{"id":791,"date":"2025-07-29T20:14:28","date_gmt":"2025-07-30T00:14:28","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=791"},"modified":"2025-10-11T16:35:45","modified_gmt":"2025-10-11T20:35:45","slug":"15-1","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/15-0\/15-1\/","title":{"rendered":"Cap\u00edtulo 15.1"},"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\n%matplotlib inline\r\npath_data = '..\/..\/..\/assets\/data\/'\r\nimport matplotlib.pyplot as plots\r\nplots.style.use('fivethirtyeight')\r\nimport math\r\nimport numpy as np\r\nfrom scipy import stats<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h1 id=\"correla-o\" style=\"text-align: center\">Correla\u00e7\u00e3o<\/h1>\n<p style=\"text-align: justify\">Nesta se\u00e7\u00e3o, desenvolveremos uma medida de qu\u00e3o fortemente agrupado um diagrama de dispers\u00e3o est\u00e1 em rela\u00e7\u00e3o a uma linha reta. Formalmente, isso \u00e9 chamado de medi\u00e7\u00e3o de <em>associa\u00e7\u00e3o linear<\/em>.<\/p>\n<pre><code><span style=\"color: black\">def r_scatter(r):\r\n    plots.figure(figsize=(5,5))\r\n    \"Gere um gr\u00e1fico de dispers\u00e3o com uma correla\u00e7\u00e3o aproximadamente r\"\r\n    x = np.random.normal(0, 1, 1000)\r\n    z = np.random.normal(0, 1, 1000)\r\n    y = r*x + (np.sqrt(1-r**2))*z\r\n    plots.scatter(x, y)\r\n    plots.xlim(-4, 4)\r\n    plots.ylim(-4, 4)<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A tabela <code>hybrid<\/code> cont\u00e9m dados sobre carros h\u00edbridos de passageiros vendidos nos Estados Unidos de 1997 a 2013. Os dados foram adaptados do arquivo de dados online do <a href=\"http:\/\/www.stat.ufl.edu\/%7Ewinner\/\">Prof. Larry Winner<\/a> da Universidade da Fl\u00f3rida. As colunas s\u00e3o:<\/p>\n<ul style=\"text-align: justify\">\n<li><code>vehicle<\/code>: modelo do carro<\/li>\n<li><code>year<\/code>: ano de fabrica\u00e7\u00e3o<\/li>\n<li><code>msrp<\/code>: pre\u00e7o de varejo sugerido pelo fabricante em d\u00f3lares de 2013<\/li>\n<li><code>acceleration<\/code>: taxa de acelera\u00e7\u00e3o em km por hora por segundo<\/li>\n<li><code>mpg<\/code>: economia de combust\u00edvel em milhas por gal\u00e3o<\/li>\n<li><code>class<\/code>: classe do modelo.<\/li>\n<\/ul>\n<pre><code><span style=\"color: black\">hybrid = Table.read_table(path_data + 'hybrid.csv')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">hybrid<\/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\">vehicle<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">year<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">msrp<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">acceleration<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">mpg<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">class<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Prius (1st Gen)<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1997<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">24509.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7.46<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">41.26<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Compact<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Tino<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2000<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">35355<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">8.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">54.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Compact<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Prius (2nd Gen)<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2000<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">26832.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7.97<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">45.23<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Compact<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Insight<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2000<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">18936.4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">9.52<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">53<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Two Seater<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Civic (1st Gen)<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2001<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">25833.4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7.04<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">47.04<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Compact<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Insight<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2001<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">19036.