{"id":2242,"date":"2023-07-23T02:52:08","date_gmt":"2023-07-23T02:52:08","guid":{"rendered":"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/"},"modified":"2023-07-23T02:52:08","modified_gmt":"2023-07-23T02:52:08","slug":"hipotese-nula-de-regressao-logistica","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/","title":{"rendered":"Compreendendo a hip\u00f3tese nula para regress\u00e3o log\u00edstica"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pt\/regressao-logistica-1\/\" target=\"_blank\" rel=\"noopener\">A regress\u00e3o log\u00edstica<\/a> \u00e9 um tipo de modelo de regress\u00e3o que podemos usar para compreender 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> quando a vari\u00e1vel de resposta \u00e9 bin\u00e1ria.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se tivermos apenas uma vari\u00e1vel preditora e uma vari\u00e1vel resposta, podemos usar <strong>a regress\u00e3o log\u00edstica simples<\/strong> , que utiliza a seguinte f\u00f3rmula para estimar a rela\u00e7\u00e3o entre as vari\u00e1veis:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>log[p(X) \/ (1-p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula no lado direito da equa\u00e7\u00e3o prev\u00ea o logaritmo das chances de a vari\u00e1vel resposta assumir o valor 1.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A regress\u00e3o log\u00edstica simples utiliza as seguintes hip\u00f3teses nulas e alternativas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A hip\u00f3tese nula afirma que o coeficiente \u03b2 <sub>1<\/sub> \u00e9 igual a zero. Em outras palavras, n\u00e3o h\u00e1 rela\u00e7\u00e3o estatisticamente significativa entre a vari\u00e1vel preditora x e a vari\u00e1vel resposta y.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A hip\u00f3tese alternativa afirma que \u03b2 <sub>1<\/sub> <em>n\u00e3o<\/em> \u00e9 igual a zero. Em outras palavras, <em>existe<\/em> uma rela\u00e7\u00e3o estatisticamente significativa entre x e y.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Se tivermos m\u00faltiplas vari\u00e1veis preditoras e uma vari\u00e1vel resposta, podemos usar <strong>regress\u00e3o log\u00edstica m\u00faltipla<\/strong> , que utiliza a seguinte f\u00f3rmula para estimar a rela\u00e7\u00e3o entre as vari\u00e1veis:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">log[p(X) \/ (1-p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> x <sub>1<\/sub> + \u03b2 <sub>2<\/sub> x <sub>2<\/sub> + \u2026 + \u03b2 <sub>k<\/sub> x <sub>k<\/sub><\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">A regress\u00e3o log\u00edstica m\u00faltipla usa as seguintes hip\u00f3teses nulas e alternativas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A hip\u00f3tese nula afirma que todos os coeficientes do modelo s\u00e3o iguais a zero. Em outras palavras, nenhuma das vari\u00e1veis preditoras possui uma rela\u00e7\u00e3o estatisticamente significativa com a vari\u00e1vel resposta y.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A hip\u00f3tese alternativa afirma que nem todos os coeficientes s\u00e3o simultaneamente iguais a zero.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os exemplos a seguir mostram como decidir se rejeita ou n\u00e3o a hip\u00f3tese nula em modelos de regress\u00e3o log\u00edstica simples e de regress\u00e3o log\u00edstica m\u00faltipla.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 1: regress\u00e3o log\u00edstica simples<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que um professor queira usar o n\u00famero de horas estudadas para prever a nota do exame que os alunos de sua turma obter\u00e3o. Recolhe dados de 20 alunos e ajusta-se a um modelo de regress\u00e3o log\u00edstica simples.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar o seguinte c\u00f3digo em R para ajustar um modelo de regress\u00e3o log\u00edstica simples:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#createdata\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.8244 -1.1738 0.7701 0.9460 1.2236  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)\n(Intercept) -0.4987 0.9490 -0.526 0.599\nhours 0.3906 0.3714 1.052 0.293\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 25,712 on 18 degrees of freedom\nAIC: 29,712\n\nNumber of Fisher Scoring iterations: 4\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-25.712, 19-18)\n\n[1] 0.2717286\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Para determinar se existe uma rela\u00e7\u00e3o estatisticamente significativa entre as horas estudadas e a nota do exame, precisamos analisar o valor geral do qui-quadrado do modelo e o valor p correspondente.