{"id":782,"date":"2023-07-28T18:44:38","date_gmt":"2023-07-28T18:44:38","guid":{"rendered":"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/"},"modified":"2023-07-28T18:44:38","modified_gmt":"2023-07-28T18:44:38","slug":"regressao-quadratica-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/","title":{"rendered":"Como realizar regress\u00e3o quadr\u00e1tica em r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Quando duas vari\u00e1veis t\u00eam uma rela\u00e7\u00e3o linear, muitas vezes podemos usar <a href=\"https:\/\/statorials.org\/pt\/regressao-linear-simples-em-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">a regress\u00e3o linear simples<\/a> para quantificar a sua rela\u00e7\u00e3o.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5772 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata1.png\" sizes=\"auto, \" srcset=\"\" alt=\"Exemplo de relacionamento linear\" width=\"442\" height=\"318\"><\/p>\n<p> <span style=\"color: #000000;\">No entanto, quando duas vari\u00e1veis t\u00eam uma rela\u00e7\u00e3o quadr\u00e1tica, podemos usar <strong>a regress\u00e3o quadr\u00e1tica<\/strong> para quantificar a sua rela\u00e7\u00e3o.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-5773 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata2.png\" sizes=\"auto, \" srcset=\"\" alt=\"Exemplo de relacionamento quadr\u00e1tico\" width=\"441\" height=\"319\"><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como realizar regress\u00e3o quadr\u00e1tica em R.<\/span><\/p>\n<h3> <strong>Exemplo: regress\u00e3o quadr\u00e1tica em R<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que queiramos compreender a rela\u00e7\u00e3o entre o n\u00famero de horas trabalhadas e a felicidade relatada. Temos os seguintes dados sobre o n\u00famero de horas trabalhadas por semana e o n\u00edvel de felicidade relatado (numa escala de 0 a 100) para 11 pessoas diferentes:<\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-6954 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadti1.png\" sizes=\"auto, \" srcset=\"\" alt=\"\" width=\"150\" height=\"248\"><\/p>\n<p> <span style=\"color: #000000;\">Use as etapas a seguir para ajustar um modelo de regress\u00e3o quadr\u00e1tica em R.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Passo 1: Insira os dados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Primeiro, criaremos um data frame contendo nossos dados:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#createdata<\/span>\ndata &lt;- data.frame(hours=c(6, 9, 12, 14, 30, 35, 40, 47, 51, 55, 60),\n                   happiness=c(14, 28, 50, 70, 89, 94, 90, 75, 59, 44, 27))\n<span style=\"color: #008080;\">\n#viewdata<\/span> \ndata\n\n   hours happiness\n1 6 14\n2 9 28\n3 12 50\n4 14 70\n5 30 89\n6 35 94\n7 40 90\n8 47 75\n9 51 59\n10 55 44\n11 60 27\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Etapa 2: visualize os dados.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, criaremos um gr\u00e1fico de dispers\u00e3o simples para visualizar os dados.<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot<\/span>\nplot(data$hours, data$happiness, pch=16)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8616 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadratiquer1.png\" alt=\"Gr\u00e1fico de dispers\u00e3o em R\" width=\"370\" height=\"336\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Podemos ver claramente que os dados n\u00e3o seguem um padr\u00e3o linear.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 3: ajuste um modelo de regress\u00e3o linear simples.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, ajustaremos um modelo de regress\u00e3o linear simples para ver qu\u00e3o bem ele se ajusta aos dados:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit linear model<\/span>\nlinearModel &lt;- lm(happiness ~ hours, data=data)\n\n<span style=\"color: #008080;\">#view model summary<\/span>\nsummary(linearModel)\n\nCall:\nlm(formula = happiness ~ hours)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-39.34 -21.99 -2.03 23.50 35.11 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)  \n(Intercept) 48.4531 17.3288 2.796 0.0208 *\nhours 0.2981 0.4599 0.648 0.5331  \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 28.72 on 9 degrees of freedom\nMultiple R-squared: 0.0446, Adjusted R-squared: -0.06156 \nF-statistic: 0.4201 on 1 and 9 DF, p-value: 0.5331\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A vari\u00e2ncia total na felicidade explicada pelo modelo \u00e9 de apenas <strong>4,46%<\/strong> , conforme mostrado pelo valor m\u00faltiplo de R ao quadrado.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 4: ajuste um modelo de regress\u00e3o quadr\u00e1tica.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A seguir, ajustaremos um modelo de regress\u00e3o quadr\u00e1tica.