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">9.52<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">53<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Two Seater<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Insight<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2002<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">19137<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">9.71<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">53<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Two Seater<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Alphard<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2003<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">38084.8<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">8.33<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">40.46<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Minivan<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Insight<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2003<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">19137<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">9.52<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">53<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Two Seater<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Civic<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2003<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">14071.9<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">8.62<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">41<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Compact<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">O gr\u00e1fico abaixo \u00e9 um gr\u00e1fico de dispers\u00e3o de <code>msrp<\/code> <em>versus<\/em> <code>acceleration<\/code>. Isso significa que <code>msrp<\/code> \u00e9 plotado no eixo vertical e <code>accelaration<\/code> na horizontal.<\/p>\n<pre><code><span style=\"color: black\">hybrid.scatter('acceleration', 'msrp')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-793\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-1.png\" alt=\"\" width=\"403\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-1.png 403w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-1-300x255.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-1-377x320.png 377w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p style=\"text-align: justify\">Observe a associa\u00e7\u00e3o positiva. A dispers\u00e3o dos pontos est\u00e1 inclinada para cima, indicando que os carros com maior acelera\u00e7\u00e3o tendem a custar mais, em m\u00e9dia; por outro lado, os carros que custam mais tendem a ter maior acelera\u00e7\u00e3o, em m\u00e9dia.<\/p>\n<p style=\"text-align: justify\">O diagrama de dispers\u00e3o de MSRP versus quilometragem mostra uma associa\u00e7\u00e3o negativa. Carros h\u00edbridos com maior quilometragem tendem a custar menos, em m\u00e9dia. Isso parece surpreendente at\u00e9 que voc\u00ea considere que carros que aceleram rapidamente tendem a ser menos eficientes em termos de combust\u00edvel e t\u00eam menor quilometragem. Como o gr\u00e1fico de dispers\u00e3o anterior mostrou, esses tamb\u00e9m eram os carros que tendiam a custar mais.<\/p>\n<pre><code><span style=\"color: black\">hybrid.scatter('mpg', 'msrp')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-794\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-2.png\" alt=\"\" width=\"403\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-2.png 403w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-2-300x255.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-2-377x320.png 377w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p style=\"text-align: justify\">Juntamente com a associa\u00e7\u00e3o negativa, o diagrama de dispers\u00e3o de pre\u00e7o versus efici\u00eancia mostra uma rela\u00e7\u00e3o n\u00e3o linear entre as duas vari\u00e1veis. Os pontos parecem estar agrupados em torno de uma curva, n\u00e3o em torno de uma linha reta.<\/p>\n<p style=\"text-align: justify\">Se restringirmos os dados apenas \u00e0 classe SUV, no entanto, a associa\u00e7\u00e3o entre pre\u00e7o e efici\u00eancia ainda \u00e9 negativa, mas a rela\u00e7\u00e3o parece ser mais linear. A rela\u00e7\u00e3o entre pre\u00e7o e acelera\u00e7\u00e3o dos SUV tamb\u00e9m mostra uma tend\u00eancia linear, mas com uma inclina\u00e7\u00e3o positiva.<\/p>\n<pre><code><span style=\"color: black\">suv = hybrid.where('class', 'SUV')\r\nsuv.scatter('mpg', 'msrp')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img decoding=\"async\" class=\"alignnone size-full wp-image-795\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-3.png\" alt=\"\" width=\"403\" height=\"343\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-3.png 403w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-3-300x255.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-3-376x320.png 376w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<pre><code><span style=\"color: black\">suv.scatter('acceleration', 'msrp')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-796\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-4.png\" alt=\"\" width=\"403\" height=\"343\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-4.png 403w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-4-300x255.