{"id":882,"date":"2023-07-28T10:44:58","date_gmt":"2023-07-28T10:44:58","guid":{"rendered":"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/"},"modified":"2023-07-28T10:44:58","modified_gmt":"2023-07-28T10:44:58","slug":"regressao-polinomial-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/","title":{"rendered":"Como realizar regress\u00e3o polinomial em python"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A an\u00e1lise de regress\u00e3o \u00e9 usada para quantificar a rela\u00e7\u00e3o entre uma ou mais vari\u00e1veis explicativas e uma vari\u00e1vel de resposta.<\/span><\/p>\n<p> <span style=\"color: #000000;\">O tipo mais comum de an\u00e1lise de regress\u00e3o \u00e9 <a href=\"https:\/\/statorials.org\/pt\/regressao-linear-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">a regress\u00e3o linear simples<\/a> , usada quando uma vari\u00e1vel preditora e uma vari\u00e1vel resposta possuem um relacionamento linear.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9521 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython1.png\" alt=\"\" width=\"371\" height=\"249\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">No entanto, \u00e0s vezes a rela\u00e7\u00e3o entre uma vari\u00e1vel preditora e uma vari\u00e1vel de resposta \u00e9 n\u00e3o linear.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, o relacionamento verdadeiro pode ser quadr\u00e1tico:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-9522 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython2.png\" alt=\"\" width=\"369\" height=\"256\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Ou pode ser c\u00fabico:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9523 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython3.png\" alt=\"\" width=\"382\" height=\"258\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Nestes casos, faz sentido utilizar <strong>a regress\u00e3o polinomial<\/strong> , que pode dar conta da rela\u00e7\u00e3o n\u00e3o linear entre as vari\u00e1veis.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Este tutorial explica como realizar regress\u00e3o polinomial em Python.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Exemplo: regress\u00e3o polinomial em Python<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que temos a seguinte vari\u00e1vel preditora (x) e vari\u00e1vel de resposta (y) em Python:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>x = [2, 3, 4, 5, 6, 7, 7, 8, 9, 11, 12]\ny = [18, 16, 15, 17, 20, 23, 25, 28, 31, 30, 29]\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Se criarmos um gr\u00e1fico de dispers\u00e3o simples desses dados, podemos ver que a rela\u00e7\u00e3o entre x e y claramente n\u00e3o \u00e9 linear:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> matplotlib.pyplot <span style=\"color: #107d3f;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#create scatterplot<\/span> \nplt.scatter(x, y)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-9524 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython4.png\" alt=\"\" width=\"383\" height=\"257\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Portanto, n\u00e3o faria sentido ajustar um modelo de regress\u00e3o linear a estes dados. Em vez disso, podemos tentar ajustar um modelo de regress\u00e3o polinomial com grau 3 usando a fun\u00e7\u00e3o <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/generated\/numpy.polyfit.html\" target=\"_blank\" rel=\"noopener noreferrer\">numpy.polyfit()<\/a> :<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n\n<span style=\"color: #008080;\">#polynomial fit with degree = 3\n<\/span>model = np.poly1d(np.polyfit(x, y, 3))\n\n<span style=\"color: #008080;\">#add fitted polynomial line to scatterplot\n<\/span>polyline = np.linspace(1, 12, 50)\nplt.scatter(x, y)\nplt.plot(polyline, model(polyline))\nplt.show()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-9525 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython5.png\" alt=\"Linha de regress\u00e3o polinomial em Python\" width=\"379\" height=\"249\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Podemos obter a equa\u00e7\u00e3o de regress\u00e3o polinomial ajustada imprimindo os coeficientes do modelo:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>print(model)\n\npoly1d([ -0.10889554, 2.25592957, -11.83877127, 33.62640038])\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A equa\u00e7\u00e3o de regress\u00e3o polinomial ajustada \u00e9:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>y = -0,109x <sup>3<\/sup> + 2,256x <sup>2<\/sup> \u2013 11,839x + 33,626<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Esta equa\u00e7\u00e3o pode ser usada para encontrar o valor esperado da vari\u00e1vel resposta dado um determinado valor da vari\u00e1vel explicativa.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Por exemplo, suponha que x = 4. O valor esperado para a vari\u00e1vel de resposta, y, seria:<\/span><\/p>\n<p> <span style=\"color: #000000;\">y = -0,109(4) <sup>3<\/sup> + 2,256(4) <sup>2<\/sup> \u2013 11,839(4) + 33,626= <b>15,39<\/b> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tamb\u00e9m podemos escrever uma fun\u00e7\u00e3o curta para obter o R-quadrado do modelo, que \u00e9 a propor\u00e7\u00e3o da vari\u00e2ncia na vari\u00e1vel de resposta que pode ser explicada pelas vari\u00e1veis preditoras.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate r-squared<\/span>\n<span style=\"color: #008000;\">def<\/span> polyfit(x, y, degree):\n    results = {}\n    coeffs = numpy.polyfit(x, y, degree)\n    p = numpy.poly1d(coeffs)\n    <span style=\"color: #008080;\">#calculate r-squared<\/span>\n    yhat = p(x)\n    ybar = numpy.sum(y)\/len(y)\n    ssreg = numpy.sum((yhat-ybar)**2)\n    sstot = numpy.sum((y - ybar)**2)\n    results['r_squared'] = ssreg \/ sstot\n\n    <span style=\"color: #008000;\">return<\/span> results\n\n<span style=\"color: #008080;\">#find r-squared of polynomial model with degree = 3\n<\/span>polyfit(x, y, 3)\n\n{'r_squared': 0.9841113454245183}\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Neste exemplo, o R quadrado do modelo \u00e9 <strong>0,9841<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Isso significa que <strong>98,41%<\/strong> da varia\u00e7\u00e3o da vari\u00e1vel resposta pode ser explicada pelas vari\u00e1veis preditoras.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A an\u00e1lise de regress\u00e3o \u00e9 usada para quantificar a rela\u00e7\u00e3o entre uma ou mais vari\u00e1veis explicativas e uma vari\u00e1vel de resposta. O tipo mais comum de an\u00e1lise de regress\u00e3o \u00e9 a regress\u00e3o linear simples , usada quando uma vari\u00e1vel preditora e uma vari\u00e1vel resposta possuem um relacionamento linear. No entanto, \u00e0s vezes a rela\u00e7\u00e3o entre [&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-882","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 polinomial em Python - Estatologia<\/title>\n<meta name=\"description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o polinomial em Python.\" \/>\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-polinomial-python\/\" \/>\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 polinomial em Python - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o polinomial em Python.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T10:44:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/polynomialpython1.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-polinomial-python\/\",\"url\":\"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/\",\"name\":\"Como realizar regress\u00e3o polinomial em Python - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-28T10:44:58+00:00\",\"dateModified\":\"2023-07-28T10:44:58+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Uma explica\u00e7\u00e3o simples sobre como realizar regress\u00e3o polinomial em Python.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/regressao-polinomial-python\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como realizar regress\u00e3o polinomial em python\"}]},{\"@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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