<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create a new variable for hours <sup>2<\/sup><\/span>\ndata$hours2 &lt;- data$hours^2\n\n<span style=\"color: #008080;\">#fit quadratic regression model<\/span>\nquadraticModel &lt;- lm(happiness ~ hours + hours2, data=data)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(quadraticModel)\n\nCall:\nlm(formula = happiness ~ hours + hours2, data = data)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-6.2484 -3.7429 -0.1812 1.1464 13.6678 \n\nCoefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -18.25364 6.18507 -2.951 0.0184 *  \nhours 6.74436 0.48551 13.891 6.98e-07 ***\nhours2 -0.10120 0.00746 -13.565 8.38e-07 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 6.218 on 8 degrees of freedom\nMultiple R-squared: 0.9602, Adjusted R-squared: 0.9502 \nF-statistic: 96.49 on 2 and 8 DF, p-value: 2.51e-06\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A vari\u00e2ncia total da felicidade explicada pelo modelo aumentou para <b>96,02%<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar o c\u00f3digo a seguir para visualizar qu\u00e3o bem o modelo se ajusta aos dados:<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create sequence of hour values<\/span>\nhourValues &lt;- seq(0, 60, 0.1)\n\n<span style=\"color: #008080;\">#create list of predicted happiness levels using quadratic model\n<\/span>happinessPredict &lt;- predict(quadraticModel, list(hours=hourValues, hours2=hourValues^2))\n\n<span style=\"color: #008080;\">#create scatterplot of original data values\n<\/span>plot(data$hours, data$happiness, pch=16)\n<span style=\"color: #008080;\">#add predicted lines based on quadratic regression model<\/span>\nlines(hourValues, happinessPredict, col='blue')\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8619 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadratiquer2.png\" alt=\"Gr\u00e1fico de dispers\u00e3o de regress\u00e3o quadr\u00e1tica em R\" width=\"399\" height=\"368\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Podemos ver que a linha de regress\u00e3o quadr\u00e1tica se ajusta muito bem aos valores dos dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 5: Interprete o modelo de regress\u00e3o quadr\u00e1tica.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Na etapa anterior, vimos que o resultado do modelo de regress\u00e3o quadr\u00e1tica foi:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>Coefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) -18.25364 6.18507 -2.951 0.0184 *  \nhours 6.74436 0.48551 13.891 6.98e-07 ***\nhours2 -0.10120 0.00746 -13.565 8.38e-07 ***\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Com base nos coeficientes aqui apresentados, a regress\u00e3o quadr\u00e1tica ajustada seria:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Felicidade = -0,1012 (horas) <sup>2<\/sup> + 6,7444 (horas) \u2013 18,2536<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos utilizar esta equa\u00e7\u00e3o para determinar a felicidade prevista de um indiv\u00edduo, dado o n\u00famero de horas que trabalha por semana.<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Por exemplo, uma pessoa que trabalha 60 horas por semana teria um n\u00edvel de felicidade de <strong>22,09<\/strong> :<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Felicidade = -0,1012(60) <sup>2<\/sup> + 6,7444(60) \u2013 18,2536 = 22,09<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por outro lado, uma pessoa que trabalha 30 horas por semana deveria ter um n\u00edvel de felicidade de <strong>92,99<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">Felicidade = -0,1012(30) <sup>2<\/sup> + 6,7444(30) \u2013 18,2536 = 92,99<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quando duas vari\u00e1veis t\u00eam uma rela\u00e7\u00e3o linear, muitas vezes podemos usar a regress\u00e3o linear simples para quantificar a sua rela\u00e7\u00e3o. No entanto, quando duas vari\u00e1veis t\u00eam uma rela\u00e7\u00e3o quadr\u00e1tica, podemos usar a regress\u00e3o quadr\u00e1tica para quantificar a sua rela\u00e7\u00e3o. Este tutorial explica como realizar regress\u00e3o quadr\u00e1tica em R. Exemplo: regress\u00e3o quadr\u00e1tica em R Suponha que [&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-782","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 regress\u00e3o quadr\u00e1tica em R - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o quadr\u00e1tica em R, incluindo um exemplo passo a passo.\" \/>\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\/regressao-quadratica-r\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como realizar regress\u00e3o quadr\u00e1tica em R - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o quadr\u00e1tica em R, incluindo um exemplo passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T18:44:38+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/quadregstata1.png\" \/>\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=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/\",\"url\":\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/\",\"name\":\"Como realizar regress\u00e3o quadr\u00e1tica em R - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T18:44:38+00:00\",\"dateModified\":\"2023-07-28T18:44:38+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o quadr\u00e1tica em R, incluindo um exemplo passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-quadratica-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como realizar regress\u00e3o quadr\u00e1tica em r\"}]},{\"@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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