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar a seguinte f\u00f3rmula para calcular o valor geral do qui-quadrado do modelo:<\/span><\/p>\n<p> <span style=\"color: #000000;\">X <sup>2<\/sup> = (desvio zero \u2013 desvio residual) \/ (Zero Df \u2013 Df residual)<\/span><\/p>\n<p> <span style=\"color: #000000;\">O valor p acaba sendo <strong>0,2717286<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Como esse valor p n\u00e3o \u00e9 inferior a 0,05, n\u00e3o rejeitamos a hip\u00f3tese nula. Em outras palavras, n\u00e3o h\u00e1 rela\u00e7\u00e3o estatisticamente significativa entre horas estudadas e notas em exames.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo 2: Regress\u00e3o log\u00edstica m\u00faltipla<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que um professor queira usar o n\u00famero de horas estudadas e o n\u00famero de exames preparat\u00f3rios realizados para prever a nota que os alunos obter\u00e3o em sua turma. Recolhe dados de 20 alunos e ajusta-se a um modelo de regress\u00e3o log\u00edstica m\u00faltipla.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Podemos usar o seguinte c\u00f3digo em R para ajustar um modelo de regress\u00e3o log\u00edstica m\u00faltipla:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3),\n                 exams=c(1, 2, 2, 1, 2, 1, 1, 3, 2, 4, 3, 2, 2, 4, 4, 5, 4, 4, 3, 5))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours+exams, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours + exams, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.5061 -0.6395 0.3347 0.6300 1.7014  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)  \n(Intercept) -3.4873 1.8557 -1.879 0.0602 .\nhours 0.3844 0.4145 0.927 0.3538  \nexams 1.1549 0.5493 2.103 0.0355 *\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 19,067 on 17 degrees of freedom\nAIC: 25,067\n\nNumber of Fisher Scoring iterations: 5\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-19.067, 19-17)\n\n[1] 0.01971255\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O valor p para a estat\u00edstica qui-quadrado geral do modelo \u00e9 <strong>0,01971255<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Como este valor p \u00e9 inferior a 0,05, rejeitamos a hip\u00f3tese nula. Ou seja, existe uma rela\u00e7\u00e3o estatisticamente significativa entre a soma das horas estudadas e dos exames preparat\u00f3rios realizados e a nota final obtida no exame.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir fornecem informa\u00e7\u00f5es adicionais sobre regress\u00e3o log\u00edstica:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/pt\/regressao-logistica-1\/\" target=\"_blank\" rel=\"noopener\">Introdu\u00e7\u00e3o \u00e0 regress\u00e3o log\u00edstica<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/como-relatar-resultados-de-regressao-logistica\/\" target=\"_blank\" rel=\"noopener\">Como relatar resultados de regress\u00e3o log\u00edstica<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/regressao-logistica-vs-regressao-linear\/\" target=\"_blank\" rel=\"noopener\">Regress\u00e3o log\u00edstica vs regress\u00e3o linear: as principais diferen\u00e7as<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regress\u00e3o log\u00edstica \u00e9 um tipo de modelo de regress\u00e3o que podemos usar para compreender a rela\u00e7\u00e3o entre uma ou mais vari\u00e1veis preditoras e uma vari\u00e1vel de resposta quando a vari\u00e1vel de resposta \u00e9 bin\u00e1ria. Se tivermos apenas uma vari\u00e1vel preditora e uma vari\u00e1vel resposta, podemos usar a regress\u00e3o log\u00edstica simples , que utiliza a [&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-2242","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>Compreendendo a hip\u00f3tese nula para regress\u00e3o log\u00edstica - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica a hip\u00f3tese nula para regress\u00e3o log\u00edstica, com v\u00e1rios exemplos.\" \/>\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\/hipotese-nula-de-regressao-logistica\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Compreendendo a hip\u00f3tese nula para regress\u00e3o log\u00edstica - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica a hip\u00f3tese nula para regress\u00e3o log\u00edstica, com v\u00e1rios exemplos.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-23T02:52:08+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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/\",\"url\":\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/\",\"name\":\"Compreendendo a hip\u00f3tese nula para regress\u00e3o log\u00edstica - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-23T02:52:08+00:00\",\"dateModified\":\"2023-07-23T02:52:08+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica a hip\u00f3tese nula para regress\u00e3o log\u00edstica, com v\u00e1rios exemplos.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/hipotese-nula-de-regressao-logistica\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Compreendendo a hip\u00f3tese nula para regress\u00e3o log\u00edstica\"}]},{\"@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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