{"id":932614,"date":"2022-01-03T08:33:00","date_gmt":"2022-01-03T11:33:00","guid":{"rendered":"https:\/\/www.estrategiaconcursos.com.br\/blog\/?p=932614"},"modified":"2021-12-29T16:52:34","modified_gmt":"2021-12-29T19:52:34","slug":"resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica","status":"publish","type":"post","link":"https:\/\/www.estrategiaconcursos.com.br\/blog\/resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica\/","title":{"rendered":"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH &#8211; Estat\u00edstica"},"content":{"rendered":"\n<p>Ol\u00e1, pessoal. Tudo certo? No artigo de hoje veremos o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH.<\/p>\n\n\n\n<p>Os assuntos que ser\u00e3o vistos:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Correla\u00e7\u00e3o Linear:<\/strong> Correla\u00e7\u00e3o de Pearson e Propriedades<\/li><li><strong>Regress\u00e3o Linear Simples:<\/strong> M\u00e9todo dos M\u00ednimos Quadrados e Coeficiente de Determina\u00e7\u00e3o<\/li><\/ul>\n\n\n\n<p>Sem mais delongas, vamos l\u00e1.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Correla\u00e7\u00e3o Linear<\/h2>\n\n\n\n<p>Vamos come\u00e7ar o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">Correla\u00e7\u00e3o<\/span>:<\/strong> mostra a for\u00e7a que mant\u00e9m duas vari\u00e1veis unidas.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Correla\u00e7\u00e3o linear<\/span><\/strong> pode ser classificada:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><span class=\"has-inline-color has-vivid-purple-color\"><strong>Direta<\/strong> <\/span>(positiva): se aumentarmos uma vari\u00e1vel, a outra tamb\u00e9m aumentar\u00e1<\/li><li><span class=\"has-inline-color has-vivid-purple-color\"><strong>Inversa<\/strong> <\/span>(negativa): se aumentarmos uma vari\u00e1vel, a outra diminuir\u00e1<\/li><li><span class=\"has-inline-color has-vivid-purple-color\"><strong>Inexistente<\/strong> <\/span>(nula): n\u00e3o existente correla\u00e7\u00e3o entre as vari\u00e1veis<\/li><li><strong><span class=\"has-inline-color has-vivid-purple-color\">Perfeita<\/span><\/strong>:&nbsp; os fen\u00f4menos se ajustam perfeitamente a uma reta<\/li><\/ul>\n\n\n\n<p>Vejamos graficamente.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"886\" height=\"728\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151636\/image-410.png\" alt=\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica\" class=\"wp-image-932615\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151636\/image-410.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151636\/image-410-300x247.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151636\/image-410-768x631.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151636\/image-410-610x501.png 610w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><figcaption>Gr\u00e1ficos de Correla\u00e7\u00e3o<\/figcaption><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Coeficiente de correla\u00e7\u00e3o linear de Pearson<\/h3>\n\n\n\n<p>Dando continuidade, o <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">coeficiente de correla\u00e7\u00e3o linear de Pearson<\/span><\/strong> mede o qu\u00e3o forte \u00e9 a rela\u00e7\u00e3o entre as duas vari\u00e1veis (X e Y).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151647\/image-411.png\" alt=\"coeficiente de correla\u00e7\u00e3o linear de Pearson\" class=\"wp-image-932616\" width=\"526\" height=\"156\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151647\/image-411.png 588w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151647\/image-411-300x89.png 300w\" sizes=\"auto, (max-width: 526px) 100vw, 526px\" \/><figcaption>coeficiente de correla\u00e7\u00e3o linear de Pearson<\/figcaption><\/figure><\/div>\n\n\n\n<p>O somat\u00f3rio pode ser descrito alternativamente da seguinte forma:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151656\/image-412.png\" alt=\"\" class=\"wp-image-932617\" width=\"786\" height=\"100\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151656\/image-412.