{"id":2448,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"sst-ssr-sse-em-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/","title":{"rendered":"Como calcular sst, ssr e sse em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Freq\u00fcentemente usamos tr\u00eas <a href=\"https:\/\/statorials.org\/pt\/sst-ssr-se\/\" target=\"_blank\" rel=\"noopener\">somas de quadrados<\/a> diferentes para medir qu\u00e3o bem uma <a href=\"https:\/\/statorials.org\/pt\/regressao-linear-1\/\" target=\"_blank\" rel=\"noopener\">linha de regress\u00e3o<\/a> se ajusta a um conjunto de dados:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Soma dos Quadrados Totais (SST) \u2013<\/strong> A soma dos quadrados das diferen\u00e7as entre os pontos de dados individuais (y <sub>i<\/sub> ) e a m\u00e9dia da vari\u00e1vel de resposta ( <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. Regress\u00e3o da Soma dos Quadrados (SSR)<\/strong> \u2013 A soma dos quadrados das diferen\u00e7as entre os pontos de dados previstos (\u0177 <sub>i<\/sub> ) e a m\u00e9dia da vari\u00e1vel de resposta ( <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. Erro da Soma dos Quadrados (SSE)<\/strong> \u2013 A soma dos quadrados das diferen\u00e7as entre os pontos de dados previstos (\u0177 <sub>i<\/sub> ) e os pontos de dados observados (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;\">O exemplo passo a passo a seguir mostra como calcular cada uma dessas m\u00e9tricas para um determinado modelo de regress\u00e3o em Python.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Etapa 1: crie os dados<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Primeiro, vamos criar um conjunto de dados contendo o n\u00famero de horas estudadas e as notas dos exames obtidas para 20 alunos diferentes em uma determinada universidade:<\/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>Passo 2: Ajustar um modelo de regress\u00e3o<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A seguir, usaremos a fun\u00e7\u00e3o <strong>OLS()<\/strong> da biblioteca <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> para ajustar um modelo de regress\u00e3o linear simples usando pontua\u00e7\u00e3o como vari\u00e1vel de resposta e horas como vari\u00e1vel preditora:<\/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>Etapa 3: Calcular SST, SSR e SSE<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Por fim, podemos utilizar as seguintes f\u00f3rmulas para calcular os valores de SST, SSR e SSE do modelo:<\/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;\">As m\u00e9tricas acabam sendo:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Soma total dos quadrados (SST):<\/strong> 1248,55<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Regress\u00e3o da Soma dos Quadrados (SSR):<\/strong> 917,4751<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Erro da soma dos quadrados (SSE):<\/strong> 331,0749<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos verificar que 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>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Voc\u00ea pode usar as seguintes calculadoras para calcular automaticamente SST, SSR e SSE para qualquer linha de regress\u00e3o linear simples:<\/span><\/p>\n<ul>\n<li> Calculadora SST<\/li>\n<li> Calculadora RSS<\/li>\n<li> Calculadora ESS<\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir explicam como calcular SST, SSR e SSE em outro software estat\u00edstico:<\/span><\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-r\/\" target=\"_blank\" rel=\"noopener\">Como calcular SST, SSR e SSE em R<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/pt\/sst-ssr-sse-no-excel\/\" target=\"_blank\" rel=\"noopener\">Como calcular SST, SSR e SSE no Excel<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Freq\u00fcentemente usamos tr\u00eas somas de quadrados diferentes para medir qu\u00e3o bem uma linha de regress\u00e3o se ajusta a um conjunto de dados: 1. Soma dos Quadrados Totais (SST) \u2013 A soma dos quadrados das diferen\u00e7as entre os pontos de dados individuais (y i ) e a m\u00e9dia da vari\u00e1vel de resposta ( y ). SST [&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-2448","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular SST, SSR e SSE em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como calcular v\u00e1rias somas de quadrados para um modelo de regress\u00e3o em Python, incluindo SST, SSR e 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\/pt\/sst-ssr-sse-em-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular SST, SSR e SSE em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como calcular v\u00e1rias somas de quadrados para um modelo de regress\u00e3o em Python, incluindo SST, SSR e SSE.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-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. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/\",\"name\":\"Como calcular SST, SSR e SSE em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-22T05:51:57+00:00\",\"dateModified\":\"2023-07-22T05:51:57+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como calcular v\u00e1rias somas de quadrados para um modelo de regress\u00e3o em Python, incluindo SST, SSR e SSE.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/sst-ssr-sse-em-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular sst, ssr e sse em python\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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