{"id":863,"date":"2025-07-29T20:55:35","date_gmt":"2025-07-30T00:55:35","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=863"},"modified":"2025-10-11T17:44:42","modified_gmt":"2025-10-11T21:44:42","slug":"15-6","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/15-0\/15-6\/","title":{"rendered":"Cap\u00edtulo 15.6"},"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-stico-num-rico\" style=\"text-align: center\">Diagn\u00f3stico Num\u00e9rico<\/h1>\n<p style=\"text-align: justify\">Al\u00e9m da visualiza\u00e7\u00e3o, podemos usar propriedades num\u00e9ricas de res\u00edduos para avaliar a qualidade da regress\u00e3o. N\u00e3o provaremos essas propriedades matematicamente. Em vez disso, iremos observ\u00e1-las por c\u00e1lculo e ver o que elas nos dizem sobre a regress\u00e3o.<\/p>\n<p style=\"text-align: justify\">Todos os fatos listados abaixo s\u00e3o v\u00e1lidos para todas as formas de gr\u00e1ficos de dispers\u00e3o, sejam eles lineares ou n\u00e3o.<\/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\ndugong = Table.read_table(path_data + 'dugongs.csv')\r\ndugong = dugong.move_to_start('Length')\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\r\n\r\ndef residual(table, x, y):\r\n    return table.column(y) - fit(table, x, y)\r\n\r\ndef 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)\r\n\r\ndef 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')\r\n\r\ndef 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\">heights = heights.with_columns(\r\n        'Fitted Value', fit(heights, 'MidParent', 'Child'),\r\n        'Residual', residual(heights, 'MidParent', 'Child')\r\n    )<\/span><\/code><\/pre>\n<h2 id=\"gr-ficos-residuais-n-o-mostram-tend-ncia\" style=\"text-align: justify\">Gr\u00e1ficos Residuais n\u00e3o Mostram Tend\u00eancia<\/h2>\n<p style=\"text-align: justify\"><strong>Para cada regress\u00e3o linear, seja boa ou ruim, o gr\u00e1fico residual n\u00e3o mostra nenhuma tend\u00eancia. No geral, \u00e9 plano. Em outras palavras, os res\u00edduos e a vari\u00e1vel preditora n\u00e3o est\u00e3o correlacionados.<\/strong><\/p>\n<p style=\"text-align: justify\">Voc\u00ea pode ver isso em todos os gr\u00e1ficos de res\u00edduos acima. Tamb\u00e9m podemos calcular a correla\u00e7\u00e3o entre a vari\u00e1vel preditora e os res\u00edduos em cada caso.<\/p>\n<pre><code><span style=\"color: black\">correlation(heights, 'MidParent', 'Residual')<\/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\">-2.719689807647064e-16<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Isso n\u00e3o parece zero, mas \u00e9 um n\u00famero min\u00fasculo que \u00e9 0, exceto pelo erro de arredondamento devido ao c\u00e1lculo. Aqui est\u00e1 novamente, correto para 10 casas decimais. O sinal de menos \u00e9 por causa do arredondamento acima.<\/p>\n<pre><code><span style=\"color: black\">round(correlation(heights, 'MidParent', 'Residual'), 10)<\/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[2]:<\/td>\n<td style=\"text-align: left\">-0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">dugong = dugong.with_columns(\r\n       'Fitted Value', fit(dugong, 'Length', 'Age'),\r\n       'Residual', residual(dugong, 'Length', 'Age')\r\n)\r\nround(correlation(dugong, 'Length', 'Residual'), 10)<\/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[3]:<\/td>\n<td style=\"text-align: left\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"m-dia-dos-res-duos\" style=\"text-align: justify\">M\u00e9dia dos Res\u00edduos<\/h2>\n<p style=\"text-align: justify\"><strong>Independentemente da forma do diagrama de dispers\u00e3o, a m\u00e9dia dos res\u00edduos \u00e9 0.