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151656\/image-412-300x38.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151656\/image-412-768x98.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151656\/image-412-610x78.png 610w\" sizes=\"auto, (max-width: 786px) 100vw, 786px\" \/><figcaption>somat\u00f3rio<\/figcaption><\/figure><\/div>\n\n\n\n<p>Para simplificar podemos descrev\u00ea-la simplesmente como:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151703\/image-413.png\" alt=\"Forma simplificada coeficiente de Pearson\" class=\"wp-image-932618\" width=\"240\" height=\"110\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151703\/image-413.png 306w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151703\/image-413-300x138.png 300w\" sizes=\"auto, (max-width: 240px) 100vw, 240px\" \/><figcaption>Forma simplificada coeficiente de Pearson<\/figcaption><\/figure><\/div>\n\n\n\n<p>Tamb\u00e9m podemos encontrar o coeficiente de Pearson pela covari\u00e2ncia entre as duas vari\u00e1veis dividida pelo desvio padr\u00e3o.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151709\/image-414.png\" alt=\" coeficiente de Pearson pela covari\u00e2ncia\" class=\"wp-image-932619\" width=\"261\" height=\"126\"\/><figcaption> coeficiente de Pearson pela covari\u00e2ncia<\/figcaption><\/figure><\/div>\n\n\n\n<p>Ainda, \u00e9 importante lembrar que o coeficiente de correla\u00e7\u00e3o de Pearson pode assumir quaisquer valores entre 1 e -1.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-luminous-vivid-amber-color\">Obs<\/span><\/strong><span class=\"has-inline-color has-luminous-vivid-amber-color\"><strong>.:<\/strong> <\/span>Caso o coeficiente de Pearson for igual a zero, n\u00e3o podemos dizer necessariamente que n\u00e3o h\u00e1 rela\u00e7\u00e3o, pois ela tamb\u00e9m poder\u00e1 ser n\u00e3o-linear.<\/p>\n\n\n\n<p>Vamos ver um exemplo num\u00e9rico da utiliza\u00e7\u00e3o da f\u00f3rmula.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo:<\/span><\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151717\/image-415.png\" alt=\"\" class=\"wp-image-932620\" width=\"259\" height=\"349\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151717\/image-415.png 286w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151717\/image-415-222x300.png 222w\" sizes=\"auto, (max-width: 259px) 100vw, 259px\" \/><figcaption>Exemplo1<\/figcaption><\/figure><\/div>\n\n\n\n<p>Teremos como m\u00e9dia de X<\/p>\n\n\n\n<p>= (6,50 + 7,50 + 8,00 + 8,50 + 9,50) \/ 5<\/p>\n\n\n\n<p>= 8<\/p>\n\n\n\n<p>E m\u00e9dia de Y<\/p>\n\n\n\n<p>(7,00 + 8,00 + 8,00 + 9,00 + 10,00) \/ 5<\/p>\n\n\n\n<p>= 8,40<\/p>\n\n\n\n<p>OK, agora veja os valores dos desvios do evento e a m\u00e9dia, al\u00e9m dos demais valores que utilizaremos na f\u00f3rmula.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151725\/image-416.png\" alt=\"\" class=\"wp-image-932621\" width=\"817\" height=\"305\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151725\/image-416.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151725\/image-416-300x112.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151725\/image-416-768x288.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151725\/image-416-610x229.png 610w\" sizes=\"auto, (max-width: 817px) 100vw, 817px\" \/><figcaption>Tabela auxiliar<\/figcaption><\/figure><\/div>\n\n\n\n<p>Assim, teremos que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"886\" height=\"306\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151730\/image-417.png\" alt=\"\" class=\"wp-image-932622\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151730\/image-417.