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-4-376x320.png 376w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p style=\"text-align: justify\">Voc\u00ea deve ter notado que podemos derivar informa\u00e7\u00f5es \u00fateis da orienta\u00e7\u00e3o geral e da forma de um diagrama de dispers\u00e3o mesmo sem prestar aten\u00e7\u00e3o \u00e0s unidades em que as vari\u00e1veis foram medidas.<\/p>\n<p style=\"text-align: justify\">De fato, poder\u00edamos plotar todas as vari\u00e1veis em unidades padr\u00e3o e os gr\u00e1ficos teriam a mesma apar\u00eancia. Isso nos d\u00e1 uma maneira de comparar o grau de linearidade em dois diagramas de dispers\u00e3o.<\/p>\n<p style=\"text-align: justify\">Lembre-se de que em uma se\u00e7\u00e3o anterior definimos a fun\u00e7\u00e3o <code>standard_units<\/code> para converter uma matriz de n\u00fameros em unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def standard_units(any_numbers):\r\n    \"Converte qualquer matriz de n\u00fameros em unidades padr\u00e3o.\"\r\n    return (any_numbers - np.mean(any_numbers))\/np.std(any_numbers)  <\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Podemos usar esta fun\u00e7\u00e3o para redesenhar os dois diagramas de dispers\u00e3o para os SUVs, com todas as vari\u00e1veis medidas em unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">Table().with_columns(\r\n    'mpg (standard units)',  standard_units(suv.column('mpg')),\r\n    'msrp (standard units)', standard_units(suv.column('msrp'))\r\n).scatter(0, 1)\r\nplots.xlim(-3, 3)\r\nplots.ylim(-3, 3);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-797\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-5.png\" alt=\"\" width=\"375\" height=\"348\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-5.png 375w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-5-300x278.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-5-345x320.png 345w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<pre><code><span style=\"color: black\">Table().with_columns(\r\n    'acceleration (standard units)', standard_units(suv.column('acceleration')),\r\n    'msrp (standard units)',         standard_units(suv.column('msrp'))\r\n).scatter(0, 1)\r\nplots.xlim(-3, 3)\r\nplots.ylim(-3, 3);<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-798\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-6.png\" alt=\"\" width=\"375\" height=\"348\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-6.png 375w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-6-300x278.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-6-345x320.png 345w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<p style=\"text-align: justify\">As associa\u00e7\u00f5es que vemos nestes gr\u00e1ficos s\u00e3o as mesmas que vimos antes. Al\u00e9m disso, como os dois diagramas de dispers\u00e3o agora s\u00e3o desenhados exatamente na mesma escala, podemos ver que a rela\u00e7\u00e3o linear no segundo diagrama \u00e9 um pouco mais difusa do que no primeiro.<\/p>\n<p style=\"text-align: justify\">Agora definiremos uma medida que usa unidades padr\u00e3o para quantificar os tipos de associa\u00e7\u00e3o que vimos.<\/p>\n<h2 id=\"o-coeficiente-de-correla-o\" style=\"text-align: justify\">O coeficiente de correla\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">O <em>coeficiente de correla\u00e7\u00e3o<\/em> mede a for\u00e7a da rela\u00e7\u00e3o linear entre duas vari\u00e1veis. Graficamente, ele mede o qu\u00e3o agrupado est\u00e1 o diagrama de dispers\u00e3o em torno de uma linha reta.<\/p>\n<p style=\"text-align: justify\">O termo <em>coeficiente de correla\u00e7\u00e3o<\/em> n\u00e3o \u00e9 f\u00e1cil de dizer, ent\u00e3o geralmente \u00e9 abreviado para <em>correla\u00e7\u00e3o<\/em> e denotado por r.<\/p>\n<p style=\"text-align: justify\">Aqui est\u00e3o alguns fatos matem\u00e1ticos sobre r que vamos observar por simula\u00e7\u00e3o.<\/p>\n<ul style=\"text-align: justify\">\n<li>O coeficiente de correla\u00e7\u00e3o r \u00e9 um n\u00famero entre -1 e 1.<\/li>\n<li>r mede at\u00e9 que ponto o diagrama de dispers\u00e3o se agrupa em torno de uma linha reta.<\/li>\n<li>r = 1 se o diagrama de dispers\u00e3o for uma linha reta perfeita inclinada para cima, e r = -1 se o diagrama de dispers\u00e3o for uma linha reta perfeita inclinada para baixo.<\/li>\n<\/ul>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o <code>r_scatter<\/code> recebe um valor de r como argumento e simula um gr\u00e1fico de dispers\u00e3o com uma correla\u00e7\u00e3o muito pr\u00f3xima de r. Devido \u00e0 aleatoriedade na simula\u00e7\u00e3o, n\u00e3o se espera que a correla\u00e7\u00e3o seja exatamente igual a r.<\/p>\n<p style=\"text-align: justify\">Chame <code>r_scatter<\/code> algumas vezes, com diferentes valores de r como argumento, e veja como o gr\u00e1fico de dispers\u00e3o muda.<\/p>\n<p style=\"text-align: justify\">Quando r=1, o gr\u00e1fico de dispers\u00e3o \u00e9 perfeitamente linear e inclinado para cima. Quando r=-1, o gr\u00e1fico de dispers\u00e3o \u00e9 perfeitamente linear e inclinado para baixo. Quando r=0, o gr\u00e1fico de dispers\u00e3o \u00e9 uma nuvem amorfa em torno do eixo horizontal, e as vari\u00e1veis s\u00e3o ditas <em>n\u00e3o correlacionadas<\/em>.