{"id":1310,"date":"2023-07-26T22:13:41","date_gmt":"2023-07-26T22:13:41","guid":{"rendered":"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/"},"modified":"2023-07-26T22:13:41","modified_gmt":"2023-07-26T22:13:41","slug":"standaryzowane-reszty-pythona","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/","title":{"rendered":"Jak obliczy\u0107 reszty standaryzowane w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Reszta<\/strong> to r\u00f3\u017cnica mi\u0119dzy warto\u015bci\u0105 obserwowan\u0105 a warto\u015bci\u0105 przewidywan\u0105 w <a href=\"https:\/\/statorials.org\/pl\/regresja-liniowa-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">modelu regresji<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Warto\u015b\u0107 rezydualna = Warto\u015b\u0107 obserwowana \u2013 Warto\u015b\u0107 przewidywana<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Je\u015bli wykre\u015blimy zaobserwowane warto\u015bci i na\u0142o\u017cymy dopasowan\u0105 lini\u0119 regresji, reszt\u0105 dla ka\u017cdej <a href=\"https:\/\/statorials.org\/pl\/obserwacja-w-statystyce\/\" target=\"_blank\" rel=\"noopener\">obserwacji<\/a> b\u0119dzie pionowa odleg\u0142o\u015b\u0107 mi\u0119dzy obserwacj\u0105 a lini\u0105 regresji:<\/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=\"Przyk\u0142ad reszty w statystyce\" width=\"487\" height=\"382\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Jeden z typ\u00f3w reszt, kt\u00f3rego cz\u0119sto u\u017cywamy do identyfikacji warto\u015bci odstaj\u0105cych w modelu regresji, nazywany jest <strong>reszt\u0105 standaryzowan\u0105<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>r <sub>ja<\/sub> = mi <sub>ja<\/sub> \/ s(e <sub>ja<\/sub> )<\/strong> = <strong>mi <sub>ja<\/sub> \/ RSE\u221a <span style=\"border-top: 1px solid black;\">1-h <sub>ii<\/sub><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>e <sub>i<\/sub> :<\/strong> i- <sup>ta<\/sup> reszta<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>RSE:<\/strong> resztkowy b\u0142\u0105d standardowy modelu<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>h <sub>ii<\/sub><\/strong> : Powstanie i <sup>-tej<\/sup> obserwacji<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">W praktyce cz\u0119sto za warto\u015b\u0107 odstaj\u0105c\u0105 uznajemy ka\u017cd\u0105 standaryzowan\u0105 reszt\u0119, kt\u00f3rej warto\u015b\u0107 bezwzgl\u0119dna jest wi\u0119ksza ni\u017c 3.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku przedstawiono krok po kroku przyk\u0142ad obliczania reszt standardowych w j\u0119zyku Python.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 1: Wprowad\u017a dane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Najpierw utworzymy ma\u0142y zbi\u00f3r danych do pracy w Pythonie:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#create dataset\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #008000;\">x<\/span> ': [8, 12, 12, 13, 14, 16, 17, 22, 24, 26, 29, 30],\n                   ' <span style=\"color: #008000;\">y<\/span> ': [41, 42, 39, 37, 35, 39, 45, 46, 39, 49, 55, 57]})\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Krok 2: Dopasuj model regresji<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie dopasujemy <a href=\"https:\/\/statorials.org\/pl\/prosta-regresja-liniowa-w-pythonie\/\" target=\"_blank\" rel=\"noopener\">prosty model regresji liniowej<\/a> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define response variable\n<\/span>y = df[' <span style=\"color: #008000;\">y<\/span> ']\n\n<span style=\"color: #008080;\">#define explanatory variable\n<\/span>x = df[' <span style=\"color: #008000;\">x<\/span> ']\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()<\/strong><\/span><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz reszty standaryzowane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczymy reszty standaryzowane modelu:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create instance of influence\n<\/span>influence = model. <span style=\"color: #3366ff;\">get_influence<\/span> ()\n\n<span style=\"color: #008080;\">#obtain standardized residuals\n<\/span>standardized_residuals = influence. <span style=\"color: #3366ff;\">reside_studentized_internal<\/span>\n\n<span style=\"color: #008080;\">#display standardized residuals\n<\/span><span style=\"color: #993300;\">print<\/span> (standardized_residuals)\n\n[ 1.40517322 0.81017562 0.07491009 -0.59323342 -1.2482053 -0.64248883\n  0.59610905 -0.05876884 -2.11711982 -0.066556 0.91057211 1.26973888]<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Z wynik\u00f3w wida\u0107, \u017ce \u017cadna ze standaryzowanych reszt nie przekracza warto\u015bci bezwzgl\u0119dnej 3. Zatem \u017cadna z obserwacji nie wydaje si\u0119 by\u0107 warto\u015bci\u0105 odstaj\u0105c\u0105.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 4: Wizualizuj reszty standaryzowane<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017cemy stworzy\u0107 wykres rozrzutu, aby zwizualizowa\u0107 warto\u015bci zmiennej predykcyjnej wzgl\u0119dem reszt standaryzowanych:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\nplt. <span style=\"color: #3366ff;\">scatter<\/span> (df.x, standardized_residuals)\nplt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #008000;\">x<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #008000;\">Standardized Residuals<\/span> ')\nplt. <span style=\"color: #3366ff;\">axhline<\/span> (y=0, color=' <span style=\"color: #008000;\">black<\/span> ', linestyle=' <span style=\"color: #008000;\">--<\/span> ', linewidth=1)\nplt. <span style=\"color: #3366ff;\">show<\/span> ()<\/span><\/span><\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/pozosta\u0142osc\/\" target=\"_blank\" rel=\"noopener\">Co to s\u0105 pozosta\u0142o\u015bci?<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/reszty-standaryzowane\/\">Co to s\u0105 reszty standaryzowane?<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/pozosta\u0142osci-standaryzowane-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 reszty standaryzowane w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/excel-znormalizowane-reszty\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 reszty standaryzowane w programie Excel<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Reszta to r\u00f3\u017cnica mi\u0119dzy warto\u015bci\u0105 obserwowan\u0105 a warto\u015bci\u0105 przewidywan\u0105 w modelu regresji . Oblicza si\u0119 go w nast\u0119puj\u0105cy spos\u00f3b: Warto\u015b\u0107 rezydualna = Warto\u015b\u0107 obserwowana \u2013 Warto\u015b\u0107 przewidywana Je\u015bli wykre\u015blimy zaobserwowane warto\u015bci i na\u0142o\u017cymy dopasowan\u0105 lini\u0119 regresji, reszt\u0105 dla ka\u017cdej obserwacji b\u0119dzie pionowa odleg\u0142o\u015b\u0107 mi\u0119dzy obserwacj\u0105 a lini\u0105 regresji: Jeden z typ\u00f3w reszt, kt\u00f3rego cz\u0119sto u\u017cywamy [&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-1310","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 obliczy\u0107 reszty standaryzowane w Pythonie<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 reszty standardowe w Pythonie.\" \/>\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\/standaryzowane-reszty-pythona\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 reszty standaryzowane w Pythonie\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 reszty standardowe w Pythonie.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T22:13:41+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/residus1-1.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=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/\",\"url\":\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/\",\"name\":\"Jak obliczy\u0107 reszty standaryzowane w Pythonie\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-26T22:13:41+00:00\",\"dateModified\":\"2023-07-26T22:13:41+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, na przyk\u0142adzie, jak obliczy\u0107 reszty standardowe w Pythonie.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/standaryzowane-reszty-pythona\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 reszty standaryzowane w pythonie\"}]},{\"@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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