{"id":850,"date":"2025-07-29T20:49:33","date_gmt":"2025-07-30T00:49:33","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=850"},"modified":"2025-10-11T17:32:20","modified_gmt":"2025-10-11T21:32:20","slug":"15-5","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/15-0\/15-5\/","title":{"rendered":"Cap\u00edtulo 15.5"},"content":{"rendered":"<div style=\"position: relative\">\n<div style=\"float: left;width: 300px;background-color: #f5f5f5;border: 1px solid #ddd;border-radius: 5px;padding: 15px;margin-right: 20px;margin-bottom: 5px;overflow: hidden\">\n<h3 style=\"margin: 0 0 10px 0;padding-bottom: 8px;border-bottom: 1px solid #ddd\">\u00cdndice<\/h3>\n<ol style=\"margin: 0;padding-left: 0;list-style-type: none\">\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/\">1. O que \u00e9 Ci\u00eancia de Dados?<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/\">1.1. Introdu\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-1\/\">1.1.1. Ferramentas Computacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-1\/1-2\/\">1.1.2. T\u00e9cnicas Estat\u00edsticas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-2\/\">1.2. Por que Ci\u00eancia de Dados?<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/\">1.3. Tra\u00e7ando os Cl\u00e1ssicos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-1\/\">1.3.1. Personagens Liter\u00e1rios<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/1-0\/1-3\/3-2\/\">1.3.2. Outro Tipo de Personagem<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/\">2. Causalidade e Experimentos<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-1\/\">2.1. John Snow e a Bomba da Broad Street<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-2\/\">2.2. O &#8220;Grande Experimento&#8221; de Snow<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-3\/\">2.3. Estabelecendo Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-4\/\">2.4. Randomiza\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/2-0\/2-5\/\">2.5. Notas Finais<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/\">3. Progamando em Python<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-1\/\">3.1. Express\u00f5es<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/\">3.2. Nomes<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-2\/2-1\/\">3.2.1. Exemplo: Taxas de Crescimento<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-3\/\">3.3. Chamadas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/3-0\/3-4\/\">3.4. Introdu\u00e7\u00e3o \u00e0s Tabelas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/\">4. Tipos de Dados<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-1\/\">4.1. N\u00fameros<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/\">4.2. Strings<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-2\/2-1\/\">4.2.1. M\u00e9todos de Strings<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/4-0\/4-3\/\">4.3. Compara\u00e7\u00f5es<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/\">5. Sequ\u00eancias<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-1\/\">5.1. Arrays<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-2\/\">5.2. Ranges<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/5-0\/5-3\/\">5.3. Mais sobre Arrays<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/\">6. Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-1\/\">6.1. Ordenando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-2\/\">6.2. Selecionando Linhas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-3\/\">6.3. Exemplo: Tend\u00eancias Populacionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/6-0\/6-4\/\">6.4. Examplo: Propor\u00e7\u00f5es de Sexos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/\">7. Visualiza\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-1\/\">7.1. Visualizando Distribui\u00e7\u00f5es<br \/>\nCateg\u00f3ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-2\/\">7.2. Visualizando Distribui\u00e7\u00f5es Num\u00e9ricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/7-0\/7-3\/\">7.3. Gr\u00e1ficos Sobrepostos<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/\">8. Fun\u00e7\u00f5es e Tabelas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-1\/\">8.1. Aplicando Fun\u00e7\u00e3o a uma Coluna<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-2\/\">8.2. Classificando por uma Vari\u00e1vel<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-3\/\">8.3. Classifica\u00e7\u00e3o Cruzada<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-4\/\">8.4. Unindo Tabelas por Colunas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/8-0\/8-5\/\">8.5. Compartilhamento de Bicicletas<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/\">9. Aleatoriedade<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-1\/\">9.1. Declara\u00e7\u00f5es