{"id":1469,"date":"2023-07-26T06:37:52","date_gmt":"2023-07-26T06:37:52","guid":{"rendered":"https:\/\/statorials.org\/tr\/sst-ssr-sse\/"},"modified":"2023-07-26T06:37:52","modified_gmt":"2023-07-26T06:37:52","slug":"sst-ssr-sse","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/sst-ssr-sse\/","title":{"rendered":"Karelerin toplam\u0131na i\u0307li\u015fkin nazik bir k\u0131lavuz: sst, ssr, sse"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/dogrusal-regresyon-1\/\" target=\"_blank\" rel=\"noopener\">Do\u011frusal regresyon,<\/a> bir veri k\u00fcmesine en iyi &#8220;uyan&#8221; \u00e7izgiyi bulmak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Regresyon \u00e7izgisinin verilere ger\u00e7ekte ne kadar iyi uydu\u011funu \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla \u00fc\u00e7 farkl\u0131 <strong>kareler toplam\u0131<\/strong> de\u011feri kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Toplam Karelerin Toplam\u0131 (SST) \u2013<\/strong> Bireysel veri noktalar\u0131 (y <sub>i<\/sub> ) ile yan\u0131t de\u011fi\u015fkeninin ortalamas\u0131 ( <span style=\"border-top: 1px solid black;\">y<\/span> ) aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = \u03a3(y <sub>ben<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. Karelerin Toplam\u0131 Regresyon (SSR)<\/strong> \u2013 Tahmin edilen veri noktalar\u0131 (\u0177 <sub>i<\/sub> ) ile yan\u0131t de\u011fi\u015fkeninin ortalamas\u0131 ( <span style=\"border-top: 1px solid black;\">y<\/span> ) aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSR = \u03a3(\u0177 <sub>ben<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. Kareler Toplam\u0131 Hatas\u0131 (SSE)<\/strong> \u2013 Tahmin edilen veri noktalar\u0131 (\u0177 <sub>i<\/sub> ) ile g\u00f6zlemlenen veri noktalar\u0131 (y <sub>i<\/sub> ) aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>ben<\/sub> \u2013 y <sub>ben<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu \u00fc\u00e7 \u00f6nlem aras\u0131nda a\u015fa\u011f\u0131daki ili\u015fki vard\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>SST = SSR + SSE<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani bu \u00f6l\u00e7\u00fcmlerden ikisini biliyorsak \u00fc\u00e7\u00fcnc\u00fcy\u00fc hesaplamak i\u00e7in basit cebir kullanabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>SSR, SST ve R-Kare<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bazen belirleme katsay\u0131s\u0131 olarak da adland\u0131r\u0131lan <a href=\"https:\/\/statorials.org\/tr\/iyi-r-kare-degeri\/\" target=\"_blank\" rel=\"noopener\">R-kare<\/a> , do\u011frusal bir regresyon modelinin bir veri k\u00fcmesine ne kadar iyi uydu\u011funun bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr. <a href=\"https:\/\/statorials.org\/tr\/degiskenleri-aciklayici-yanitlar\/\" target=\"_blank\" rel=\"noopener\">Yan\u0131t<\/a> de\u011fi\u015fkenindeki, yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan a\u00e7\u0131klanabilen varyans\u0131n oran\u0131n\u0131 temsil eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">R-kare de\u011feri 0 ila 1 aras\u0131nda de\u011fi\u015febilir. 0 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hi\u00e7bir \u015fekilde a\u00e7\u0131klanamayaca\u011f\u0131n\u0131 g\u00f6sterir. 1 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hatas\u0131z olarak m\u00fckemmel bir \u015fekilde a\u00e7\u0131klanabilece\u011fini g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">SSR ve SST&#8217;yi kullanarak R kareyi \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>R kare = SSR \/ SST<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir regresyon modeli i\u00e7in SSR 137,5 ve SST 156 ise R kareyi \u015fu \u015fekilde hesaplar\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">R kare = 137,5 \/ 156 = 0,8814<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu bize yan\u0131t de\u011fi\u015fkenindeki de\u011fi\u015fimin %88,14&#8217;\u00fcn\u00fcn yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan a\u00e7\u0131klanabilece\u011fini