<\/strong><\/p>\n<p style=\"text-align: justify\">Isso \u00e9 an\u00e1logo ao fato de que, se voc\u00ea pegar qualquer lista de n\u00fameros e calcular a lista de desvios em rela\u00e7\u00e3o \u00e0 m\u00e9dia, a m\u00e9dia dos desvios ser\u00e1 0.<\/p>\n<p style=\"text-align: justify\">Em todos os gr\u00e1ficos de res\u00edduos acima, voc\u00ea viu a linha horizontal em 0 passando pelo centro do gr\u00e1fico. Isso \u00e9 uma visualiza\u00e7\u00e3o desse fato.<\/p>\n<p style=\"text-align: justify\">Como exemplo num\u00e9rico, aqui est\u00e1 a m\u00e9dia dos res\u00edduos na regress\u00e3o das alturas das crian\u00e7as com base nas alturas dos pais.<\/p>\n<pre><code><span style=\"color: black\">round(np.mean(heights.column('Residual')), 10)<\/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[4]:<\/td>\n<td style=\"text-align: left\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">O mesmo acontece com a m\u00e9dia dos res\u00edduos na regress\u00e3o da idade dos dugongos em seu comprimento. A m\u00e9dia dos res\u00edduos \u00e9 0, fora o erro de arredondamento.<\/p>\n<pre><code><span style=\"color: black\">round(np.mean(dugong.column('Residual')), 10)<\/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[5]:<\/td>\n<td style=\"text-align: left\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"sd-dos-res-duos\" style=\"text-align: justify\">SD dos Res\u00edduos<\/h2>\n<p style=\"text-align: justify\"><strong>Independentemente da forma do gr\u00e1fico de dispers\u00e3o, o desvio padr\u00e3o (SD) dos res\u00edduos \u00e9 uma fra\u00e7\u00e3o do desvio padr\u00e3o da vari\u00e1vel resposta. A fra\u00e7\u00e3o \u00e9 \u221a(1-r<sup>2<\/sup>).<\/strong><\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\">SD dos res\u00edduos = \u221a(1-r<sup>2<\/sup>) \u22c5 SD de y<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Em breve veremos como isso mede a precis\u00e3o da estimativa de regress\u00e3o. Mas primeiro, vamos confirmar isso com um exemplo.<\/p>\n<p style=\"text-align: justify\">No caso das alturas dos filhos e alturas dos pais, o desvio padr\u00e3o dos res\u00edduos \u00e9 de cerca de 3,39 polegadas.<\/p>\n<pre><code><span style=\"color: black\">np.std(heights.column('Residual'))<\/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[6]:<\/td>\n<td style=\"text-align: left\">3.3880799163953426<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Isso \u00e9 o mesmo que \u221a(1-r<sup>2<\/sup>) vezes o SD da vari\u00e1vel de resposta:<\/p>\n<pre><code><span style=\"color: black\">r = correlation(heights, 'MidParent', 'Child')\r\nnp.sqrt(1 - r**2) * np.std(heights.column('Child'))<\/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[7]:<\/td>\n<td style=\"text-align: left\">3.388079916395342<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">O mesmo \u00e9 verdade para a regress\u00e3o da quilometragem na acelera\u00e7\u00e3o de carros h\u00edbridos. A correla\u00e7\u00e3o <em>r<\/em> \u00e9 negativa (cerca de -0,5), mas r^2 \u00e9 positiva e, portanto, \u221a(1-r<sup>2<\/sup>)\u00a0 \u00e9 uma fra\u00e7\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">r = correlation(hybrid, 'acceleration', 'mpg')\r\nr<\/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[8]:<\/td>\n<td style=\"text-align: left\">-0.5060703843771186<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">hybrid = hybrid.with_columns(\r\n     'fitted mpg', fit(hybrid, 'acceleration', 'mpg'),\r\n     'residual', residual(hybrid, 'acceleration', 'mpg')\r\n)\r\nnp.std(hybrid.column('residual')), np.sqrt(1 - r**2)*np.std(hybrid.column('mpg'))<\/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[9]:<\/td>\n<td