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151730\/image-417-300x104.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151730\/image-417-768x265.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151730\/image-417-610x211.png 610w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><figcaption>C\u00e1lculos<\/figcaption><\/figure><\/div>\n\n\n\n<p>r = 5 \/ (5 x 5,2)^-2<\/p>\n\n\n\n<p><strong>r = 0,9805<\/strong> (aproximadamente)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Propriedades do Coeficiente de Correla\u00e7\u00e3o<\/h3>\n\n\n\n<p>Agora vejamos duas importantes propriedades do Coeficiente de Correla\u00e7\u00e3o.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">1\u00aa Propriedade:<\/span><\/strong> n\u00e3o sofre altera\u00e7\u00e3o quando uma constante \u00e9 adicionada \/subtra\u00edda uma vari\u00e1vel.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">2\u00aa Propriedade:<\/span><\/strong> n\u00e3o sofre altera\u00e7\u00e3o quando uma constante \u00e9 multiplicada\/dividida. Entretanto, constantes com sinais contr\u00e1rios, o coeficiente mudar\u00e1 de sinal.<\/li><\/ul>\n\n\n\n<p>Essa segunda propriedade pode ser um pouco mais dif\u00edcil de entender, ent\u00e3o vamos exemplificar. Para simplificarmos, saiba que o coeficiente de Pearson para os dados a seguir \u00e9 igual a 1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"183\" height=\"286\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151737\/image-418.png\" alt=\"\" class=\"wp-image-932623\"\/><figcaption>Exemplo 2<\/figcaption><\/figure><\/div>\n\n\n\n<p>Agora vamos multiplicar os valores de X por -2 e Y por +2.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151743\/image-419.png\" alt=\"\" class=\"wp-image-932624\" width=\"274\" height=\"266\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151743\/image-419.png 370w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151743\/image-419-300x291.png 300w\" sizes=\"auto, (max-width: 274px) 100vw, 274px\" \/><figcaption>C\u00e1lculos &#8211;  Exemplo 2<\/figcaption><\/figure><\/div>\n\n\n\n<p>Teremos as seguintes m\u00e9dias<\/p>\n\n\n\n<p>M\u00e9dia de X = (2+ 4 + 6 + 8 + 10) \/ 5<\/p>\n\n\n\n<p>M\u00e9dia de X = 6<\/p>\n\n\n\n<p>M\u00e9dia de Y = [(-12) + (-14) + (-16) + (-18) + (-20)] \/ 5<\/p>\n\n\n\n<p>M\u00e9dia de Y = -16<\/p>\n\n\n\n<p>Utilizando a tabela auxiliar de c\u00e1lculo, assim como j\u00e1 fizemos teremos que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151751\/image-420.png\" alt=\"\" class=\"wp-image-932625\" width=\"697\" height=\"331\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151751\/image-420.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151751\/image-420-300x143.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151751\/image-420-768x365.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151751\/image-420-610x290.png 610w\" sizes=\"auto, (max-width: 697px) 100vw, 697px\" \/><figcaption> tabela auxiliar  &#8211; exemplo 2<\/figcaption><\/figure><\/div>\n\n\n\n<p>r = &#8211; 40 x (40 x 40)^-2<\/p>\n\n\n\n<p>ou seja,<\/p>\n\n\n\n<p>r (2x, -2Y) = -1<\/p>\n\n\n\n<p>Veja que o valor do coeficiente n\u00e3o mudou, entretanto seu sinal foi alterado.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Regress\u00e3o Linear Simples<\/h2>\n\n\n\n<p>Vamos dar continuidade ao Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH, vendo agora a Regress\u00e3o Linear Simples.<\/p>\n\n\n\n<p>Basicamente a <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">Regress\u00e3o Linear Simples<\/span><\/strong> busca explicar a rela\u00e7\u00e3o de uma vari\u00e1vel (vari\u00e1vel dependente &#8211; Y) com outra vari\u00e1vel (vari\u00e1vel independente &#8211; X).