Condicionais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-2\/\">9.2. Itera\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-3\/\">9.3. Simula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-4\/\">9.4. O Problema de Monty Hall<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/9-0\/9-5\/\">9.5. Encontrando Probabilidades<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/\">10. Amostragem e Distribui\u00e7\u00f5es Emp\u00edricas<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-1\/\">10.1. Distribui\u00e7\u00f5es Emp\u00edricas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-2\/\">10.2. Amostragem de uma Popula\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-3\/\">10.3. Distribui\u00e7\u00e3o Emp\u00edrica de uma<br \/>\nEstat\u00edstica<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/10-0\/10-4\/\">10.4. Amostragem Aleat\u00f3ria em Python <\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/\">11. Testando Hip\u00f3teses<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-1\/\">11.1. Avaliando um Modelo<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-2\/\">11.2. M\u00faltiplas Categorias<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-3\/\">11.3. Decis\u00f5es e Incertezas<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/11-0\/11-4\/\">11.4. Probabilidades de Erro<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/\">12. Comparando Duas Amostras<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-1\/\">12.1. Teste A\/B<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-2\/\">12.2. Causalidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/12-0\/12-3\/\">12.3. Esvaziar<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/\">13. Estima\u00e7\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-1\/\">13.1. Percentis<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-2\/\">13.2. O Bootstrap<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-3\/\">13.3. Intervalos de Confian\u00e7a<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/13-0\/13-4\/\">13.4. Usando Intervalos de Confian\u00e7a<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/\">14. Por que a M\u00e9dia \u00e9 Importante<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-1\/\">14.1. Propriedades da M\u00e9dia<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-2\/\">14.2. Variabilidade<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-3\/\">14.3. O DP e a Curva Normal<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-4\/\">14.4. Teorema Central do Limite<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-5\/\">14.5. Variabilidade da M\u00e9dia da Amostra<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/14-0\/14-6\/\">14.6. Escolhendo um Tamanho de Amostra<\/a><\/li>\n<\/ul>\n<\/li>\n<li style=\"margin-bottom: 5px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/\">15. Previs\u00e3o<\/a>\n<ul style=\"margin: 5px 0 5px 15px;padding-left: 10px;list-style-type: none;border-left: 1px solid #ddd\">\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-1\/\">15.1. Correla\u00e7\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-2\/\">15.2. Linha de Regress\u00e3o<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-3\/\">15.3. M\u00e9todo dos M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-4\/\">15.4. Regress\u00e3o de M\u00ednimos Quadrados<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-5\/\">15.5. Diagn\u00f3sticos Visuais<\/a><\/li>\n<li style=\"margin-bottom: 3px\"><a style=\"padding: 2px 0\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-6\/\">15.6. Diagn\u00f3stico Num\u00e9rico<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<p><!-- Main Content --><\/p>\n<div style=\"overflow: hidden\">\n<p><!--###########################################################################################################################################################--><\/p>\n<pre><code><span style=\"color: black\">from datascience import *\r\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport numpy as np\r\nfrom scipy import stats\r\n\r\nimport matplotlib\r\nmatplotlib.use('Agg')\r\n%matplotlib inline\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"diagn-sticos-visuais\" style=\"text-align: center\">Diagn\u00f3sticos Visuais<\/h1>\n<p style=\"text-align: justify\">Suponha que um cientista de dados tenha decidido usar a regress\u00e3o linear para estimar valores de uma vari\u00e1vel (chamada de vari\u00e1vel de resposta) com base em outra vari\u00e1vel (chamada de preditora). Para ver qu\u00e3o bem esse m\u00e9todo de estimativa funciona, o cientista de dados deve medir qu\u00e3o distantes as estimativas est\u00e3o dos valores reais. Essas diferen\u00e7as s\u00e3o chamadas de <em>res\u00edduos<\/em>.