style=\"text-align: left\">(9.43273683343029, 9.43273683343029)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Agora vamos ver como o desvio padr\u00e3o dos res\u00edduos \u00e9 uma medida de qu\u00e3o boa \u00e9 a regress\u00e3o. Lembre-se de que a m\u00e9dia dos res\u00edduos \u00e9 0. Portanto, quanto menor for o desvio padr\u00e3o dos res\u00edduos, mais pr\u00f3ximos os res\u00edduos estar\u00e3o de 0. Em outras palavras, se o desvio padr\u00e3o dos res\u00edduos for pequeno, o tamanho geral dos erros na regress\u00e3o ser\u00e1 pequeno.<\/p>\n<p style=\"text-align: justify\">Os casos extremos s\u00e3o quando <em>r=1<\/em> ou <em>r=-1<\/em>. Em ambos os casos, \u221a(1-r<sup>2<\/sup>) = 0. Portanto, os res\u00edduos t\u00eam uma m\u00e9dia de 0 e um desvio padr\u00e3o de 0 tamb\u00e9m, e, portanto, os res\u00edduos s\u00e3o todos iguais a 0. A linha de regress\u00e3o faz um trabalho perfeito de estimativa. Como vimos anteriormente neste cap\u00edtulo, se <em>r = \u00b1 1<\/em>, o diagrama de dispers\u00e3o \u00e9 uma linha reta perfeita e \u00e9 a mesma que a linha de regress\u00e3o, portanto, n\u00e3o h\u00e1 erro na estimativa de regress\u00e3o.<\/p>\n<p style=\"text-align: justify\">Mas geralmente <em>r<\/em> n\u00e3o est\u00e1 nos extremos. Se <em>r<\/em> n\u00e3o for nem <em>\u00b1 1<\/em> nem 0, ent\u00e3o \u221a(1-r<sup>2<\/sup>) \u00e9 uma fra\u00e7\u00e3o adequada, e o tamanho geral aproximado do erro da estimativa de regress\u00e3o est\u00e1 entre 0 e o desvio padr\u00e3o de <em>y<\/em>.<\/p>\n<p style=\"text-align: justify\">O pior caso \u00e9 quando <em>r = 0<\/em>. Ent\u00e3o \u221a(1-r<sup>2<\/sup>) =1, e o desvio padr\u00e3o dos res\u00edduos \u00e9 igual ao desvio padr\u00e3o de <em>y<\/em>. Isso \u00e9 consistente com a observa\u00e7\u00e3o de que, se <em>r=0<\/em>, ent\u00e3o a linha de regress\u00e3o \u00e9 uma linha plana na m\u00e9dia de <em>y<\/em>. Nessa situa\u00e7\u00e3o, o erro quadr\u00e1tico m\u00e9dio da regress\u00e3o \u00e9 o desvio quadr\u00e1tico m\u00e9dio em rela\u00e7\u00e3o \u00e0 m\u00e9dia de <em>y<\/em>, que \u00e9 o desvio padr\u00e3o de <em>y<\/em>. Em termos pr\u00e1ticos, se <em>r = 0<\/em>, ent\u00e3o n\u00e3o h\u00e1 associa\u00e7\u00e3o linear entre as duas vari\u00e1veis, portanto, n\u00e3o h\u00e1 benef\u00edcio em usar a regress\u00e3o linear.<\/p>\n<h2 id=\"outra-maneira-de-interpretar-r-\" style=\"text-align: justify\">Outra Maneira de Interpretar <em>r<\/em><\/h2>\n<p style=\"text-align: justify\">Podemos reescrever o resultado acima para dizer que, independentemente da forma do diagrama de dispers\u00e3o,<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\"><sup>Desvio padr\u00e3o dos res\u00edduos<\/sup>\u2044<sub>Desvio padr\u00e3o de y<\/sub> = \u221a(1-r<sup>2<\/sup>)<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Um resultado complementar \u00e9 que, independentemente da forma do diagrama de dispers\u00e3o, o desvio padr\u00e3o dos valores ajustados \u00e9 uma fra\u00e7\u00e3o do desvio padr\u00e3o dos valores observados de <em>y<\/em>. A fra\u00e7\u00e3o \u00e9 | r |.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\"><sup>Desvio padr\u00e3o dos valores ajustados<\/sup>\u2044<sub>Desvio padr\u00e3o de y<\/sub> = | r |<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Para ver de onde vem a fra\u00e7\u00e3o, observe que os valores ajustados est\u00e3o todos na linha de regress\u00e3o, enquanto os valores observados de <em>y<\/em> s\u00e3o as alturas de todos os pontos no diagrama de dispers\u00e3o e s\u00e3o mais vari\u00e1veis.