<\/p>\n<pre><code><span style=\"color: black\">r_scatter(0.9)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-799\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-7.png\" alt=\"\" width=\"356\" height=\"329\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-7.png 356w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-7-300x277.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-7-346x320.png 346w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<pre><code><span style=\"color: black\">r_scatter(0.25)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-800\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-8.png\" alt=\"\" width=\"356\" height=\"329\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-8.png 356w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-8-300x277.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-8-346x320.png 346w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<pre><code><span style=\"color: black\">r_scatter(0)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-801\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-9.png\" alt=\"\" width=\"356\" height=\"329\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-9.png 356w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-9-300x277.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-9-346x320.png 346w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<pre><code><span style=\"color: black\">r_scatter(-0.55)<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-802\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-10.png\" alt=\"\" width=\"356\" height=\"329\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-10.png 356w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-10-300x277.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-10-346x320.png 346w\" sizes=\"(max-width: 356px) 100vw, 356px\" \/><\/p>\n<h2 id=\"calculando-r-\" style=\"text-align: justify\">Calculando <em>r<\/em><\/h2>\n<p style=\"text-align: justify\">A f\u00f3rmula para r n\u00e3o \u00e9 aparente a partir de nossas observa\u00e7\u00f5es at\u00e9 agora. Ela possui uma base matem\u00e1tica que est\u00e1 fora do escopo desta aula. No entanto, como veremos, o c\u00e1lculo \u00e9 direto e nos ajuda a entender v\u00e1rias das propriedades de r.<\/p>\n<p style=\"text-align: justify\"><strong>F\u00f3rmula para r<\/strong>:<\/p>\n<p style=\"text-align: justify\"><strong>r \u00e9 a m\u00e9dia dos produtos das duas vari\u00e1veis, quando ambas as vari\u00e1veis s\u00e3o medidas em unidades padr\u00e3o.<\/strong><\/p>\n<p style=\"text-align: justify\">Aqui est\u00e3o os passos no c\u00e1lculo. Vamos aplicar os passos a uma tabela simples de valores de x e y.<\/p>\n<pre><code><span style=\"color: black\">x = np.arange(1, 7, 1)\r\ny = make_array(2, 3, 1, 5, 2, 7)\r\nt = Table().with_columns(\r\n        'x', x,\r\n        'y', y\r\n    )\r\nt<\/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\">x<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">y<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/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\">4<\/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\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Com base no diagrama de dispers\u00e3o, esperamos que r seja positivo, mas n\u00e3o igual a 1.<\/p>\n<pre><code><span style=\"color: black\">t.scatter(0, 1, s=30, color='red')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-803\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-11.png\" alt=\"\" width=\"358\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-11.png 358w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-11-300x287.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-11-335x320.png 335w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/p>\n<p style=\"text-align: justify\"><strong>Passo 1.<\/strong> Converta cada vari\u00e1vel em unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">t_su = t.with_columns(\r\n        'x (standard units)', standard_units(x),\r\n        'y (standard units)', standard_units(y)\r\n    )\r\nt_su<\/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\">x<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">y<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">x (standard units)<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">y (standard units)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.46385<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.648886<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.87831<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.162221<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.29277<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.13555<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.29277<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.811107<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.87831<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.648886<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.46385<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.78444<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Passo 2.