g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>SST, SSR, SSE&#8217;yi hesaplay\u0131n:<\/strong><\/span> <span style=\"color: #000000;\"><strong>ad\u0131m ad\u0131m \u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Alt\u0131 farkl\u0131 \u00f6\u011frencinin okudu\u011fu saat say\u0131s\u0131n\u0131 ve final s\u0131nav puanlar\u0131n\u0131 g\u00f6steren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14549 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre1.png\" alt=\"\" width=\"211\" height=\"186\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Baz\u0131 istatistiksel yaz\u0131l\u0131mlar\u0131 ( <a href=\"https:\/\/statorials.org\/tr\/rde-basit-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">R<\/a> , <a href=\"https:\/\/statorials.org\/tr\/basit-dogrusal-regresyon-excel\/\" target=\"_blank\" rel=\"noopener\">Excel<\/a> , <a href=\"https:\/\/statorials.org\/tr\/pythonda-basit-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">Python<\/a> gibi) veya hatta elle kullanarak, en uygun \u00e7izginin \u015f\u00f6yle oldu\u011funu g\u00f6rebiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Puan = 66,615 + 5,0769*(Saat)<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14550 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre2.png\" alt=\"\" width=\"541\" height=\"405\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">En uygun denklemin do\u011frusunu \u00f6\u011frendikten sonra SST, SSR ve SSE&#8217;yi hesaplamak i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: Yan\u0131t de\u011fi\u015fkeninin ortalamas\u0131n\u0131 hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Yan\u0131t de\u011fi\u015fkeninin ( <span style=\"border-top: 1px solid black;\">y<\/span> ) ortalamas\u0131 <strong>81<\/strong> olarak ortaya \u00e7\u0131k\u0131yor.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14551 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre3.png\" alt=\"\" width=\"284\" height=\"185\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Her g\u00f6zlem i\u00e7in tahmin edilen de\u011feri hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra her \u00f6\u011frenci i\u00e7in \u00f6ng\u00f6r\u00fclen s\u0131nav puan\u0131n\u0131 () hesaplamak i\u00e7in en uygun denklem sat\u0131r\u0131n\u0131 kullanabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin bir saat ders \u00e7al\u0131\u015fan \u00f6\u011frenci i\u00e7in \u00f6ng\u00f6r\u00fclen s\u0131nav notu \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Puan = 66,615 + 5,0769*(1) = <strong>71,69<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her \u00f6\u011frenci i\u00e7in tahmin edilen puan\u0131 bulmak i\u00e7in ayn\u0131 yakla\u015f\u0131m\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14552 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre4.png\" alt=\"\" width=\"359\" height=\"185\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: Toplam kareler toplam\u0131n\u0131 (SST) hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra toplam karelerin toplam\u0131n\u0131 hesaplayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, ilk \u00f6\u011frenci i\u00e7in karelerin toplam\u0131 \u015fu \u015fekildedir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">(y <sub>ben<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup> = (68 \u2013 81) <sup>2<\/sup> = <strong>169<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her \u00f6\u011frencinin karelerinin toplam\u0131n\u0131 bulmak i\u00e7in ayn\u0131 yakla\u015f\u0131m\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14553 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre5.png\" alt=\"\" width=\"449\" height=\"243\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Toplam kareler toplam\u0131 <strong>316<\/strong> \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Kareler toplam\u0131 regresyonunu (SSR) hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra kareler toplam\u0131 regresyonunu hesaplayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, birinci \u00f6\u011frenci i\u00e7in kareler toplam\u0131 regresyonu \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">( <sub>\u0177i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup> = (71,69 \u2013 81) <sup>2<\/sup> = <b>86,64<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her \u00f6\u011frenci i\u00e7in kareler toplam\u0131n\u0131n regresyonunu bulmak i\u00e7in ayn\u0131 yakla\u015f\u0131m\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14554 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre6.png\" alt=\"\" width=\"518\" height=\"239\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Kareler toplam\u0131 regresyonu <strong>279,23<\/strong> olarak \u00e7\u0131k\u0131yor.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Kareler toplam\u0131 hatas\u0131n\u0131n (SSE) hesaplanmas\u0131.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra kareler toplam\u0131n\u0131n hatas\u0131n\u0131 hesaplayabiliriz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, birinci \u00f6\u011frencinin kareler toplam\u0131 hatas\u0131 \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">(\u0177 <sub>ben<\/sub> \u2013 y <sub>ben<\/sub> ) <sup>2<\/sup> = (71,69 \u2013 68) <sup>2<\/sup> = <b>13,63<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Her \u00f6\u011frenci i\u00e7in hatan\u0131n karelerinin toplam\u0131n\u0131 bulmak i\u00e7in ayn\u0131 yakla\u015f\u0131m\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14555 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/sommecarre7.png\" alt=\"Do\u011frusal regresyon i\u00e7in SST, SSR ve SSE'yi hesaplama \u00f6rne\u011fi\" width=\"606\" height=\"235\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">SST = SSR + SSE oldu\u011funu do\u011frulayabiliriz<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/li>\n<li> <span style=\"color: #000000;\">316 = 279,23 + 36,77<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Regresyon modelinin R karesini a\u015fa\u011f\u0131daki denklemi kullanarak da hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">R kare = SSR \/ SST<\/span><\/li>\n<li> <span style=\"color: #000000;\">R kare = 279,23 \/ 316<\/span><\/li>\n<li> <span style=\"color: #000000;\">R kare = 0,8836<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu bize s\u0131nav puanlar\u0131ndaki farkl\u0131l\u0131\u011f\u0131n <strong>%88,36&#8217;s\u0131n\u0131n<\/strong> \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131yla a\u00e7\u0131klanabilece\u011fini s\u00f6yl\u00fcyor.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Herhangi bir basit do\u011frusal regresyon \u00e7izgisi i\u00e7in SST, SSR ve SSE&#8217;yi otomatik olarak hesaplamak amac\u0131yla a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131lar\u0131 kullanabilirsiniz:<\/span><\/p>\n<p> SST hesaplay\u0131c\u0131<br \/> RSS hesaplay\u0131c\u0131<br \/> ESS hesaplay\u0131c\u0131<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do\u011frusal regresyon, bir veri k\u00fcmesine en iyi &#8220;uyan&#8221; \u00e7izgiyi bulmak i\u00e7in kullan\u0131l\u0131r. Regresyon \u00e7izgisinin verilere ger\u00e7ekte ne kadar iyi uydu\u011funu \u00f6l\u00e7mek i\u00e7in s\u0131kl\u0131kla \u00fc\u00e7 farkl\u0131 kareler toplam\u0131 de\u011feri kullan\u0131r\u0131z: 1. Toplam Karelerin Toplam\u0131 (SST) \u2013 Bireysel veri noktalar\u0131 (y i ) ile yan\u0131t de\u011fi\u015fkeninin ortalamas\u0131 ( y ) aras\u0131ndaki farklar\u0131n karelerinin toplam\u0131. SST = \u03a3(y [&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-1469","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>Karelerin Toplam\u0131na \u0130li\u015fkin Nazik Bir K\u0131lavuz: SST, SSR, SSE - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde SST, SSR ve SSE dahil olmak \u00fczere do\u011frusal regresyondaki kareler toplam\u0131n\u0131n ayr\u0131nt\u0131l\u0131 bir a\u00e7\u0131klamas\u0131 sunulmaktad\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\/sst-ssr-sse\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Karelerin Toplam\u0131na \u0130li\u015fkin Nazik Bir K\u0131lavuz: SST, SSR, SSE - 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