{"id":3560,"date":"2023-07-16T20:16:40","date_gmt":"2023-07-16T20:16:40","guid":{"rendered":"https:\/\/statorials.org\/pt\/ols-regressao-python\/"},"modified":"2023-07-16T20:16:40","modified_gmt":"2023-07-16T20:16:40","slug":"ols-regressao-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/ols-regressao-python\/","title":{"rendered":"Como realizar a regress\u00e3o ols em python (com exemplo)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A regress\u00e3o de m\u00ednimos quadrados ordin\u00e1rios (OLS) \u00e9 um m\u00e9todo que nos permite encontrar uma linha que melhor descreve a rela\u00e7\u00e3o entre uma ou mais vari\u00e1veis preditoras e uma <a href=\"https:\/\/statorials.org\/pt\/respostas-explicativas-das-variaveis\/\" target=\"_blank\" rel=\"noopener\">vari\u00e1vel de resposta<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este m\u00e9todo nos permite encontrar a seguinte equa\u00e7\u00e3o:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0177=b <sub>0<\/sub> + b <sub>1<\/sub> x<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0177<\/strong> : O valor estimado da resposta<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>0<\/sub><\/strong> : A origem da linha de regress\u00e3o<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>b <sub>1<\/sub><\/strong> : A inclina\u00e7\u00e3o da linha de regress\u00e3o<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Esta equa\u00e7\u00e3o pode nos ajudar a compreender a rela\u00e7\u00e3o entre o preditor e a vari\u00e1vel de resposta e pode ser usada para prever o valor de uma vari\u00e1vel de resposta dado o valor da vari\u00e1vel preditora.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O exemplo passo a passo a seguir mostra como realizar a regress\u00e3o OLS em Python.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><b>Etapa 1: crie os dados<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Para este exemplo, criaremos um conjunto de dados contendo as duas vari\u00e1veis a seguir para 15 alunos:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">N\u00famero total de horas estudadas<\/span><\/li>\n<li> <span style=\"color: #000000;\">Resultado de exame<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Realizaremos uma regress\u00e3o OLS, usando horas como vari\u00e1vel preditora e pontua\u00e7\u00e3o no exame como vari\u00e1vel resposta.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O c\u00f3digo a seguir mostra como criar esse conjunto de dados falso em pandas:<\/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<span style=\"color: #008080;\">\n#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours score\n0 1 64\n1 2 66\n2 4 76\n3 5 73\n4 5 74\n5 6 81\n6 6 83\n7 7 82\n8 8 80\n9 10 88\n10 11 84\n11 11 82\n12 12 91\n13 12 93\n14 14 89<\/strong><\/pre>\n<h2> <span style=\"color: #000000;\"><b>Etapa 2: realizar uma regress\u00e3o OLS<\/b><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A seguir, podemos usar as fun\u00e7\u00f5es do m\u00f3dulo <a href=\"https:\/\/www.statsmodels.org\/stable\/index.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> para realizar uma regress\u00e3o OLS, usando <strong>horas<\/strong> como vari\u00e1vel preditora e pontua\u00e7\u00e3o como vari\u00e1vel <strong>de resposta<\/strong> :<\/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> statsmodels.api <span style=\"color: #008000;\">as<\/span> sm\n<\/span>\n#define predictor and response variables\n<span style=\"color: #000000;\">y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[' <span style=\"color: #ff0000;\">hours<\/span> ']<\/span>\n\n#add constant to predictor variables\n<span style=\"color: #000000;\">x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n<\/span>\n#fit linear regression model\n<span style=\"color: #000000;\">model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/span>\n#view model summary\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.831\nModel: OLS Adj. R-squared: 0.818\nMethod: Least Squares F-statistic: 63.91\nDate: Fri, 26 Aug 2022 Prob (F-statistic): 2.25e-06\nTime: 10:42:24 Log-Likelihood: -39,594\nNo. Observations: 15 AIC: 83.19\nDf Residuals: 13 BIC: 84.60\nModel: 1                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 65.3340 2.106 31.023 0.000 60.784 69.884\nhours 1.9824 0.248 7.995 0.000 1.447 2.518\n==================================================== ============================\nOmnibus: 4,351 Durbin-Watson: 1,677\nProb(Omnibus): 0.114 Jarque-Bera (JB): 1.329\nSkew: 0.092 Prob(JB): 0.515\nKurtosis: 1.554 Cond. No. 19.2\n==================================================== ============================<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Na coluna <strong>coef<\/strong> , podemos ver os coeficientes de regress\u00e3o e escrever a seguinte equa\u00e7\u00e3o de regress\u00e3o ajustada:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pontua\u00e7\u00e3o = 65,334 + 1,9824*(horas)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Isso significa que cada hora adicional estudada est\u00e1 associada a um aumento m\u00e9dio na pontua\u00e7\u00e3o do exame de <strong>1,9824<\/strong> pontos.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O valor original de <strong>65.334<\/strong> nos indica a nota m\u00e9dia esperada no exame para um aluno que estuda zero horas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos usar essa equa\u00e7\u00e3o para encontrar a pontua\u00e7\u00e3o esperada no exame com base no n\u00famero de horas que um aluno estuda.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, um aluno que estuda 10 horas dever\u00e1 obter nota <strong>85.158<\/strong> no exame:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Pontua\u00e7\u00e3o = 65,334 + 1,9824*(10) = 85,158<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Veja como interpretar o restante do resumo do modelo:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>P(&gt;|t|):<\/strong> Este \u00e9 o valor p associado aos coeficientes do modelo. Como o valor p para <em>horas<\/em> (0,000) \u00e9 inferior a 0,05, podemos afirmar que existe uma associa\u00e7\u00e3o estatisticamente significativa entre <em>horas<\/em> e <em>pontua\u00e7\u00e3o<\/em> .