<\/p>\n\n\n\n<p>Quanto a correla\u00e7\u00e3o, temos que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"128\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151805\/image-421.png\" alt=\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica\" class=\"wp-image-932626\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151805\/image-421.png 491w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151805\/image-421-300x78.png 300w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><figcaption>Regress\u00e3o Linear Simples<\/figcaption><\/figure><\/div>\n\n\n\n<p>Yi = Vari\u00e1vel dependente para uma s\u00e9rie de observa\u00e7\u00f5es<\/p>\n\n\n\n<p>Xi = Vari\u00e1vel independente para uma s\u00e9rie de observa\u00e7\u00f5es<\/p>\n\n\n\n<p>\u03b2 = coeficiente angular<\/p>\n\n\n\n<p>\u03b1 = coeficiente linear<\/p>\n\n\n\n<p>\u03f5i = componente aleat\u00f3rio <span class=\"has-inline-color has-vivid-purple-color\">-&gt; demonstra os desvios quando se tentar aproximar uma s\u00e9rie de observa\u00e7\u00f5es Xi por meio de uma reta Yi (correla\u00e7\u00e3o n\u00e3o perfeita)<\/span><\/p>\n\n\n\n<p>Como qualquer modelo, a regress\u00e3o linear exige alguns requisitos.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Requisitos:<\/span><\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>E (\u03f5i) = 0<\/strong> -&gt; m\u00e9dia dos erros \u00e9 igual a zero<\/li><li><strong>VAR (\u03f5i) = Constante<\/strong> -&gt; A vari\u00e2ncia do erro \u00e9 constante, trata-se da propriedade da homocedasticia.<\/li><li><strong>Cov&nbsp; (\u03f5i, \u03f5j ) = 0<\/strong> -&gt; os erros n\u00e3o s\u00e3o correlacionados, ou seja, s\u00e3o independentes.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">M\u00e9todo dos M\u00ednimos Quadrados<\/h3>\n\n\n\n<p>Continuando o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH, agora vejamos o<span class=\"has-inline-color has-vivid-cyan-blue-color\"> <strong>M\u00e9todo dos M\u00ednimos Quadrados<\/strong>.<\/span><\/p>\n\n\n\n<p>Basicamente ele busca a reta que minimiza a soma dos quadrados dos desvios.<\/p>\n\n\n\n<p>Utilizaremos a seguinte express\u00e3o:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151817\/image-422.png\" alt=\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica\" class=\"wp-image-932627\" width=\"277\" height=\"100\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151817\/image-422.png 331w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151817\/image-422-300x109.png 300w\" sizes=\"auto, (max-width: 277px) 100vw, 277px\" \/><figcaption>M\u00e9todo dos M\u00ednimos Quadrados<\/figcaption><\/figure><\/div>\n\n\n\n<p>Em que \u201cb\u201d pode ser encontrado das seguintes formas<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"891\" height=\"120\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151836\/image-423.png\" alt=\"\" class=\"wp-image-932628\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151836\/image-423.png 891w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151836\/image-423-300x40.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151836\/image-423-768x103.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151836\/image-423-610x82.png 610w\" sizes=\"auto, (max-width: 891px) 100vw, 891px\" \/><figcaption>coeficiente angular<\/figcaption><\/figure><\/div>\n\n\n\n<p>Ou de forma simplificada,<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"156\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151843\/image-424.png\" alt=\" coeficiente angular simplificado\" class=\"wp-image-932629\"\/><figcaption> coeficiente angular simplificado<\/figcaption><\/figure><\/div>\n\n\n\n<p>E \u201ca\u201d:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"89\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151849\/image-425.png\" alt=\"\" class=\"wp-image-932630\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151849\/image-425.png 319w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151849\/image-425-300x84.png 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><figcaption>coeficiente linear<\/figcaption><\/figure><\/div>\n\n\n\n<p>Para exemplificar, vamos utilizar a tabela auxiliar de c\u00e1lculo.