{"id":2250,"date":"2023-07-23T02:09:39","date_gmt":"2023-07-23T02:09:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/regresyon-egiminin-standart-hatasi\/"},"modified":"2023-07-23T02:09:39","modified_gmt":"2023-07-23T02:09:39","slug":"regresyon-egiminin-standart-hatasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/regresyon-egiminin-standart-hatasi\/","title":{"rendered":"Regresyon e\u011fiminin standart hatas\u0131n\u0131 anlamak"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Bir regresyon e\u011fiminin standart hatas\u0131,<\/strong> bir regresyon e\u011fiminin tahmin edilmesindeki &#8220;belirsizli\u011fi&#8221; \u00f6l\u00e7menin bir yoludur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-20553 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand1.png\" alt=\"Regresyon e\u011fiminin standart hatas\u0131 form\u00fcl\u00fc\" width=\"239\" height=\"69\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : toplam \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y <sub>i<\/sub><\/strong> : yan\u0131t de\u011fi\u015fkeninin ger\u00e7ek de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0177 <sub>i<\/sub><\/strong> : yan\u0131t de\u011fi\u015fkeninin tahmin edilen de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>i<\/sub><\/strong> : tahmin de\u011fi\u015fkeninin ger\u00e7ek de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x\u0304<\/strong> : tahmin de\u011fi\u015fkeninin ortalama de\u011feri<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Standart hata ne kadar k\u00fc\u00e7\u00fck olursa, regresyon e\u011fimi i\u00e7in katsay\u0131 tahmini etraf\u0131ndaki de\u011fi\u015fkenlik de o kadar d\u00fc\u015f\u00fck olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Regresyon e\u011fiminin standart hatas\u0131, \u00e7o\u011fu istatistiksel yaz\u0131l\u0131m\u0131n regresyon \u00e7\u0131kt\u0131s\u0131nda bir &#8220;standart hata&#8221; s\u00fctununda g\u00f6r\u00fcnt\u00fclenecektir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20554 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand2.png\" alt=\"\" width=\"524\" height=\"315\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, bir regresyon e\u011fiminin standart hatas\u0131n\u0131n iki farkl\u0131 senaryoda nas\u0131l yorumlanaca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Regresyon E\u011fiminin K\u00fc\u00e7\u00fck Standart Hatas\u0131n\u0131 Yorumlama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir profes\u00f6r\u00fcn, ders saati say\u0131s\u0131 ile s\u0131n\u0131f\u0131ndaki \u00f6\u011frencilerin final s\u0131nav notlar\u0131 aras\u0131ndaki ili\u015fkiyi anlamak istedi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">25 \u00f6\u011frenciden veri toplar ve a\u015fa\u011f\u0131daki da\u011f\u0131l\u0131m grafi\u011fini olu\u015fturur:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20555 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand3.png\" alt=\"\" width=\"529\" height=\"328\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki de\u011fi\u015fken aras\u0131nda a\u00e7\u0131k\u00e7a pozitif bir ili\u015fki vard\u0131r. \u00c7al\u0131\u015f\u0131lan saat say\u0131s\u0131 artt\u0131k\u00e7a s\u0131nav puan\u0131 da olduk\u00e7a \u00f6ng\u00f6r\u00fclebilir bir oranda artmaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Daha sonra yorday\u0131c\u0131 de\u011fi\u015fken olarak \u00e7al\u0131\u015f\u0131lan saatleri ve yan\u0131t de\u011fi\u015fkeni olarak final s\u0131nav notunu kullanarak basit bir do\u011frusal regresyon modeli uygulad\u0131.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki tabloda regresyon sonu\u00e7lar\u0131 g\u00f6sterilmektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20556 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand4.png\" alt=\"\" width=\"533\" height=\"319\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Yorday\u0131c\u0131 de\u011fi\u015fken \u201c\u00e7al\u0131\u015fma saati\u201dnin katsay\u0131s\u0131 5.487&#8217;dir. Bu bize, \u00e7al\u0131\u015f\u0131lan her ek saatin s\u0131nav puan\u0131nda ortalama <strong>5.487<\/strong> puanl\u0131k bir art\u0131\u015fla ili\u015fkili oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart hata <strong>0,419&#8217;dur<\/strong> ve bu, regresyon e\u011fimi i\u00e7in bu tahmin etraf\u0131ndaki de\u011fi\u015fkenli\u011fin bir \u00f6l\u00e7\u00fcs\u00fcn\u00fc temsil eder.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu de\u011feri, &#8220;\u00e7al\u0131\u015f\u0131lan saat&#8221; yorday\u0131c\u0131 de\u011fi\u015fkenine ili\u015fkin t-istatisti\u011fini hesaplamak i\u00e7in kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">t istatisti\u011fi = katsay\u0131 tahmini \/ standart hata<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-istatisti\u011fi = 5,487 \/ 0,419<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-istatisti\u011fi = 13.112<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu test istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri 0,000 olup, &#8220;\u00e7al\u0131\u015f\u0131lan saat&#8221; ile final s\u0131nav notu aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fkinin oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Regresyon e\u011fiminin standart hatas\u0131, regresyon e\u011fiminin katsay\u0131 tahminine k\u0131yasla k\u00fc\u00e7\u00fck oldu\u011fundan, yorday\u0131c\u0131 de\u011fi\u015fken istatistiksel olarak anlaml\u0131yd\u0131.