g\u00f6zlem i\u00e7eriyorsa, model 100 tahmin edilen de\u011fer \u00fcretecek ve sonu\u00e7ta toplamda 100 art\u0131k elde edilecektir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">T\u00fcm art\u0131klar\u0131n toplam\u0131 s\u0131f\u0131rd\u0131r.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Art\u0131klar\u0131n ortalama de\u011feri s\u0131f\u0131rd\u0131r.<\/span><\/li>\n<\/ul>\n<h3> <strong>Kal\u0131nt\u0131lar pratikte nas\u0131l kullan\u0131l\u0131r?<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Uygulamada regresyonda art\u0131klar \u00fc\u00e7 farkl\u0131 nedenden dolay\u0131 kullan\u0131l\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Modelin yeterlili\u011fini de\u011ferlendirin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Uygun bir regresyon \u00e7izgisi \u00fcretti\u011fimizde, t\u00fcm karelerin toplam\u0131 olan <em>art\u0131k kareler toplam\u0131n\u0131 (RSS)<\/em> hesaplayabiliriz. RSS ne kadar d\u00fc\u015f\u00fck olursa, regresyon modeli verilere o kadar iyi uyar.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Normallik varsay\u0131m\u0131n\u0131 kontrol edin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener noreferrer\">Do\u011frusal regresyonun temel varsay\u0131mlar\u0131ndan<\/a> biri art\u0131klar\u0131n normal da\u011f\u0131ld\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu hipotezi test etmek i\u00e7in, bir modelin art\u0131klar\u0131n\u0131n normal da\u011f\u0131l\u0131ma uyup uymad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in kullanabilece\u011fimiz bir grafik t\u00fcr\u00fc olan QQ grafi\u011fini olu\u015fturabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Grafikteki noktalar kabaca d\u00fcz bir \u00e7apraz \u00e7izgi olu\u015fturuyorsa normallik varsay\u0131m\u0131 kar\u015f\u0131lanm\u0131\u015ft\u0131r.<\/span> <\/p>\n<figure id=\"attachment_9410\" aria-describedby=\"caption-attachment-9410\" style=\"width: 493px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-9410 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/qqplotpython1.png\" alt=\"\" width=\"493\" height=\"326\" srcset=\"\" sizes=\"auto, \"><figcaption id=\"caption-attachment-9410\" class=\"wp-caption-text\"> <span style=\"color: #000000;\"><strong>QQ Grafi\u011fi \u00d6rne\u011fi<\/strong><\/span><\/figcaption><\/figure>\n<p> <span style=\"color: #000000;\"><strong>3. E\u015f varyans varsay\u0131m\u0131n\u0131 kontrol edin.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Do\u011frusal regresyonun di\u011fer bir temel varsay\u0131m\u0131, art\u0131klar\u0131n her x seviyesinde sabit varyansa sahip olmas\u0131d\u0131r. Buna homoskedastisite denir. Durum b\u00f6yle olmad\u0131\u011f\u0131nda, art\u0131klar <a href=\"https:\/\/statorials.org\/tr\/degisen-varyans-regresyonu\/\" target=\"_blank\" rel=\"noopener noreferrer\">de\u011fi\u015fen varyanstan<\/a> muzdariptir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu varsay\u0131m\u0131n kar\u015f\u0131lan\u0131p kar\u015f\u0131lanmad\u0131\u011f\u0131n\u0131 kontrol etmek i\u00e7in, art\u0131klar\u0131 modelin tahmin edilen de\u011ferlerine g\u00f6re g\u00f6steren bir da\u011f\u0131l\u0131m grafi\u011fi olan bir <a href=\"https:\/\/statorials.org\/tr\/excelde-artik-iz-nasil-olusturulur\/\" target=\"_blank\" rel=\"noopener noreferrer\">art\u0131klar grafi\u011fi<\/a> olu\u015fturabiliriz.<\/span> <\/p>\n<figure id=\"attachment_12427\" aria-describedby=\"caption-attachment-12427\" style=\"width: 496px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-12427 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus6.png\" alt=\"Art\u0131k De\u011ferleri ve D\u00fczeltilmi\u015f De\u011ferleri Grafiklendirme \u00d6rne\u011fi\" width=\"496\" height=\"363\" srcset=\"\" sizes=\"auto, \"><figcaption id=\"caption-attachment-12427\" class=\"wp-caption-text\"> <span style=\"color: #000000;\"><strong>Art\u0131k De\u011ferleri ve D\u00fczeltilmi\u015f De\u011ferleri Grafiklendirme \u00d6rne\u011fi<\/strong><\/span><\/figcaption><\/figure>\n<p> <span style=\"color: #000000;\">E\u011fer art\u0131klar grafikte net bir trend olmadan yakla\u015f\u0131k olarak s\u0131f\u0131r etraf\u0131nda e\u015fit bir \u015fekilde da\u011f\u0131lm\u0131\u015fsa, o zaman genellikle e\u015fvaryans varsay\u0131m\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 s\u00f6yleriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">Basit Do\u011frusal Regresyona Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u00c7oklu Do\u011frusal Regresyona Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-varsayimlari\/\" target=\"_blank\" rel=\"noopener noreferrer\">Do\u011frusal regresyonun d\u00f6rt varsay\u0131m\u0131<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/excelde-artik-iz-nasil-olusturulur\/\" target=\"_blank\" rel=\"noopener noreferrer\">Excel&#8217;de Art\u0131k Grafik Nas\u0131l Olu\u015fturulur<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Art\u0131k ,regresyon analizinde g\u00f6zlemlenen bir de\u011fer ile tahmin edilen bir de\u011fer aras\u0131ndaki farkt\u0131r. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: Art\u0131k = G\u00f6zlemlenen de\u011fer \u2013 Tahmin edilen de\u011fer Do\u011frusal regresyonun amac\u0131n\u0131n, bir veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fken ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi \u00f6l\u00e7mek oldu\u011funu hat\u0131rlay\u0131n. Bunu yapmak i\u00e7in do\u011frusal regresyon, en k\u00fc\u00e7\u00fck kareler regresyon \u00e7izgisi ad\u0131 verilen, verilere [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1258","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0130statistiklerde art\u0131klar nelerdir? - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, birka\u00e7 \u00f6rnek de dahil olmak \u00fczere kal\u0131nt\u0131lar\u0131n h\u0131zl\u0131 bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\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\/kalinti\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0130statistiklerde art\u0131klar nelerdir? - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde, birka\u00e7 \u00f6rnek de dahil olmak \u00fczere kal\u0131nt\u0131lar\u0131n h\u0131zl\u0131 bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/kalinti\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T02:51:27+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus1-1.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=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/kalinti\/\",\"url\":\"https:\/\/statorials.org\/tr\/kalinti\/\",\"name\":\"\u0130statistiklerde art\u0131klar nelerdir? - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-27T02:51:27+00:00\",\"dateModified\":\"2023-07-27T02:51:27+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde, birka\u00e7 \u00f6rnek de dahil olmak \u00fczere kal\u0131nt\u0131lar\u0131n h\u0131zl\u0131 bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/kalinti\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/kalinti\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/kalinti\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"I\u0307statistiklerde art\u0131klar nelerdir?\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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