{"id":1212,"date":"2023-07-27T06:42:18","date_gmt":"2023-07-27T06:42:18","guid":{"rendered":"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/"},"modified":"2023-07-27T06:42:18","modified_gmt":"2023-07-27T06:42:18","slug":"regressao-linear-multipla-manualmente","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/","title":{"rendered":"Regress\u00e3o linear m\u00faltipla manualmente (passo a passo)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pt\/regressao-linear-multipla\/\" target=\"_blank\" rel=\"noopener noreferrer\">A regress\u00e3o linear m\u00faltipla<\/a> \u00e9 um m\u00e9todo que podemos usar para quantificar a rela\u00e7\u00e3o entre duas ou mais vari\u00e1veis preditoras e uma <a href=\"https:\/\/statorials.org\/pt\/respostas-explicativas-das-variaveis\/\" target=\"_blank\" rel=\"noopener noreferrer\">vari\u00e1vel de resposta<\/a> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como realizar manualmente a regress\u00e3o linear m\u00faltipla.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Exemplo: regress\u00e3o linear m\u00faltipla manualmente<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Suponha que temos o seguinte conjunto de dados com uma vari\u00e1vel de resposta <em>y<\/em> e duas vari\u00e1veis preditoras x <sub>1<\/sub> e x <sub>2<\/sub> :<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12005 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multbyhand1.png\" alt=\"\" width=\"223\" height=\"193\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Conclua as etapas a seguir para ajustar um modelo de regress\u00e3o linear m\u00faltipla a esse conjunto de dados.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 1: Calcule x <sub>1<\/sub> <sup>2<\/sup> , x <sub>2<\/sub> <sup>2<\/sup> , x <sub>1<\/sub> y, x <sub>2<\/sub> y e x <sub>1<\/sub> x <sub>2<\/sub> .<\/strong><\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12006 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multbyhand2.png\" alt=\"Regress\u00e3o linear m\u00faltipla manualmente\" width=\"668\" height=\"239\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 2: Calcule as somas de regress\u00e3o.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Em seguida, execute os seguintes c\u00e1lculos de soma de regress\u00e3o:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><sub>\u03a3x12<\/sub> <sup>=<\/sup><\/span> <span style=\"color: #000000;\"><sup>\u03a3X12<\/sup> <sub>\u2013<\/sub> ( <sub>\u03a3X1<\/sub> ) <sup>2<\/sup> \/ n = 38,767 \u2013 (555) <sup>2\/8<\/sup> = <strong>263,875<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>\u03a3x22<\/sub> <sup>=<\/sup><\/span> <span style=\"color: #000000;\"><sup>\u03a3X22<\/sup> <sub>\u2013<\/sub> ( <sub>\u03a3X2<\/sub> ) <sup>2<\/sup> \/ n = 2823 \u2013 (145) <sup>2\/8<\/sup> = <strong>194,875<\/strong><\/span><\/li>\n<li> \u03a3 <span style=\"color: #000000;\">x <sub>1<\/sub><\/span> <span style=\"color: #000000;\"><sub>y<\/sub> <sub>=<\/sub> <strong>\u03a3<\/strong><\/span><\/li>\n<li> \u03a3 <span style=\"color: #000000;\">x <sub>2<\/sub><\/span> <span style=\"color: #000000;\"><sub>y<\/sub> <sub>=<\/sub> <strong>\u03a3<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>\u03a3<\/sub> <sub>x<\/sub> <sub>1<\/sub> <sub>x<\/sub> <strong>2<\/strong><\/span> <span style=\"color: #000000;\"><sub>=<\/sub> <sub>\u03a3<\/sub><\/span> <\/li>\n<\/ul>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12007 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multbyhand3.png\" alt=\"Exemplo de regress\u00e3o linear m\u00faltipla manualmente\" width=\"667\" height=\"278\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 3: Calcule b <sub>0<\/sub> , b <sub>1<\/sub> e b <sub>2<\/sub> .<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para calcular b <sub>1<\/sub> \u00e9: [(\u03a3x <sub>2<\/sub> <sup>2<\/sup> )(\u03a3x <sub>1<\/sub> y) \u2013 (\u03a3x <sub>1<\/sub> x <sub>2<\/sub> )(\u03a3x <sub>2<\/sub> y)] \/ [(\u03a3x <sub>1<\/sub> <sup>2<\/sup> )(\u03a3x <sub>2<\/sub> <sup>2<\/sup> ) \u2013 (\u03a3x <sub>1<\/sub> x <sub>2<\/sub> ) <sup>2<\/sup> ]<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Ent\u00e3o, <strong>b <sub>1<\/sub><\/strong> = [(194,875)(1162,5) \u2013 (-200,375)(-953,5)] \/ [(263,875) (194,875) \u2013 (-200,375) <sup>2<\/sup> ] = <strong>3,148<\/strong><\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para calcular b <sub>2<\/sub> \u00e9: [(\u03a3x <sub>1<\/sub> <sup>2<\/sup> )(\u03a3x <sub>2<\/sub> y) \u2013 (\u03a3x <sub>1<\/sub> x <sub>2<\/sub> )(\u03a3x <sub>1<\/sub> y)] \/ [(\u03a3x <sub>1<\/sub> <sup>2<\/sup> )(\u03a3x <sub>2<\/sub> <sup>2<\/sup> ) \u2013 (\u03a3x <sub>1<\/sub> x <sub>2<\/sub> ) <sup>2<\/sup> ]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Ent\u00e3o, <strong>b <sub>2<\/sub><\/strong> = [(263,875)(-953,5) \u2013 (-200,375)(1152,5)] \/ [(263,875) (194,875) \u2013 (-200,375) <sup>2<\/sup> ] = <strong>-1,656<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A f\u00f3rmula para calcular b <sub>0<\/sub> \u00e9: <span style=\"text-decoration: overline;\">y<\/span> \u2013 b <sub>1<\/sub> <span style=\"text-decoration: overline;\">X<\/span> <sub>1<\/sub> \u2013 b <sub>2<\/sub> <span style=\"text-decoration: overline;\">X<\/span> <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Assim, <strong>b <sub>0<\/sub><\/strong> = 181,5 \u2013 3,148(69,375) \u2013 (-1,656)(18,125) = <strong>-6,867<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Etapa 5: coloque b <sub>0<\/sub> , b <sub>1<\/sub> e b <sub>2<\/sub> na equa\u00e7\u00e3o de regress\u00e3o linear estimada.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A equa\u00e7\u00e3o de regress\u00e3o linear estimada \u00e9: \u0177 = b <sub>0<\/sub> + b <sub>1<\/sub> *x <sub>1<\/sub> + b <sub>2<\/sub> *x <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Em nosso exemplo, \u00e9 <strong>\u0177 = -6,867 + 3,148x <sub>1<\/sub> \u2013 1,656x <sub>2<\/sub><\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Como interpretar uma equa\u00e7\u00e3o de regress\u00e3o linear m\u00faltipla<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Veja como interpretar esta equa\u00e7\u00e3o de regress\u00e3o linear estimada: \u0177 = -6,867 + 3,148x <sub>1<\/sub> \u2013 1,656x <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><sub>b0<\/sub> = -6,867<\/strong> . Quando ambas as vari\u00e1veis preditoras s\u00e3o iguais a zero, o valor m\u00e9dio de y \u00e9 -6,867.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><sub>b1<\/sub> = 3,148<\/strong> . Um aumento de uma unidade em x <sub>1<\/sub> est\u00e1 associado a um aumento de 3,148 unidades em y, em m\u00e9dia, assumindo que x <sub>2<\/sub> permanece constante.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><sub>b2<\/sub> = -1,656<\/strong> . Um aumento de uma unidade em x <sub>2<\/sub> est\u00e1 associado a uma diminui\u00e7\u00e3o de 1.656 unidades em y, em m\u00e9dia, assumindo que x <sub>1<\/sub> permanece constante.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Recursos adicionais<\/span><\/strong><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pt\/regressao-linear-multipla\/\" target=\"_blank\" rel=\"noopener noreferrer\">Uma introdu\u00e7\u00e3o \u00e0 regress\u00e3o linear m\u00faltipla<\/a><br \/> Como realizar regress\u00e3o linear simples manualmente<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regress\u00e3o linear m\u00faltipla \u00e9 um m\u00e9todo que podemos usar para quantificar a rela\u00e7\u00e3o entre duas ou mais vari\u00e1veis preditoras e uma vari\u00e1vel de resposta . Este tutorial explica como realizar manualmente a regress\u00e3o linear m\u00faltipla. Exemplo: regress\u00e3o linear m\u00faltipla manualmente Suponha que temos o seguinte conjunto de dados com uma vari\u00e1vel de resposta 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-1212","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>Regress\u00e3o Linear M\u00faltipla Manual (Passo a Passo) - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial explica como realizar a regress\u00e3o linear m\u00faltipla manualmente, com 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-linear-multipla-manualmente\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Regress\u00e3o Linear M\u00faltipla Manual (Passo a Passo) - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial explica como realizar a regress\u00e3o linear m\u00faltipla manualmente, com um exemplo passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T06:42:18+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multbyhand1.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=\"2 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/\",\"url\":\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/\",\"name\":\"Regress\u00e3o Linear M\u00faltipla Manual (Passo a Passo) - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-27T06:42:18+00:00\",\"dateModified\":\"2023-07-27T06:42:18+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial explica como realizar a regress\u00e3o linear m\u00faltipla manualmente, com um exemplo passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-manualmente\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Regress\u00e3o linear m\u00faltipla manualmente (passo a passo)\"}]},{\"@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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