{"id":2449,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"sst-ssr-sse-in-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/","title":{"rendered":"Hoe sst, ssr en sse in python te berekenen"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">We gebruiken vaak drie verschillende <a href=\"https:\/\/statorials.org\/nl\/sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">kwadratensommen<\/a> om te meten hoe goed een <a href=\"https:\/\/statorials.org\/nl\/lineaire-regressie-1\/\" target=\"_blank\" rel=\"noopener\">regressielijn<\/a> bij een reeks gegevens past:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Som van totale kwadraten (SST) \u2013<\/strong> De som van de kwadraten van de verschillen tussen individuele gegevenspunten (y <sub>i<\/sub> ) en het gemiddelde van de responsvariabele ( <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. Som van kwadratenregressie (SSR)<\/strong> \u2013 De som van de kwadraten van de verschillen tussen de voorspelde gegevenspunten (\u0177 <sub>i<\/sub> ) en het gemiddelde van de responsvariabele ( <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. Som van kwadratenfout (SSE)<\/strong> \u2013 De som van de kwadraten van de verschillen tussen de voorspelde datapunten (\u0177 <sub>i<\/sub> ) en de waargenomen datapunten (y <sub>i<\/sub> ).<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>ik<\/sub> \u2013 y <sub>ik<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">In het volgende stapsgewijze voorbeeld ziet u hoe u elk van deze metrieken voor een bepaald regressiemodel in Python kunt berekenen.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Stap 1: Cre\u00eber de gegevens<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Laten we eerst een dataset maken met het aantal gestudeerde uren en de behaalde examenscores voor 20 verschillende studenten aan een bepaalde universiteit:<\/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>Stap 2: Pas een regressiemodel toe<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Vervolgens zullen we de functie <strong>OLS()<\/strong> uit de <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels-<\/a> bibliotheek gebruiken om een eenvoudig lineair regressiemodel in te passen met score als responsvariabele en uren als voorspellende variabele:<\/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>Stap 3: Bereken SST, SSR en SSE<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Ten slotte kunnen we de volgende formules gebruiken om de SST-, SSR- en SSE-waarden van het model te berekenen:<\/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;\">De statistieken blijken te zijn:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Totale som van kwadraten (SST):<\/strong> 1248,55<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Som van kwadratenregressie (SSR):<\/strong> 917,4751<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Som van kwadratenfout (SSE):<\/strong> 331,0749<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">We kunnen verifi\u00ebren dat 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>Aanvullende bronnen<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">U kunt de volgende rekenmachines gebruiken om SST, SSR en SSE automatisch te berekenen voor elke eenvoudige lineaire regressielijn:<\/span><\/p>\n<ul>\n<li> SST-calculator<\/li>\n<li> RSS-calculator<\/li>\n<li> ESS-calculator<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">In de volgende tutorials wordt uitgelegd hoe u SST, SSR en SSE in andere statistische software kunt berekenen:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-r\/\" target=\"_blank\" rel=\"noopener\">Hoe SST, SSR en SSE in R te berekenen<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-excel\/\" target=\"_blank\" rel=\"noopener\">Hoe SST, SSR en SSE in Excel te berekenen<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>We gebruiken vaak drie verschillende kwadratensommen om te meten hoe goed een regressielijn bij een reeks gegevens past: 1. Som van totale kwadraten (SST) \u2013 De som van de kwadraten van de verschillen tussen individuele gegevenspunten (y i ) en het gemiddelde van de responsvariabele ( y ). SST = \u03a3(y i \u2013 y ) [&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-2449","post","type-post","status-publish","format-standard","hentry","category-gids"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Hoe SST, SSR en SSE te berekenen in Python - Statorials<\/title>\n<meta name=\"description\" content=\"In deze tutorial wordt uitgelegd hoe u verschillende kwadratensommen kunt berekenen voor een regressiemodel in Python, inclusief SST, SSR en 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\/nl\/sst-ssr-sse-in-python\/\" \/>\n<meta property=\"og:locale\" content=\"de_DE\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Hoe SST, SSR en SSE te berekenen in Python - Statorials\" \/>\n<meta property=\"og:description\" content=\"In deze tutorial wordt uitgelegd hoe u verschillende kwadratensommen kunt berekenen voor een regressiemodel in Python, inclusief SST, SSR en SSE.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/\" \/>\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=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Verfasst von\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Gesch\u00e4tzte Lesezeit\" \/>\n\t<meta name=\"twitter:data2\" content=\"2\u00a0Minuten\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/\",\"url\":\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/\",\"name\":\"Hoe SST, SSR en SSE te berekenen in Python - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/nl\/#website\"},\"datePublished\":\"2023-07-22T05:51:57+00:00\",\"dateModified\":\"2023-07-22T05:51:57+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\"},\"description\":\"In deze tutorial wordt uitgelegd hoe u verschillende kwadratensommen kunt berekenen voor een regressiemodel in Python, inclusief SST, SSR en SSE.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/#breadcrumb\"},\"inLanguage\":\"de\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/nl\/sst-ssr-sse-in-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Thuis\",\"item\":\"https:\/\/statorials.org\/nl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Hoe sst, ssr en sse in python te berekenen\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/nl\/#website\",\"url\":\"https:\/\/statorials.org\/nl\/\",\"name\":\"Statorials\",\"description\":\"Uw gids voor statistische competentie\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/nl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"de\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/d4b8842173cca1bb62cdec41860e4219\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"de\",\"@id\":\"https:\/\/statorials.org\/nl\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/nl\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Ik ben Benjamin, een gepensioneerde hoogleraar statistiek die nu een toegewijde Statorials-lesgever is. 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