{"id":2447,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"sst-ssr-sse-w-pythonie","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/","title":{"rendered":"Jak obliczy\u0107 sst, ssr i sse w pythonie"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Cz\u0119sto u\u017cywamy trzech r\u00f3\u017cnych <a href=\"https:\/\/statorials.org\/pl\/sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">sum warto\u015bci kwadrat\u00f3w,<\/a> aby zmierzy\u0107, jak dobrze <a href=\"https:\/\/statorials.org\/pl\/regresja-liniowa-1\/\" target=\"_blank\" rel=\"noopener\">linia regresji<\/a> pasuje do zbioru danych:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Suma kwadrat\u00f3w ca\u0142kowitych (SST) \u2013<\/strong> Suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy poszczeg\u00f3lnymi punktami danych (y <sub>i<\/sub> ) a \u015bredni\u0105 zmiennej odpowiedzi ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = \u03a3(y <sub>i<\/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. Regresja sumy kwadrat\u00f3w (SSR)<\/strong> \u2013 Suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy przewidywanymi punktami danych (\u0177 <sub>i<\/sub> ) a \u015bredni\u0105 zmiennej odpowiedzi ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSR = \u03a3(\u0177 <sub>i<\/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. B\u0142\u0105d sumy kwadrat\u00f3w (SSE)<\/strong> \u2013 Suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy przewidywanymi punktami danych (\u0177 <sub>i<\/sub> ) i obserwowanymi punktami danych (y <sub>i<\/sub> ).<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>i<\/sub> \u2013 y <sub>i<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad pokazuje krok po kroku, jak obliczy\u0107 ka\u017cd\u0105 z tych metryk dla danego modelu regresji w Pythonie.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Krok 1: Utw\u00f3rz dane<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Najpierw utw\u00f3rzmy zbi\u00f3r danych zawieraj\u0105cy liczb\u0119 przepracowanych godzin i wyniki egzamin\u00f3w uzyskane dla 20 r\u00f3\u017cnych student\u00f3w na danej uczelni:<\/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 pandas DataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 1, 1, 2, 2, 2, 2, 2, 3, 3,\n                             3, 4, 4, 4, 5, 5, 6, 7, 7, 8],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [68, 76, 74, 80, 76, 78, 81, 84, 86, 83,\n                             88, 85, 89, 94, 93, 94, 96, 89, 92, 97]})\n\n<span style=\"color: #008080;\">#view first five rows of DataFrame\n<\/span>df. <span style=\"color: #3366ff;\">head<\/span> ()\n\n\thours score\n0 1 68\n1 1 76\n2 1 74\n3 2 80\n4 2 76\n<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><strong>Krok 2: Dopasuj model regresji<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie u\u017cyjemy funkcji <strong>OLS()<\/strong> z biblioteki <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> , aby dopasowa\u0107 prosty model regresji liniowej, wykorzystuj\u0105c wynik jako zmienn\u0105 odpowiedzi i godziny jako zmienn\u0105 predykcyjn\u0105:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <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: #ff0000;\">score<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variable\n<\/span>x = df[[' <span style=\"color: #ff0000;\">hours<\/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> ()\n<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><strong>Krok 3: Oblicz SST, SSR i SSE<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Na koniec mo\u017cemy u\u017cy\u0107 nast\u0119puj\u0105cych wzor\u00f3w do obliczenia warto\u015bci SST, SSR i SSE modelu:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#calculate\n<\/span>sse = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> ) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (sse)\n\n331.07488479262696\n\n<span style=\"color: #008080;\">#calculate ssr\n<\/span>ssr = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> . <span style=\"color: #3366ff;\">mean<\/span> ()) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (ssr)\n\n917.4751152073725\n\n<span style=\"color: #008080;\">#calculate sst\n<\/span>sst = ssr + sse\n<span style=\"color: #008000;\">print<\/span> (sst)\n\n1248.5499999999995\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Metryki okazuj\u0105 si\u0119 nast\u0119puj\u0105ce:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Ca\u0142kowita suma kwadrat\u00f3w (SST):<\/strong> 1248,55<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Regresja sumy kwadrat\u00f3w (SSR):<\/strong> 917,4751<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Suma b\u0142\u0119d\u00f3w kwadrat\u00f3w (SSE):<\/strong> 331,0749<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Mo\u017cemy sprawdzi\u0107, \u017ce SST = SSR + SSE:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/li>\n<li> <span style=\"color: #000000;\">1248,55 = 917,4751 + 331,0749<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Mo\u017cesz u\u017cy\u0107 nast\u0119puj\u0105cych kalkulator\u00f3w, aby automatycznie obliczy\u0107 SST, SSR i SSE dla dowolnej prostej linii regresji liniowej:<\/span><\/p>\n<ul>\n<li> Kalkulator SST<\/li>\n<li> Kalkulator RSS<\/li>\n<li> Kalkulator ESS<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017csze samouczki wyja\u015bniaj\u0105, jak obliczy\u0107 SST, SSR i SSE w innym oprogramowaniu statystycznym:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 SST, SSR i SSE w R<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-excelu\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 SST, SSR i SSE w Excelu<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Cz\u0119sto u\u017cywamy trzech r\u00f3\u017cnych sum warto\u015bci kwadrat\u00f3w, aby zmierzy\u0107, jak dobrze linia regresji pasuje do zbioru danych: 1. Suma kwadrat\u00f3w ca\u0142kowitych (SST) \u2013 Suma kwadrat\u00f3w r\u00f3\u017cnic pomi\u0119dzy poszczeg\u00f3lnymi punktami danych (y i ) a \u015bredni\u0105 zmiennej odpowiedzi ( y ). SST = \u03a3(y i \u2013 y ) 2 2. Regresja sumy kwadrat\u00f3w (SSR) \u2013 Suma [&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-2447","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 SST, SSR i SSE w Pythonie - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 r\u00f3\u017cne sumy kwadrat\u00f3w dla modelu regresji w j\u0119zyku Python, w tym SST, SSR i SSE.\" \/>\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\/sst-ssr-sse-w-pythonie\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak obliczy\u0107 SST, SSR i SSE w Pythonie - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 r\u00f3\u017cne sumy kwadrat\u00f3w dla modelu regresji w j\u0119zyku Python, w tym SST, SSR i SSE.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-22T05:51:57+00:00\" \/>\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\/sst-ssr-sse-w-pythonie\/\",\"url\":\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/\",\"name\":\"Jak obliczy\u0107 SST, SSR i SSE w Pythonie - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-22T05:51:57+00:00\",\"dateModified\":\"2023-07-22T05:51:57+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak obliczy\u0107 r\u00f3\u017cne sumy kwadrat\u00f3w dla modelu regresji w j\u0119zyku Python, w tym SST, SSR i SSE.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/sst-ssr-sse-w-pythonie\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak obliczy\u0107 sst, ssr i sse 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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