<\/strong> Multiplique cada par de unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">t_product = t_su.with_column('product of standard units', t_su.column(2) * t_su.column(3))\r\nt_product<\/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\">x<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">y<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">x (standard units)<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">y (standard units)<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">product of standard units<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.46385<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.648886<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.949871<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.87831<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.162221<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.142481<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.29277<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-1.13555<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.332455<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.29277<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.811107<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.237468<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.87831<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.648886<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.569923<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">6<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.46385<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.78444<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.61215<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Passo 3.<\/strong> r \u00e9 a m\u00e9dia dos produtos computados no Passo 2.<\/p>\n<pre><code><span style=\"color: black\"># r \u00e9 a m\u00e9dia dos produtos das unidades padr\u00e3o\r\n\r\nr = np.mean(t_product.column(4))\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[1]:<\/td>\n<td style=\"text-align: left\">0.6174163971897709<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Como esperado, r \u00e9 positivo, mas n\u00e3o \u00e9 igual a 1.<\/p>\n<h2 id=\"propriedades-de-r-\" style=\"text-align: justify\">Propriedades de <em>r<\/em><\/h2>\n<p style=\"text-align: justify\">O c\u00e1lculo mostra que:<\/p>\n<ul style=\"text-align: justify\">\n<li>r \u00e9 um n\u00famero puro. Ele n\u00e3o possui unidades. Isso ocorre porque r \u00e9 baseado em unidades padr\u00e3o.<\/li>\n<li>r n\u00e3o \u00e9 afetado pela mudan\u00e7a de unidades em nenhum dos eixos. Isso tamb\u00e9m ocorre porque r \u00e9 baseado em unidades padr\u00e3o.<\/li>\n<li>r n\u00e3o \u00e9 afetado pela troca dos eixos. Algebraicamente, isso ocorre porque o produto das unidades padr\u00e3o n\u00e3o depende de qual vari\u00e1vel \u00e9 chamada de x e qual \u00e9 y. Geometricamente, a troca de eixos reflete o gr\u00e1fico de dispers\u00e3o em rela\u00e7\u00e3o \u00e0 linha y=x, mas n\u00e3o altera a quantidade de agrupamento nem o sinal da associa\u00e7\u00e3o.<\/li>\n<\/ul>\n<pre><code><span style=\"color: black\">t.scatter('y', 'x', s=30, color='red')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-804\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-12.png\" alt=\"\" width=\"358\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-12.png 358w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-12-300x287.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-12-335x320.png 335w\" sizes=\"(max-width: 358px) 100vw, 358px\" \/><\/p>\n<h2 id=\"a-fun-o-correlation-\" style=\"text-align: justify\">A fun\u00e7\u00e3o <code>correlation<\/code><\/h2>\n<p style=\"text-align: justify\">Estaremos calculando correla\u00e7\u00f5es repetidamente, ent\u00e3o ser\u00e1 \u00fatil definir uma fun\u00e7\u00e3o que as calcule executando todas as etapas descritas acima. Vamos definir uma fun\u00e7\u00e3o <code>correlation<\/code> que recebe uma tabela e os r\u00f3tulos de duas colunas no tabela. A fun\u00e7\u00e3o retorna r, a m\u00e9dia dos produtos desses valores de coluna em unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def correlation(t, x, y):\r\n    return np.mean(standard_units(t.column(x))*standard_units(t.column(y)))<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Vamos chamar a fun\u00e7\u00e3o nas colunas <code>x<\/code> e <code>y<\/code> de <code>t<\/code>. A fun\u00e7\u00e3o retorna a mesma resposta para a correla\u00e7\u00e3o entre x e y que obtivemos pela aplica\u00e7\u00e3o direta de a f\u00f3rmula para r.<\/p>\n<pre><code><span style=\"color: black\">correlation(t, 'x', 'y')<\/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\">0.6174163971897709<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Como notamos, a ordem em que as vari\u00e1veis s\u00e3o especificadas n\u00e3o importa.