{"id":1313,"date":"2023-07-26T22:01:06","date_gmt":"2023-07-26T22:01:06","guid":{"rendered":"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/"},"modified":"2023-07-26T22:01:06","modified_gmt":"2023-07-26T22:01:06","slug":"zdalny-pyton-kuchenny","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/","title":{"rendered":"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 cooka w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Odleg\u0142o\u015b\u0107 Cooka<\/strong> s\u0142u\u017cy do identyfikacji wp\u0142ywowych <a href=\"https:\/\/statorials.org\/pl\/obserwacja-w-statystyce\/\" target=\"_blank\" rel=\"noopener\">obserwacji<\/a> w modelu regresji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Wz\u00f3r na odleg\u0142o\u015b\u0107 Cooka to:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>re <sub>ja<\/sub><\/strong> = (r <sub>ja<\/sub> <sup>2<\/sup> \/ p*MSE) * (h <sub>ii<\/sub> \/ (1-h <sub>ii<\/sub> ) <sup>2<\/sup> )<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>r<\/strong> <sub><strong>i<\/strong><\/sub> jest i- <sup>t\u0105<\/sup> reszt\u0105<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p<\/strong> to liczba wsp\u00f3\u0142czynnik\u00f3w w modelu regresji<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>MSE<\/strong> to b\u0142\u0105d \u015bredniokwadratowy<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>h<\/strong> <sub>ii<\/sub> to <sup>i-<\/sup> warto\u015b\u0107 d\u017awigni<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Zasadniczo odleg\u0142o\u015b\u0107 Cooka mierzy, jak bardzo zmieni\u0105 si\u0119 wszystkie dopasowane warto\u015bci modelu po usuni\u0119ciu i- <sup>tej<\/sup> obserwacji.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Im wi\u0119ksza warto\u015b\u0107 odleg\u0142o\u015bci Cooka, tym wi\u0119kszy wp\u0142yw ma dana obserwacja.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z regu\u0142y ka\u017cd\u0105 obserwacj\u0119 z odleg\u0142o\u015bci\u0105 Cooka wi\u0119ksz\u0105 ni\u017c 4\/n (gdzie <em>n<\/em> = liczba obserwacji og\u00f3\u0142em) uwa\u017ca si\u0119 za maj\u0105c\u0105 du\u017cy wp\u0142yw.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W tym samouczku przedstawiono krok po kroku przyk\u0142ad obliczenia odleg\u0142o\u015bci Cooka dla danego modelu regresji 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 odleg\u0142o\u015b\u0107 gotowania<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie obliczymy odleg\u0142o\u015b\u0107 Cooka dla ka\u017cdej obserwacji w modelu:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#suppress scientific notation\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\nn.p. <span style=\"color: #3366ff;\">set_printoptions<\/span> (suppress= <span style=\"color: #008000;\">True<\/span> )\n\n<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 Cook's distance for each observation\n<\/span>cooks = influence. <span style=\"color: #3366ff;\">cooks_distance<\/span>\n\n<span style=\"color: #008080;\">#display Cook's distances\n<\/span><span style=\"color: #993300;\">print<\/span> (cooks)\n\n(array([0.368, 0.061, 0.001, 0.028, 0.105, 0.022, 0.017, 0. , 0.343,\n        0. , 0.15 , 0.349]),\n array([0.701, 0.941, 0.999, 0.973, 0.901, 0.979, 0.983, 1. , 0.718,\n        1. , 0.863, 0.713]))\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Domy\u015blnie funkcja <strong>Cooks_distance()<\/strong> wy\u015bwietla tablic\u0119 warto\u015bci odleg\u0142o\u015bci Cooka dla ka\u017cdej obserwacji, po kt\u00f3rej nast\u0119puje tablica odpowiednich warto\u015bci p.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Odleg\u0142o\u015b\u0107 Cooka dla obserwacji nr 1: <strong>0,368<\/strong> (warto\u015b\u0107 p: 0,701)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Odleg\u0142o\u015b\u0107 Cooka dla obserwacji nr 2: <strong>0,061<\/strong> (warto\u015b\u0107 p: 0,941)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Odleg\u0142o\u015b\u0107 Cooka dla obserwacji nr 3: <strong>0,001<\/strong> (warto\u015b\u0107 p: 0,999)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">I tak dalej.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Krok 4: Wizualizuj odleg\u0142o\u015bci kucharza<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017cemy utworzy\u0107 wykres rozrzutu, aby zwizualizowa\u0107 warto\u015bci zmiennej predykcyjnej w funkcji odleg\u0142o\u015bci Cooka dla ka\u017cdej obserwacji:<\/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, cooks[0])\nplt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #008000;\">x<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #008000;\">Cooks Distance<\/span> ')\nplt. <span style=\"color: #3366ff;\">show<\/span> ()<\/span><\/span><\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12869 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cuisinierspython1.png\" alt=\"Odleg\u0142o\u015b\u0107 Cooka w Pythonie\" width=\"420\" height=\"284\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ko\u0144cowe przemy\u015blenia<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Nale\u017cy zauwa\u017cy\u0107, \u017ce do <em>identyfikacji<\/em> potencjalnie wp\u0142ywaj\u0105cych obserwacji nale\u017cy stosowa\u0107 odleg\u0142o\u015b\u0107 Cooka.<\/span> <span style=\"color: #000000;\">To, \u017ce obserwacja ma wp\u0142yw, nie oznacza, \u017ce nale\u017cy j\u0105 usun\u0105\u0107 ze zbioru danych.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw nale\u017cy sprawdzi\u0107, czy obserwacja nie jest wynikiem b\u0142\u0119du we wpisie danych lub innego dziwnego zdarzenia. Je\u015bli oka\u017ce si\u0119, \u017ce jest to prawid\u0142owa warto\u015b\u0107, mo\u017cesz zdecydowa\u0107, czy nale\u017cy j\u0105 usun\u0105\u0107, pozostawi\u0107 bez zmian, czy po prostu zast\u0105pi\u0107 j\u0105 warto\u015bci\u0105 alternatywn\u0105, tak\u0105 jak mediana.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Odleg\u0142o\u015b\u0107 Cooka s\u0142u\u017cy do identyfikacji wp\u0142ywowych obserwacji w modelu regresji. Wz\u00f3r na odleg\u0142o\u015b\u0107 Cooka to: re ja = (r ja 2 \/ p*MSE) * (h ii \/ (1-h ii ) 2 ) Z\u0142oto: r i jest i- t\u0105 reszt\u0105 p to liczba wsp\u00f3\u0142czynnik\u00f3w w modelu regresji MSE to b\u0142\u0105d \u015bredniokwadratowy h ii to i- warto\u015b\u0107 [&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-1313","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 odleg\u0142o\u015b\u0107 Cooka w Pythonie<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono na przyk\u0142adzie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Cooka 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\/zdalny-pyton-kuchenny\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 Cooka w Pythonie\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono na przyk\u0142adzie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Cooka w Pythonie.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-26T22:01:06+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cuisinierspython1.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\/zdalny-pyton-kuchenny\/\",\"url\":\"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/\",\"name\":\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 Cooka w Pythonie\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-26T22:01:06+00:00\",\"dateModified\":\"2023-07-26T22:01:06+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono na przyk\u0142adzie, jak obliczy\u0107 odleg\u0142o\u015b\u0107 Cooka w Pythonie.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/zdalny-pyton-kuchenny\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 odleg\u0142o\u015b\u0107 cooka 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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