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Bir Regresyon E\u011fiminin B\u00fcy\u00fck Standart Hatas\u0131n\u0131n Yorumlanmas\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ba\u015fka bir profes\u00f6r\u00fcn, kendi s\u0131n\u0131f\u0131ndaki \u00f6\u011frencilerin ders saatleriyle final s\u0131nav notlar\u0131 aras\u0131ndaki ili\u015fkiyi anlamak istedi\u011fini varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">25 \u00f6\u011frenciden veri topluyor ve a\u015fa\u011f\u0131daki da\u011f\u0131l\u0131m grafi\u011fini olu\u015fturuyor:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20557 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand5.png\" alt=\"\" width=\"529\" height=\"329\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">\u0130ki de\u011fi\u015fken aras\u0131nda hafif pozitif bir ili\u015fki oldu\u011fu g\u00f6r\u00fclmektedir. \u00c7al\u0131\u015fma saati artt\u0131k\u00e7a s\u0131nav puan\u0131 da genel olarak art\u0131yor ancak \u00f6ng\u00f6r\u00fclebilir bir oranda de\u011fil.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Profes\u00f6r\u00fcn daha sonra yorday\u0131c\u0131 de\u011fi\u015fken olarak \u00e7al\u0131\u015f\u0131lan saatleri ve yan\u0131t de\u011fi\u015fkeni olarak final s\u0131nav notunu kullanarak basit bir do\u011frusal regresyon modeline uydu\u011funu varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki tabloda regresyon sonu\u00e7lar\u0131 g\u00f6sterilmektedir:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-20558 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/stand6.png\" alt=\"\" width=\"533\" height=\"320\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Yorday\u0131c\u0131 de\u011fi\u015fken \u201c\u00e7al\u0131\u015fma saati\u201dnin katsay\u0131s\u0131 1,7919&#8217;dur. Bu bize, \u00e7al\u0131\u015f\u0131lan her ek saatin s\u0131nav puan\u0131nda ortalama <strong>1,7919&#8217;luk<\/strong> bir art\u0131\u015fla ili\u015fkili oldu\u011funu s\u00f6yl\u00fcyor.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Standart hata <strong>1,0675&#8217;tir<\/strong> ve bu, regresyon e\u011fimi i\u00e7in bu tahmin etraf\u0131ndaki de\u011fi\u015fkenli\u011fin bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu de\u011feri, &#8220;\u00e7al\u0131\u015f\u0131lan saat&#8221; yorday\u0131c\u0131 de\u011fi\u015fkenine ili\u015fkin t-istatisti\u011fini hesaplamak i\u00e7in kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">t istatisti\u011fi = katsay\u0131 tahmini \/ standart hata<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-istatisti\u011fi = 1,7919 \/ 1,0675<\/span><\/li>\n<li> <span style=\"color: #000000;\">t-istatisti\u011fi = 1,678<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu test istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri 0,107&#8217;dir. Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131 i\u00e7in \u201c\u00e7al\u0131\u015f\u0131lan saat\u201d ile final s\u0131nav notu aras\u0131nda istatistiksel olarak anlaml\u0131 bir ili\u015fkinin olmad\u0131\u011f\u0131 anla\u015f\u0131lmaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Regresyon e\u011fiminin standart hatas\u0131, regresyon e\u011fiminin katsay\u0131 tahminine g\u00f6re b\u00fcy\u00fck oldu\u011fundan, yorday\u0131c\u0131 de\u011fi\u015fken istatistiksel olarak anlaml\u0131 <em>de\u011fildi<\/em> .<\/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\">Basit Do\u011frusal Regresyona Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/coklu-dogrusal-regresyon\/\" target=\"_blank\" rel=\"noopener\">\u00c7oklu Do\u011frusal Regresyona Giri\u015f<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/regresyon-yorumlama-tablosunu-okuyun\/\" target=\"_blank\" rel=\"noopener\">Regresyon Tablosu Nas\u0131l Okunmal\u0131 ve Yorumlanmal\u0131<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir regresyon e\u011fiminin standart hatas\u0131, bir regresyon e\u011fiminin tahmin edilmesindeki &#8220;belirsizli\u011fi&#8221; \u00f6l\u00e7menin bir yoludur. A\u015fa\u011f\u0131daki \u015fekilde hesaplan\u0131r: Alt\u0131n: n : toplam \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc y i : yan\u0131t de\u011fi\u015fkeninin ger\u00e7ek de\u011feri \u0177 i : yan\u0131t de\u011fi\u015fkeninin tahmin edilen de\u011feri x i : tahmin de\u011fi\u015fkeninin ger\u00e7ek de\u011feri x\u0304 : tahmin de\u011fi\u015fkeninin ortalama de\u011feri Standart hata ne kadar [&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-2250","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>Bir Regresyon E\u011fiminin Standart Hatas\u0131n\u0131 Anlamak - Statoryaller<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, bir regresyon e\u011fiminin standart hatas\u0131n\u0131n \u00f6rneklerle basit 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\/regresyon-egiminin-standart-hatasi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bir Regresyon E\u011fiminin Standart Hatas\u0131n\u0131 Anlamak - 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