<\/p>\n<pre><code><span style=\"color: black\">correlation(t, 'y', 'x')<\/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\">0.6174163971897709<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Chamar <code>correlation<\/code> nas colunas da tabela <code>suv<\/code> nos d\u00e1 a correla\u00e7\u00e3o entre pre\u00e7o e quilometragem, bem como a correla\u00e7\u00e3o entre pre\u00e7o e acelera\u00e7\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">correlation(suv, 'mpg', 'msrp')<\/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\">-0.6667143635709919<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">correlation(suv, 'acceleration', 'msrp')<\/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\">0.48699799279959155<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Esses valores confirmam o que t\u00ednhamos observado:<\/p>\n<ul style=\"text-align: justify\">\n<li>Existe uma associa\u00e7\u00e3o negativa entre pre\u00e7o e efici\u00eancia, enquanto a associa\u00e7\u00e3o entre pre\u00e7o e acelera\u00e7\u00e3o \u00e9 positiva.<\/li>\n<li>A rela\u00e7\u00e3o linear entre pre\u00e7o e acelera\u00e7\u00e3o \u00e9 um pouco mais fraca (correla\u00e7\u00e3o cerca de 0,5) do que entre pre\u00e7o e quilometragem (correla\u00e7\u00e3o cerca de -0,67).<\/li>\n<\/ul>\n<p style=\"text-align: justify\">Correla\u00e7\u00e3o \u00e9 um conceito simples e poderoso, mas \u00e0s vezes \u00e9 mal utilizado. Antes de usar r, \u00e9 importante estar ciente do que a correla\u00e7\u00e3o mede e do que n\u00e3o mede.<\/p>\n<h2 id=\"associa-o-n-o-implica-causalidade\" style=\"text-align: justify\">Associa\u00e7\u00e3o n\u00e3o implica Causalidade<\/h2>\n<p style=\"text-align: justify\">Correla\u00e7\u00e3o mede apenas associa\u00e7\u00e3o. Correla\u00e7\u00e3o n\u00e3o implica causalidade. Embora a correla\u00e7\u00e3o entre o peso e a habilidade matem\u00e1tica das crian\u00e7as em um distrito escolar possa ser positiva, isso n\u00e3o significa que fazer matem\u00e1tica fa\u00e7a as crian\u00e7as ficarem mais pesadas ou que ganhar peso melhore as habilidades matem\u00e1ticas das crian\u00e7as. Idade \u00e9 uma vari\u00e1vel de confus\u00e3o: crian\u00e7as mais velhas s\u00e3o tanto mais pesadas quanto melhores em matem\u00e1tica do que crian\u00e7as mais novas, em m\u00e9dia.<\/p>\n<h2 id=\"correla-o-mede-associa-o-linear\" style=\"text-align: justify\">Correla\u00e7\u00e3o Mede Associa\u00e7\u00e3o Linear<\/h2>\n<p style=\"text-align: justify\">Correla\u00e7\u00e3o mede apenas um tipo de associa\u00e7\u00e3o \u2013 linear. Vari\u00e1veis que t\u00eam forte associa\u00e7\u00e3o n\u00e3o linear podem ter correla\u00e7\u00e3o muito baixa. Aqui est\u00e1 um exemplo de vari\u00e1veis que t\u00eam uma rela\u00e7\u00e3o quadr\u00e1tica perfeita y = x^2, mas t\u00eam correla\u00e7\u00e3o igual a 0.<\/p>\n<pre><code><span style=\"color: black\">new_x = np.arange(-4, 4.1, 0.5)\r\nnonlinear = Table().with_columns(\r\n        'x', new_x,\r\n        'y', new_x**2\r\n    )\r\nnonlinear.scatter('x', 'y', s=30, color='r')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-805\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-13.png\" alt=\"\" width=\"367\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-13.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-13-300x280.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-13-343x320.png 343w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<pre><code><span style=\"color: black\">correlation(nonlinear, 'x', 'y')<\/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\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2 id=\"a-correla-o-afetada-por-outliers\" style=\"text-align: justify\">A Correla\u00e7\u00e3o \u00e9 Afetada por Outliers<\/h2>\n<p style=\"text-align: justify\">Outliers podem ter um grande efeito na correla\u00e7\u00e3o. Aqui est\u00e1 um exemplo onde um gr\u00e1fico de dispers\u00e3o para o qual r \u00e9 igual a 1 \u00e9 transformado em um gr\u00e1fico para o qual r \u00e9 igual a 0, pela adi\u00e7\u00e3o de apenas um ponto perif\u00e9rico .<\/p>\n<pre><code><span style=\"color: black\">line = Table().with_columns(\r\n        'x', make_array(1, 2, 3, 4),\r\n        'y', make_array(1, 2, 3, 4)\r\n    )\r\nline.scatter('x', 'y', s=30, color='r')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-806\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-14.png\" alt=\"\" width=\"372\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-14.png 372w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-14-300x276.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-14-348x320.png 348w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<pre><code><span style=\"color: black\">correlation(line, 'x', 'y')<\/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\">1.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">outlier = Table().with_columns(\r\n        'x', make_array(1, 2, 3, 4, 5),\r\n        'y', make_array(1, 2, 3, 4, 0)\r\n    )\r\noutlier.scatter('x', 'y', s=30, color='r')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-807\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-15.png\" alt=\"\" width=\"372\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-15.png 372w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-15-300x276.