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\">residual = observed value &#8211; regression estimate<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Um res\u00edduo \u00e9 o que sobra \u2013 o res\u00edduo \u2013 ap\u00f3s a estimativa.<\/p>\n<p style=\"text-align: justify\">Os res\u00edduos s\u00e3o as dist\u00e2ncias verticais dos pontos \u00e0 linha de regress\u00e3o. H\u00e1 um res\u00edduo para cada ponto no diagrama de dispers\u00e3o. O res\u00edduo \u00e9 a diferen\u00e7a entre o valor observado de <em>y<\/em> e o valor ajustado de <em>y<\/em>, ent\u00e3o para o ponto <em>(x, y)<\/em>,<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">residual = y &#8211; fitted value of y = y &#8211; height of regression line at x<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o <code>residual<\/code> calcula os res\u00edduos. O c\u00e1lculo assume todas as fun\u00e7\u00f5es relevantes que j\u00e1 definimos: <code>standard_units<\/code>, <code>correlation<\/code>, <code>slope<\/code>, <code>intercept<\/code>, e <code>fit<\/code>.<\/p>\n<pre><code><span style=\"color: black\">family_heights = Table.read_table(path_data + 'family_heights.csv')\r\nheights = family_heights.select('midparentHeight', 'childHeight')\r\nheights = heights.relabel(0, 'MidParent').relabel(1, 'Child')\r\nhybrid = Table.read_table(path_data + 'hybrid.csv')<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">def standard_units(x):\r\n    return (x - np.mean(x))\/np.std(x)\r\n\r\ndef correlation(table, x, y):\r\n    x_in_standard_units = standard_units(table.column(x))\r\n    y_in_standard_units = standard_units(table.column(y))\r\n    return np.mean(x_in_standard_units * y_in_standard_units)\r\n\r\ndef slope(table, x, y):\r\n    r = correlation(table, x, y)\r\n    return r * np.std(table.column(y))\/np.std(table.column(x))\r\n\r\ndef intercept(table, x, y):\r\n    a = slope(table, x, y)\r\n    return np.mean(table.column(y)) -  a * np.mean(table.column(x))\r\n\r\ndef fit(table, x, y):\r\n    a = slope(table, x, y)\r\n    b = intercept(table, x, y)\r\n    return a * table.column(x) + b<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">def residual(table, x, y):\r\n    return table.column(y) - fit(table, x, y)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\">Continuando nosso exemplo de estimativa da altura dos filhos adultos (a resposta) com base na altura dos pais m\u00e9dios (o preditor), vamos calcular os valores ajustados e os res\u00edduos.<\/p>\n<pre><code><span style=\"color: black\">heights = heights.with_columns(\r\n        'Fitted Value', fit(heights, 'MidParent', 'Child'),\r\n        'Residual', residual(heights, 'MidParent', 'Child')\r\n    )\r\nheights<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">MidParent<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Child<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Fitted Value<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Residual<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.48763<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.51237<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.71237<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.71237<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.91576<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.91576<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">65.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-4.08424<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">65.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-4.08424<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.06<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">71<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5645<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.43553<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.06<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5645<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.564467<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Quando h\u00e1 tantas vari\u00e1veis para trabalhar, \u00e9 sempre \u00fatil come\u00e7ar com a visualiza\u00e7\u00e3o. A fun\u00e7\u00e3o <code>scatter_fit<\/code> desenha o gr\u00e1fico de dispers\u00e3o dos dados, bem como a linha de regress\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def scatter_fit(table, x, y):\r\n    table.scatter(x, y, s=15)\r\n    plots.plot(table.column(x), fit(table, x, y), lw=4, color='gold')\r\n    plots.xlabel(x)\r\n    plots.ylabel(y)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">scatter_fit(heights, 'MidParent', 'Child')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-852\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-1.png\" alt=\"\" width=\"367\" height=\"346\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-1.