<\/p>\n<pre><code><span style=\"color: black\">scatter_fit(heights, 'MidParent', 'Child')<\/span><\/code><\/pre>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-865\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-6-1.png\" alt=\"\" width=\"367\" height=\"346\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-6-1.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-6-1-300x283.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-6-1-339x320.png 339w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<p style=\"text-align: justify\">Os valores ajustados variam de cerca de 64 a cerca de 71, enquanto as alturas de todas as crian\u00e7as s\u00e3o um pouco mais vari\u00e1veis, variando de cerca de 55 a 80.<\/p>\n<p style=\"text-align: justify\">Para verificar o resultado numericamente, basta calcular os dois lados da identidade.<\/p>\n<pre><code><span style=\"color: black\">correlation(heights, 'MidParent', 'Child')<\/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[10]:<\/td>\n<td style=\"text-align: left\">0.32094989606395924<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Aqui est\u00e1 a raz\u00e3o entre o SD dos valores ajustados e o SD dos valores observados de peso ao nascer:<\/p>\n<pre><code><span style=\"color: black\">np.std(heights.column('Fitted Value'))\/np.std(heights.column('Child'))<\/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[11]:<\/td>\n<td style=\"text-align: left\">0.32094989606395957<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">A propor\u00e7\u00e3o \u00e9 igual a <em>r<\/em>, confirmando nosso resultado.<\/p>\n<p style=\"text-align: justify\">Onde entra o valor absoluto? Primeiro, observe que os SDs n\u00e3o podem ser negativos, nem uma propor\u00e7\u00e3o de SDs. Ent\u00e3o, o que acontece quando <em>r<\/em> \u00e9 negativo? O exemplo de efici\u00eancia de combust\u00edvel e acelera\u00e7\u00e3o nos mostrar\u00e1.<\/p>\n<pre><code><span style=\"color: black\">correlation(hybrid, 'acceleration', 'mpg')<\/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[12]:<\/td>\n<td style=\"text-align: left\">-0.5060703843771186<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">np.std(hybrid.column('fitted mpg'))\/np.std(hybrid.column('mpg'))<\/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[13]:<\/td>\n<td style=\"text-align: left\">0.5060703843771186<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">A raz\u00e3o entre os dois desvio padr\u00e3o (DPs) \u00e9 | r |.<\/p>\n<p style=\"text-align: justify\">Uma maneira mais comum de expressar esse resultado \u00e9 lembrar que<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">vari\u00e2ncia = desvio m\u00e9dio quadr\u00e1tico em rela\u00e7\u00e3o \u00e0 m\u00e9dia = DP<sup>2<\/sup><\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">e, portanto, ao elevar ao quadrado ambos os lados do nosso resultado,<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\"><sup>vari\u00e2ncia dos valores ajustados<\/sup>\u2044<sub>vari\u00e2ncia de y<\/sub> = r<sup>2<\/sup><\/div>\n<p>&nbsp;<\/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\/15-5\/\">\u2190 Cap\u00edtulo 15.5 &#8211; Diagn\u00f3sticos Visuais<\/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-863","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/863","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=863"}],"version-history":[{"count":5,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/863\/revisions"}],"predecessor-version":[{"id":1080,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/863\/revisions\/1080"}],"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=863"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=863"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}