<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>R-quadrado:<\/strong> Isso nos diz que o percentual de varia\u00e7\u00e3o nas notas dos exames pode ser explicado pelo n\u00famero de horas estudadas. Nesse caso, <strong>83,1%<\/strong> da varia\u00e7\u00e3o nas notas pode ser explicada pelas horas estudadas.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Estat\u00edstica F e valor p:<\/strong> A estat\u00edstica F ( <strong>63,91<\/strong> ) e o valor p correspondente ( <strong>2,25e-06<\/strong> ) nos dizem a signific\u00e2ncia geral do modelo de regress\u00e3o, ou seja, se as vari\u00e1veis preditoras no modelo s\u00e3o \u00fateis para explicar a varia\u00e7\u00e3o. na vari\u00e1vel de resposta. Como o valor p neste exemplo \u00e9 inferior a 0,05, nosso modelo \u00e9 estatisticamente significativo e <em>as horas<\/em> s\u00e3o consideradas \u00fateis para explicar a varia\u00e7\u00e3o <em>da pontua\u00e7\u00e3o<\/em> .<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Etapa 3: visualize a linha de melhor ajuste<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Finalmente, podemos usar o pacote de visualiza\u00e7\u00e3o de dados <strong>matplotlib<\/strong> para visualizar a linha de regress\u00e3o ajustada aos pontos de dados reais:<\/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<\/span>\n#find line of best fit\n<span style=\"color: #000000;\">a, b = np. <span style=\"color: #3366ff;\">polyfit<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], <span style=\"color: #008000;\">1<\/span> )\n<\/span>\n#add points to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">scatter<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], color=' <span style=\"color: #ff0000;\">purple<\/span> ')\n<\/span>\n#add line of best fit to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">plot<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], a*df[' <span style=\"color: #ff0000;\">hours<\/span> ']+b)\n<\/span>\n#add fitted regression equation to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">text<\/span> ( <span style=\"color: #008000;\">1<\/span> , <span style=\"color: #008000;\">90<\/span> , 'y = ' + '{:.3f}'.format(b) + ' + {:.3f}'.format(a) + 'x', size= <span style=\"color: #008000;\">12<\/span> )\n\n<span style=\"color: #008080;\">#add axis labels\n<\/span>plt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #ff0000;\">Hours Studied<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #ff0000;\">Exam Score<\/span> ')\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-29456 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne11.jpg\" alt=\"\" width=\"502\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Os pontos roxos representam os pontos de dados reais e a linha azul representa a linha de regress\u00e3o ajustada.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m usamos a fun\u00e7\u00e3o <strong>plt.text()<\/strong> para adicionar a equa\u00e7\u00e3o de regress\u00e3o ajustada ao canto superior esquerdo do gr\u00e1fico.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olhando para o gr\u00e1fico, parece que a linha de regress\u00e3o ajustada captura muito bem a rela\u00e7\u00e3o entre a vari\u00e1vel <strong>horas<\/strong> e a vari\u00e1vel <strong>pontua\u00e7\u00e3o<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir explicam como realizar outras tarefas comuns em Python:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/regressao-logistica-python\/\" target=\"_blank\" rel=\"noopener\">Como realizar regress\u00e3o log\u00edstica em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/regressao-exponencial-python\/\" target=\"_blank\" rel=\"noopener\">Como realizar regress\u00e3o exponencial em Python<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/aico-em-python\/\" target=\"_blank\" rel=\"noopener\">Como calcular AIC de modelos de regress\u00e3o em Python<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regress\u00e3o de m\u00ednimos quadrados ordin\u00e1rios (OLS) \u00e9 um m\u00e9todo que nos permite encontrar uma linha que melhor descreve a rela\u00e7\u00e3o entre uma ou mais vari\u00e1veis preditoras e uma vari\u00e1vel de resposta . Este m\u00e9todo nos permite encontrar a seguinte equa\u00e7\u00e3o: \u0177=b 0 + b 1 x Ouro: \u0177 : O valor estimado da resposta [&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-3560","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 realizar a regress\u00e3o OLS em Python (com exemplo) - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial fornece um exemplo passo a passo de como realizar regress\u00e3o de m\u00ednimos quadrados ordin\u00e1rios (OLS) em Python.\" \/>\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\/ols-regressao-python\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como realizar a regress\u00e3o OLS em Python (com exemplo) - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial fornece um exemplo passo a passo de como realizar regress\u00e3o de m\u00ednimos quadrados ordin\u00e1rios (OLS) em Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/ols-regressao-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-16T20:16:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne11.jpg\" \/>\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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/ols-regressao-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/ols-regressao-python\/\",\"name\":\"Como realizar a regress\u00e3o OLS em Python (com exemplo) - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-16T20:16:40+00:00\",\"dateModified\":\"2023-07-16T20:16:40+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial fornece um exemplo passo a passo de como realizar regress\u00e3o de m\u00ednimos quadrados ordin\u00e1rios (OLS) em Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/ols-regressao-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/ols-regressao-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/ols-regressao-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como realizar a regress\u00e3o ols em python (com exemplo)\"}]},{\"@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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