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo:<\/span><\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"886\" height=\"310\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151901\/image-426.png\" alt=\"\" class=\"wp-image-932631\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151901\/image-426.png 886w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151901\/image-426-300x105.png 300w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151901\/image-426-768x269.png 768w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151901\/image-426-610x213.png 610w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><\/figure><\/div>\n\n\n\n<p>Teremos que,<\/p>\n\n\n\n<p>b = -5 \/ 14<\/p>\n\n\n\n<p>b = -0,357<\/p>\n\n\n\n<p>E \u201ca\u201d ser\u00e1:<\/p>\n\n\n\n<p>a = 8 \u2013 (-0,357) x 7<\/p>\n\n\n\n<p>a = 8 + 2,499<\/p>\n\n\n\n<p>a = 10,499<\/p>\n\n\n\n<p>Logo, temos a reta de regress\u00e3o estimada:<\/p>\n\n\n\n<p>Y = 10,499 -0,357 . X<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Coeficiente de Determina\u00e7\u00e3o<\/h3>\n\n\n\n<p>Para finalizar o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH.<\/p>\n\n\n\n<p>O <strong><span class=\"has-inline-color has-vivid-cyan-blue-color\">coeficiente de determina\u00e7\u00e3o<\/span><\/strong> (R\u00b2) mede a qualidade do ajuste proporcionado pela reta de regress\u00e3o<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"284\" height=\"180\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151909\/image-427.png\" alt=\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica\" class=\"wp-image-932632\"\/><figcaption>coeficiente de determina\u00e7\u00e3o<\/figcaption><\/figure><\/div>\n\n\n\n<p>Perceba que se trata de um valor ao quadrado,<\/p>\n\n\n\n<p>Sendo que:<\/p>\n\n\n\n<p><strong>SQT<\/strong> (Soma dos Quadrados Totais) = <strong>SQM<\/strong> (soma dos quadrados do modelo de regress\u00e3o) + <strong>SQR<\/strong> (soma dos quadrados dos res\u00edduos)<\/p>\n\n\n\n<p>Em que a soma dos quadrados do modelo de regress\u00e3o (SQM) pode ser definida pelas formas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"329\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151918\/image-428.png\" alt=\"\" class=\"wp-image-932633\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151918\/image-428.png 418w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151918\/image-428-300x236.png 300w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><figcaption> soma dos quadrados do modelo de regress\u00e3o <\/figcaption><\/figure><\/div>\n\n\n\n<p>E a soma dos quadrados dos res\u00edduos (SQR):<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"140\" src=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151925\/image-429.png\" alt=\"\" class=\"wp-image-932634\" srcset=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151925\/image-429.png 357w, https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/12\/19151925\/image-429-300x118.png 300w\" sizes=\"auto, (max-width: 357px) 100vw, 357px\" \/><figcaption> E a soma dos quadrados dos res\u00edduos (SQR): <\/figcaption><\/figure><\/div>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-green-cyan-color\">Exemplo:<\/span><\/strong> (VUNESP 2020\/EBSERH) Numa regress\u00e3o linear simples em que foi utilizada uma amostra com 52 observa\u00e7\u00f5es, a soma dos quadrados totais e de 50 e a soma dos quadrados dos res\u00edduos e de 20. O coeficiente de determina\u00e7\u00e3o ser\u00e1:<\/p>\n\n\n\n<p>R\u00b2 = SQM \/ SQT<\/p>\n\n\n\n<p>R\u00b2 = (SQT \u2013 SQR) \/ SQT<\/p>\n\n\n\n<p>R\u00b2 = (50 \u2013 20) \/ 50<\/p>\n\n\n\n<p>R\u00b2 = 0,6<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Considera\u00e7\u00f5es Finais<\/h2>\n\n\n\n<p>Pessoal, chegamos ao final dos Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH. Espero que o artigo tenha sido \u00fatil para seu estudo.