{"id":1892,"date":"2023-07-24T13:45:54","date_gmt":"2023-07-24T13:45:54","guid":{"rendered":"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/"},"modified":"2023-07-24T13:45:54","modified_gmt":"2023-07-24T13:45:54","slug":"oblicz-recznie-r-do-kwadratu","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/","title":{"rendered":"Jak r\u0119cznie obliczy\u0107 r-kwadrat"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">W statystyce <strong>R kwadrat<\/strong> (R <sup>2<\/sup> ) mierzy cz\u0119\u015b\u0107 wariancji<a href=\"https:\/\/statorials.org\/pl\/zmienne-odpowiedzi-wyjasniajace\/\" target=\"_blank\" rel=\"noopener\">zmiennej odpowiedzi<\/a> , kt\u00f3r\u0105 mo\u017cna wyja\u015bni\u0107 zmienn\u0105 predykcyjn\u0105 w modelu regresji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Do obliczenia R do kwadratu u\u017cywamy nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">R <sup>2<\/sup> = [ (n\u03a3xy \u2013 (\u03a3x)(\u03a3y)) \/ (\u221a <span style=\"border-top: 1px solid black;\">n\u03a3x <sup>2<\/sup> -(\u03a3x) <sup>2<\/sup><\/span> * \u221a <span style=\"border-top: 1px solid black;\">n\u03a3y <sup>2<\/sup> -(\u03a3y) <sup>2<\/sup><\/span> ) ] <sup>2<\/sup><\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje krok po kroku, jak r\u0119cznie obliczy\u0107 wsp\u00f3\u0142czynnik R-kwadrat dla danego modelu regresji.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 1: Utw\u00f3rz zbi\u00f3r danych<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Najpierw utw\u00f3rzmy zbi\u00f3r danych:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-18120 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/r2hand1.png\" alt=\"\" width=\"163\" height=\"289\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 2: Oblicz niezb\u0119dne wska\u017aniki<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczmy ka\u017cd\u0105 metryk\u0119, kt\u00f3rej potrzebujemy we wzorze <sup>R2<\/sup> :<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-18121 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/r2hand2.png\" alt=\"\" width=\"440\" height=\"300\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz R do kwadratu<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na koniec zintegrujemy ka\u017cd\u0105 metryk\u0119 ze wzorem na <sup>R2<\/sup> :<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">R <sup>2<\/sup> = [ (n\u03a3xy \u2013 (\u03a3x)(\u03a3y)) \/ (\u221a <span style=\"border-top: 1px solid black;\">n\u03a3x <sup>2<\/sup> -(\u03a3x) <sup>2<\/sup><\/span> * \u221a <span style=\"border-top: 1px solid black;\">n\u03a3y <sup>2<\/sup> -(\u03a3y) <sup>2<\/sup><\/span> ) ] <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\">R <sup>2<\/sup> = [ (8*(2169) \u2013 (72)(223)) \/ (\u221a <span style=\"border-top: 1px solid black;\">8*(818)-(72) <sup>2<\/sup><\/span> * \u221a <span style=\"border-top: 1px solid black;\">8*(6447)-(223) <sup>2<\/sup><\/span> ) ] <sup>2<\/sup><\/span><\/li>\n<li> <span style=\"color: #000000;\"><sup>R2<\/sup> = 0,6686<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Uwaga:<\/strong> <em>n<\/em> we wzorze reprezentuje liczb\u0119 obserwacji w zbiorze danych i w tym przyk\u0142adzie oznacza n = 8 obserwacji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zak\u0142adaj\u0105c, \u017ce <em>x<\/em> jest zmienn\u0105 predykcyjn\u0105, a <em>y<\/em> jest zmienn\u0105 odpowiedzi w tym modelu regresji, R-kwadrat modelu wynosi <strong>0,6686<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">To m\u00f3wi nam, \u017ce 66,86% zmienno\u015bci zmiennej <em>y<\/em> mo\u017cna wyja\u015bni\u0107 zmienn\u0105 <em>x<\/em> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/regresja-liniowa-1\/\" target=\"_blank\" rel=\"noopener\">Wprowadzenie do prostej regresji liniowej<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/wielokrotna-regresja-liniowa\/\" target=\"_blank\" rel=\"noopener\">Wprowadzenie do wielokrotnej regresji liniowej<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/r-vs-r-do-kwadratu\/\" target=\"_blank\" rel=\"noopener\">R vs R-Square: jaka jest r\u00f3\u017cnica?<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/dobra-wartosc-r-do-kwadratu\/\" target=\"_blank\" rel=\"noopener\">Jaka jest dobra warto\u015b\u0107 R-kwadrat?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>W statystyce R kwadrat (R 2 ) mierzy cz\u0119\u015b\u0107 wariancjizmiennej odpowiedzi , kt\u00f3r\u0105 mo\u017cna wyja\u015bni\u0107 zmienn\u0105 predykcyjn\u0105 w modelu regresji. Do obliczenia R do kwadratu u\u017cywamy nast\u0119puj\u0105cego wzoru: R 2 = [ (n\u03a3xy \u2013 (\u03a3x)(\u03a3y)) \/ (\u221a n\u03a3x 2 -(\u03a3x) 2 * \u221a n\u03a3y 2 -(\u03a3y) 2 ) ] 2 Poni\u017cszy przyk\u0142ad pokazuje krok po [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1892","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak r\u0119cznie obliczy\u0107 R-kwadrat - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak r\u0119cznie obliczy\u0107 wsp\u00f3\u0142czynnik r-kwadrat dla modelu regresji, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\" \/>\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\/pl\/oblicz-recznie-r-do-kwadratu\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak r\u0119cznie obliczy\u0107 R-kwadrat - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak r\u0119cznie obliczy\u0107 wsp\u00f3\u0142czynnik r-kwadrat dla modelu regresji, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-24T13:45:54+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/r2hand1.png\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuta\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/\",\"url\":\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/\",\"name\":\"Jak r\u0119cznie obliczy\u0107 R-kwadrat - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-24T13:45:54+00:00\",\"dateModified\":\"2023-07-24T13:45:54+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak r\u0119cznie obliczy\u0107 wsp\u00f3\u0142czynnik r-kwadrat dla modelu regresji, \u0142\u0105cznie z przyk\u0142adem krok po kroku.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/oblicz-recznie-r-do-kwadratu\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak r\u0119cznie obliczy\u0107 r-kwadrat\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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