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-1-300x283.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-1-339x320.png 339w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p style=\"text-align: justify\">Um <em>gr\u00e1fico residual<\/em> pode ser desenhado plotando os res\u00edduos em rela\u00e7\u00e3o \u00e0 vari\u00e1vel preditora. A fun\u00e7\u00e3o <code>residual_plot<\/code> faz exatamente isso.<\/p>\n<pre><code><span style=\"color: black\">def residual_plot(table, x, y):\r\n    x_array = table.column(x)\r\n    t = Table().with_columns(\r\n            x, x_array,\r\n            'residuals', residual(table, x, y)\r\n        )\r\n    t.scatter(x, 'residuals', color='r')\r\n    xlims = make_array(min(x_array), max(x_array))\r\n    plots.plot(xlims, make_array(0, 0), color='darkblue', lw=4)\r\n    plots.title('Residual Plot')<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">residual_plot(heights, 'MidParent', 'Child')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-853\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-2.png\" alt=\"\" width=\"370\" height=\"363\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-2.png 370w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-2-300x294.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-2-326x320.png 326w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p style=\"text-align: justify\">As alturas dos pais m\u00e9dios est\u00e3o no eixo horizontal, como no gr\u00e1fico de dispers\u00e3o original. Mas agora o eixo vertical mostra os res\u00edduos. Observe que o gr\u00e1fico parece estar centralizado em torno da linha horizontal no n\u00edvel 0 (mostrado em azul escuro). Observe tamb\u00e9m que o gr\u00e1fico n\u00e3o mostra nenhuma tend\u00eancia ascendente ou descendente. Observaremos mais tarde que esta falta de tend\u00eancia \u00e9 verdadeira para todas as regress\u00f5es.<\/p>\n<h2 id=\"diagn-stico-de-regress-o\" style=\"text-align: justify\">Diagn\u00f3stico de Regress\u00e3o<\/h2>\n<p style=\"text-align: justify\">Os gr\u00e1ficos residuais nos ajudam a fazer avalia\u00e7\u00f5es visuais da qualidade de uma an\u00e1lise de regress\u00e3o linear. Tais avalia\u00e7\u00f5es s\u00e3o chamadas de <em>diagn\u00f3sticos<\/em>. A fun\u00e7\u00e3o <code>regression_diagnostic_plots<\/code> desenha o gr\u00e1fico de dispers\u00e3o original, bem como o gr\u00e1fico residual para facilitar a compara\u00e7\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def regression_diagnostic_plots(table, x, y):\r\n    scatter_fit(table, x, y)\r\n    residual_plot(table, x, y)<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">regression_diagnostic_plots(heights, 'MidParent', 'Child')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-854\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-3.png\" alt=\"\" width=\"367\" height=\"346\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-3.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-3-300x283.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-3-339x320.png 339w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-855\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-4.png\" alt=\"\" width=\"370\" height=\"363\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-4.png 370w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-4-300x294.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-4-326x320.png 326w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p style=\"text-align: justify\">Este gr\u00e1fico de res\u00edduos indica que a regress\u00e3o linear foi um m\u00e9todo razo\u00e1vel de estimativa. Observe como os res\u00edduos est\u00e3o distribu\u00eddos de forma bastante sim\u00e9trica acima e abaixo da linha horizontal em 0, correspondendo ao gr\u00e1fico de dispers\u00e3o original sendo aproximadamente sim\u00e9trico acima e abaixo. Note tamb\u00e9m que a dispers\u00e3o vertical do gr\u00e1fico \u00e9 bastante uniforme ao longo dos valores mais comuns das alturas das crian\u00e7as. Em outras palavras, com exce\u00e7\u00e3o de alguns pontos fora do padr\u00e3o, o gr\u00e1fico n\u00e3o \u00e9 mais estreito em alguns lugares e mais largo em outros.<\/p>\n<p style=\"text-align: justify\">Em outras palavras, a precis\u00e3o da regress\u00e3o parece ser aproximadamente a mesma ao longo do intervalo observado da vari\u00e1vel preditora.<\/p>\n<p style=\"text-align: justify\"><strong>O gr\u00e1fico de res\u00edduos de uma boa regress\u00e3o n\u00e3o mostra nenhum padr\u00e3o. Os res\u00edduos parecem semelhantes, acima e abaixo da linha horizontal em 0, ao longo do intervalo da vari\u00e1vel preditora.