<\/p>\n\n\n\n<p>Obviamente trata-se de um resumo apenas com as principais partes da mat\u00e9ria, as aulas s\u00e3o bem aprofundadas nas explica\u00e7\u00f5es e exerc\u00edcios resolvidos, al\u00e9m de outros assuntos n\u00e3o tratados no artigo, mas que s\u00e3o importantes como <strong>Coeficiente de Determina\u00e7\u00e3o Ajustado, Quadrados M\u00e9dios e Estat\u00edstica F (Raz\u00e3o F)<\/strong>, assim n\u00e3o deixe de acompanhar as aulas para o aprofundamento necess\u00e1rio.<\/p>\n\n\n\n<p>Trata-se de um assunto que exige, de fato, muita pr\u00e1tica por meio de exerc\u00edcios. Assim, al\u00e9m dos exerc\u00edcios da aula, n\u00e3o deixe de treinar pelo nosso sistema de quest\u00f5es.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><a href=\"https:\/\/concursos.estrategiaeducacional.com.br\/\">Sistema de Quest\u00f5es (SQ) \u2013 Estrat\u00e9gia Concursos<\/a><\/p>\n\n\n\n<p>Gostou do artigo? N\u00e3o deixe de seguir<\/p>\n\n\n\n<p><a href=\"https:\/\/www.instagram.com\/resumospassarin\/\">https:\/\/www.instagram.com\/resumospassarin\/<\/a><\/p>\n\n\n\n<h2 class=\"has-text-align-center wp-block-heading\" id=\"h-cursos-e-assinaturas\">Cursos e Assinaturas<\/h2>\n\n\n\n<div class=\"container\" id=\"boxes\">\n  <div class=\"row\">\n\n    <div class=\"col-sm\">\n      <div class=\"estrategia\" id=\"box-assinatura\">\n        <h3 class=\"titulo-assinatura\">Assinatura Concursos<\/h3>\n        <p class=\"subtitulo-assinatura\">Assinatura de 1 ano ou 2 anos<\/p>\n        <div class=\"box-botao\">\n          <a class=\"btn-assinatura\" target=\"_blank\" href=\"https:\/\/www.estrategiaconcursos.com.br\/assinaturas\/\" role=\"button\" rel=\"noopener noreferrer\">ASSINE AGORA<\/a>\n        <\/div>\n      <\/div><\/div><\/div><\/div>\n\n\n\n<div class=\"container\" id=\"boxes\">\n  <div class=\"row\">\n\n    <div class=\"col-sm\" id=\"boxes-concursos\">\n      <div style=\"background-color: #005DAD;\" class=\"conteudo-concursos\" id=\"box-concursos\">\n        <h3 class=\"titulo-assinatura\">Concursos Abertos<\/h3>\n        <p class=\"subtitulo-assinatura\">Os editais publicados<\/p>\n        <div class=\"box-botao\">\n          <a class=\"btn-assinatura\" target=\"_blank\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-abertos\/\" role=\"button\" rel=\"noopener noreferrer\">Conhe\u00e7a Agora<\/a>\n        <\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"col-sm\" id=\"boxes-concursos\">\n      <div style=\"background-color: #1A7ED5;\" class=\"conteudo-concursos\" id=\"box-concursos\">\n        <h3 class=\"titulo-assinatura\">Concursos 2021<\/h3>\n        <p class=\"subtitulo-assinatura\">As oportunidades previstas<\/p>\n        <div class=\"box-botao\">\n          <a class=\"btn-assinatura\" target=\"_blank\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-2021\/\" role=\"button\" rel=\"noopener noreferrer\">Conhe\u00e7a Agora<\/a>\n        <\/div>\n      <\/div>\n    <\/div>\n\n    <div class=\"col-sm\" id=\"boxes-concursos\">\n      <div style=\"background-color: #419FF0;\" class=\"conteudo-concursos\" id=\"box-concursos\">\n        <h3 class=\"titulo-assinatura\">Concursos 2022<\/h3>\n        <p class=\"subtitulo-assinatura\">Vagas para o pr\u00f3ximo ano<\/p>\n        <div class=\"box-botao\">\n          <a class=\"btn-assinatura\" target=\"_blank\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/concursos-2022\/\" role=\"button\" rel=\"noopener