{"id":1566,"date":"2023-07-25T20:42:10","date_gmt":"2023-07-25T20:42:10","guid":{"rendered":"https:\/\/statorials.org\/pt\/regressao-de-potencia-em-r\/"},"modified":"2023-07-25T20:42:10","modified_gmt":"2023-07-25T20:42:10","slug":"regressao-de-potencia-em-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regressao-de-potencia-em-r\/","title":{"rendered":"Como realizar a regress\u00e3o de pot\u00eancia em r (passo a passo)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>A regress\u00e3o de pot\u00eancia<\/strong> \u00e9 um tipo de regress\u00e3o n\u00e3o linear que assume a seguinte forma:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = <sup>axb<\/sup><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>y:<\/strong> a vari\u00e1vel de resposta<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x:<\/strong> a vari\u00e1vel preditiva<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>a, b:<\/strong> os coeficientes de regress\u00e3o que descrevem a rela\u00e7\u00e3o entre <em>x<\/em> e <em>y<\/em><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Este tipo de regress\u00e3o \u00e9 utilizado para modelar situa\u00e7\u00f5es em que a <a href=\"https:\/\/statorials.org\/pt\/respostas-explicativas-das-variaveis\/\" target=\"_blank\" rel=\"noopener\">vari\u00e1vel resposta<\/a> \u00e9 igual \u00e0 vari\u00e1vel preditora elevada a uma pot\u00eancia.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O exemplo passo a passo a seguir mostra como realizar uma regress\u00e3o de pot\u00eancia para um determinado conjunto de dados em R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 1: crie os dados<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Primeiro, vamos criar dados falsos para duas vari\u00e1veis: x e y.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data<\/span>\nx=1:20\ny=c(1, 8, 5, 7, 6, 20, 15, 19, 23, 37, 33, 38, 49, 50, 56, 52, 70, 89, 97, 115)<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 2: visualize os dados<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A seguir, vamos criar um gr\u00e1fico de dispers\u00e3o para visualizar a rela\u00e7\u00e3o entre x e y:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot<\/span>\nplot(x, y)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15543 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/puissancer1.png\" alt=\"\" width=\"450\" height=\"416\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">O gr\u00e1fico mostra que existe uma clara rela\u00e7\u00e3o de poder entre as duas vari\u00e1veis. Assim, parece sensato ajustar uma equa\u00e7\u00e3o de regress\u00e3o de pot\u00eancia aos dados, em vez de um modelo de regress\u00e3o linear.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Etapa 3: Ajustar o modelo de regress\u00e3o de pot\u00eancia<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A seguir, usaremos a fun\u00e7\u00e3o <strong>lm()<\/strong> para ajustar um modelo de regress\u00e3o aos dados, especificando que R deve usar a vari\u00e1vel de resposta log e a vari\u00e1vel preditora log ao ajustar o modelo:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the model\n<\/span>model &lt;- lm(log(y)~ log(x))\n\n<span style=\"color: #008080;\">#view the output of the model\n<\/span>summary(model)\n\nCall:\nlm(formula = log(y) ~ log(x))\n\nResiduals:\n     Min 1Q Median 3Q Max \n-0.67014 -0.17190 -0.05341 0.16343 0.93186 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 0.15333 0.20332 0.754 0.461    \nlog(x) 1.43439 0.08996 15.945 4.62e-12 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 0.3187 on 18 degrees of freedom\nMultiple R-squared: 0.9339, Adjusted R-squared: 0.9302 \nF-statistic: 254.2 on 1 and 18 DF, p-value: 4.619e-12<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">O <a href=\"https:\/\/statorials.org\/pt\/um-guia-simples-para-compreender-o-teste-f-para-significancia-geral-na-regressao\/\" target=\"_blank\" rel=\"noopener\">valor F geral<\/a> do modelo \u00e9 252,1 e o valor p correspondente \u00e9 extremamente baixo (4,619e-12), indicando que o modelo como um todo \u00e9 \u00fatil.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Usando os coeficientes da tabela de sa\u00edda, podemos ver que a equa\u00e7\u00e3o de regress\u00e3o de pot\u00eancia ajustada \u00e9:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>ln(y) = 0,15333 + 1,43439ln(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Aplicando <em>e<\/em> a ambos os lados, podemos reescrever a equa\u00e7\u00e3o da seguinte forma:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>y = e <sup>0,15333 + 1,43439ln(x)<\/sup><\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>y = 1,1657x <sup>1,43439<\/sup><\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos usar esta equa\u00e7\u00e3o para prever a vari\u00e1vel de resposta, <em>y<\/em> , com base no valor da vari\u00e1vel preditora, <em>x<\/em> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, se <em>x<\/em> = 12, ent\u00e3o prever\u00edamos que <em>y<\/em> seria <strong>41,167<\/strong> :<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = 1,1657(12) <sup>1,43439<\/sup> = 41,167<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>B\u00f4nus:<\/strong> sinta-se \u00e0 vontade para usar esta calculadora de regress\u00e3o de pot\u00eancia online para calcular automaticamente a equa\u00e7\u00e3o de regress\u00e3o de pot\u00eancia para um determinado preditor e vari\u00e1vel de resposta.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pt\/regressao-linear-multipla-r\/\" target=\"_blank\" rel=\"noopener\">Como realizar regress\u00e3o linear m\u00faltipla em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/regressao-exponencial-em-r\/\" target=\"_blank\" rel=\"noopener\">Como realizar regress\u00e3o exponencial em R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/regressao-logaritmica-em-r\/\" target=\"_blank\" rel=\"noopener\">Como realizar regress\u00e3o logar\u00edtmica em R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A regress\u00e3o de pot\u00eancia \u00e9 um tipo de regress\u00e3o n\u00e3o linear que assume a seguinte forma: y = axb Ouro: y: a vari\u00e1vel de resposta x: a vari\u00e1vel preditiva a, b: os coeficientes de regress\u00e3o que descrevem a rela\u00e7\u00e3o entre x e y Este tipo de regress\u00e3o \u00e9 utilizado para modelar situa\u00e7\u00f5es em que 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-1566","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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