<\/strong><\/p>\n<h2 id=\"detectando-n-o-linearidade\" style=\"text-align: justify\">Detectando N\u00e3o Linearidade<\/h2>\n<p style=\"text-align: justify\">Desenhar o gr\u00e1fico de dispers\u00e3o dos dados geralmente d\u00e1 uma indica\u00e7\u00e3o de se a rela\u00e7\u00e3o entre as duas vari\u00e1veis \u00e9 n\u00e3o linear. Muitas vezes, no entanto, \u00e9 mais f\u00e1cil detectar n\u00e3o linearidade em um gr\u00e1fico de res\u00edduos do que no gr\u00e1fico de dispers\u00e3o original. Isso geralmente se deve \u00e0s escalas dos dois gr\u00e1ficos: o gr\u00e1fico de res\u00edduos nos permite aumentar o zoom nos erros e, portanto, facilita a identifica\u00e7\u00e3o de padr\u00f5es.<\/p>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-856 aligncenter\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-5.jpg\" alt=\"\" width=\"737\" height=\"393\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-5.jpg 737w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-5-300x160.jpg 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-5-600x320.jpg 600w\" sizes=\"(max-width: 737px) 100vw, 737px\" \/><\/p>\n<p style=\"text-align: justify\">Nossos dados s\u00e3o um <a href=\"http:\/\/www.statsci.org\/data\/oz\/dugongs.html\">conjunto de dados<\/a> sobre a idade e o comprimento dos dugongos, que s\u00e3o mam\u00edferos marinhos relacionados aos peixes-boi e vacas-marinhas (imagem da <a href=\"https:\/\/commons.wikimedia.org\/wiki\/File:Dugong_dugon.jpg\">Wikimedia Commons<\/a>). Os dados est\u00e3o em uma tabela chamada <code>dugong<\/code>. A idade \u00e9 medida em anos e o comprimento em metros. Como os dugongos tendem a n\u00e3o acompanhar seus anivers\u00e1rios, as idades s\u00e3o estimadas com base em vari\u00e1veis como a condi\u00e7\u00e3o de seus dentes.<\/p>\n<pre><code><span style=\"color: black\">dugong = Table.read_table(path_data + 'dugongs.csv')\r\ndugong = dugong.move_to_start('Length')\r\ndugong<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">Length<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Age<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.85<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.5<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.87<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.5<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.77<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.5<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.02<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.5<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.27<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.15<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.26<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.35<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.47<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Se pud\u00e9ssemos medir o comprimento de um dugongo, o que poder\u00edamos dizer sobre a sua idade? Vamos examinar o que os nossos dados dizem. Aqui est\u00e1 uma regress\u00e3o da idade (a resposta) no comprimento (o preditor). A correla\u00e7\u00e3o entre as duas vari\u00e1veis \u200b\u200b\u00e9 substancial, em 0,83.<\/p>\n<pre><code><span style=\"color: black\">correlation(dugong, 'Length', 'Age')<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-spacing: 0;border-collapse: collapse;width: auto;margin-left: 1em\">\n<tbody>\n<tr>\n<td style=\"text-align: right;color: #888;padding-right: 0.5em\">Out[1]:<\/td>\n<td style=\"text-align: left\">0.8296474554905714<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Apesar da alta correla\u00e7\u00e3o, o gr\u00e1fico mostra um padr\u00e3o curvo que \u00e9 muito mais vis\u00edvel no gr\u00e1fico residual.<\/p>\n<pre><code><span style=\"color: black\">regression_diagnostic_plots(dugong, 'Length', 'Age')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-857\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-6.png\" alt=\"\" width=\"367\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-6.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-6-300x280.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-6-343x320.png 343w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-858\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-7.png\" alt=\"\" width=\"370\" height=\"363\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-7.png 370w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-7-300x294.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-7-326x320.png 326w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p style=\"text-align: justify\">Enquanto voc\u00ea pode identificar a n\u00e3o linearidade na dispers\u00e3o original, ela \u00e9 mais claramente evidente no gr\u00e1fico de res\u00edduos.<\/p>\n<p style=\"text-align: justify\">No extremo inferior dos comprimentos, os res\u00edduos s\u00e3o quase todos positivos; depois s\u00e3o quase todos negativos; e, em seguida, positivos novamente no extremo superior dos comprimentos. Em outras palavras, as estimativas de regress\u00e3o t\u00eam um padr\u00e3o de serem muito altas, depois muito baixas, depois altas novamente. Isso significa que teria sido melhor usar uma curva em vez de uma linha reta para estimar as idades.