noreferrer\">Conhe\u00e7a Agora<\/a>\n        <\/div>\n      <\/div>\n    <\/div>\n\n  <\/div>\n<\/div>\n\n\n\n<div class=\"container\" id=\"boxes\">\n  <div class=\"row\">\n\n    <div class=\"col-sm\">\n      <div class=\"banner-tribunal\" id=\"box-assinatura\">\n        <h3 class=\"titulo-assinatura\">Cursos para Carreiras Jur\u00eddicas<\/h3>\n        <p class=\"subtitulo-assinatura\">Conhe\u00e7a os cursos<\/p>\n        <div class=\"box-botao\">\n          <a class=\"btn-assinatura\" target=\"_blank\" href=\"https:\/\/www.estrategiaconcursos.com.br\/cursosPorConcurso\/assinaturas-carreira-juridica\/\" rel=\"noopener noreferrer\">Conhe\u00e7a mais<\/a>\n        <\/div>\n      <\/div>\n      <p class=\"texto-auxiliar\">Prepare-se com o melhor material e com quem mais aprova em Concursos P\u00fablicos em todo o pa\u00eds.<\/p>\n    <\/div>\n\n  <\/div>\n<\/div>\n\n\n\n<p>At\u00e9 mais e bons estudos!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ol\u00e1, pessoal. Tudo certo? No artigo de hoje veremos o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH. Os assuntos que ser\u00e3o vistos: Correla\u00e7\u00e3o Linear: Correla\u00e7\u00e3o de Pearson e Propriedades Regress\u00e3o Linear Simples: M\u00e9todo dos M\u00ednimos Quadrados e Coeficiente de Determina\u00e7\u00e3o Sem mais delongas, vamos l\u00e1. Correla\u00e7\u00e3o Linear Vamos come\u00e7ar o Resumo sobre Correla\u00e7\u00e3o Linear [&hellip;]<\/p>\n","protected":false},"author":1763,"featured_media":901957,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"post_tipo":"article","footnotes":""},"categories":[220183],"tags":[],"tax_estado":[219974],"class_list":["post-932614","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fiscal-municipal","tax_estado-mg"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.2 (Yoast SEO v27.2) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica<\/title>\n<meta name=\"description\" content=\"Veja neste artigo o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH, sobre a Correla\u00e7\u00e3o de Pearson e Coeficiente de Determina\u00e7\u00e3o.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH - Estat\u00edstica\" \/>\n<meta property=\"og:description\" content=\"Veja neste artigo o Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH, sobre a Correla\u00e7\u00e3o de Pearson e Coeficiente de Determina\u00e7\u00e3o.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.estrategiaconcursos.com.br\/blog\/resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica\/\" \/>\n<meta property=\"og:site_name\" content=\"Estrat\u00e9gia Concursos\" \/>\n<meta property=\"article:published_time\" content=\"2022-01-03T11:33:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/dhg1h5j42swfq.cloudfront.net\/2021\/11\/05185713\/iss-bh-2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"819\" \/>\n\t<meta property=\"og:image:height\" content=\"460\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Leonardo Menezes Passarin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:site\" content=\"@EstratConcursos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Leonardo Menezes Passarin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. tempo de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"NewsArticle\",\"@id\":\"https:\/\/www.estrategiaconcursos.com.br\/blog\/resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.estrategiaconcursos.com.br\/blog\/resumo-sobre-correlacao-linear-e-regressao-para-iss-bh-estatistica\/\"},\"author\":{\"name\":\"Leonardo Menezes Passarin\",\"@id\":\"https:\/\/www.estrategiaconcursos.com.br\/blog\/#\/schema\/person\/245b44e43eb13f0dbd04a7a078cd0d0d\"},\"headline\":\"Resumo sobre Correla\u00e7\u00e3o Linear e Regress\u00e3o para ISS-BH &#8211; 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