<\/p>\n<p style=\"text-align: justify\"><strong>Quando um gr\u00e1fico de res\u00edduos mostra um padr\u00e3o, pode haver uma rela\u00e7\u00e3o n\u00e3o linear entre as vari\u00e1veis.<\/strong><\/p>\n<h2 id=\"detectando-heterocedasticidade\" style=\"text-align: justify\">Detectando Heterocedasticidade<\/h2>\n<p style=\"text-align: justify\"><em>Heterocedasticidade<\/em> \u00e9 uma palavra que certamente ser\u00e1 de interesse para aqueles que est\u00e3o se preparando para competi\u00e7\u00f5es de soletra\u00e7\u00e3o. Para os cientistas de dados, seu interesse reside em seu significado, que \u00e9 &#8220;distribui\u00e7\u00e3o desigual&#8221;.<\/p>\n<p style=\"text-align: justify\">Lembre-se da tabela <code>hybrid<\/code> que cont\u00e9m dados sobre carros h\u00edbridos nos EUA. Aqui est\u00e1 uma regress\u00e3o da efici\u00eancia de combust\u00edvel sobre a taxa de acelera\u00e7\u00e3o. A associa\u00e7\u00e3o \u00e9 negativa: carros que aceleram rapidamente tendem a ser menos eficientes.<\/p>\n<pre><code><span style=\"color: black\">regression_diagnostic_plots(hybrid, 'acceleration', 'mpg')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-859\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-8.png\" alt=\"\" width=\"367\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-8.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-8-300x280.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-8-343x320.png 343w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-860\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-9.png\" alt=\"\" width=\"379\" height=\"363\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-9.png 379w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-9-300x287.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-5-9-334x320.png 334w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p style=\"text-align: justify\">Observe como o gr\u00e1fico residual se alarga em dire\u00e7\u00e3o ao limite inferior das acelera\u00e7\u00f5es. Em outras palavras, a variabilidade no tamanho dos erros \u00e9 maior para valores baixos de acelera\u00e7\u00e3o do que para valores altos. A varia\u00e7\u00e3o desigual \u00e9 frequentemente mais facilmente percebida em um valor residual gr\u00e1fico de dispers\u00e3o do que no gr\u00e1fico de dispers\u00e3o original.<\/p>\n<p style=\"text-align: justify\"><strong>Se o gr\u00e1fico residual mostrar varia\u00e7\u00e3o desigual em rela\u00e7\u00e3o \u00e0 linha horizontal em 0, as estimativas de regress\u00e3o n\u00e3o ser\u00e3o igualmente precisas em todo o intervalo da vari\u00e1vel preditora.<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p><!--###########################################################################################################################################################--><\/p>\n<table width=\"100%\">\n<tbody>\n<tr>\n<td align=\"left\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-4\/\">\u2190 Cap\u00edtulo 15.4 &#8211; Regress\u00e3o de M\u00ednimos Quadrados<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-6\/\">Cap\u00edtulo 15.6 &#8211; Diagn\u00f3stico Num\u00e9rico \u2192<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><!--###########################################################################################################################################################--><\/p>\n<\/div>\n<\/div>\n<div style=\"clear: both;height: 1px;margin-top: -1px\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u00cdndice 1. O que \u00e9 Ci\u00eancia de Dados? 1.1. Introdu\u00e7\u00e3o 1.1.1. Ferramentas Computacionais 1.1.2. T\u00e9cnicas Estat\u00edsticas 1.2. Por que Ci\u00eancia de Dados? 1.3. Tra\u00e7ando os Cl\u00e1ssicos 1.3.1. Personagens Liter\u00e1rios 1.3.2. Outro Tipo de Personagem 2. Causalidade e Experimentos 2.1. John Snow e a Bomba da Broad Street 2.2. O &#8220;Grande Experimento&#8221; de Snow 2.3. Estabelecendo [&hellip;]<\/p>\n","protected":false},"author":21894,"featured_media":0,"parent":787,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"coauthors":[14],"class_list":["post-850","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/users\/21894"}],"replies":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/comments?post=850"}],"version-history":[{"count":5,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/850\/revisions"}],"predecessor-version":[{"id":1078,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/850\/revisions\/1078"}],"up":[{"embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/787"}],"wp:attachment":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}