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-15-348x320.png 348w\" sizes=\"(max-width: 372px) 100vw, 372px\" \/><\/p>\n<pre><code><span style=\"color: black\">correlation(outlier, 'x', 'y')<\/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\">0.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<h2 id=\"as-correla-es-ecol-gicas-devem-ser-interpretadas-com-cuidado\" style=\"text-align: justify\">As Correla\u00e7\u00f5es Ecol\u00f3gicas devem ser Interpretadas com Cuidado<\/h2>\n<p style=\"text-align: justify\">Correla\u00e7\u00f5es baseadas em dados agregados podem ser enganosas. Como exemplo, aqui est\u00e3o dados sobre as pontua\u00e7\u00f5es do SAT de Leitura Cr\u00edtica e Matem\u00e1tica em 2014. H\u00e1 um ponto para cada um dos 50 estados e um para Washington, D.C. A coluna <code>Taxa de Participa\u00e7\u00e3o<\/code> cont\u00e9m a porcentagem de alunos do \u00faltimo ano do ensino m\u00e9dio que fizeram o teste. As tr\u00eas pr\u00f3ximas colunas mostram a pontua\u00e7\u00e3o m\u00e9dia no estado em cada parte do teste, e a coluna final \u00e9 a m\u00e9dia das pontua\u00e7\u00f5es totais no teste.<\/p>\n<pre><code><span style=\"color: black\">sat2014 = Table.read_table(path_data + 'sat2014.csv').sort('State')\r\nsat2014<\/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\">State<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Participation Rate<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Critical Reading<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Math<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Writing<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Combined<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Alabama<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">6.7<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">547<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">538<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">532<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1617<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Alaska<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">54.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">507<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">503<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">475<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1485<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Arizona<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">36.4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">522<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">525<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">500<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1547<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Arkansas<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">4.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">573<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">571<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">554<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1698<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">California<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">60.3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">498<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">510<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">496<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1504<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Colorado<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">14.3<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">582<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">586<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">567<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1735<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Connecticut<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">88.4<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">507<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">510<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">508<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1525<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Delaware<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">100<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">456<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">459<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">444<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1359<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">District of Columbia<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">100<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">440<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">438<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">431<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1309<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">Florida<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">491<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">485<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">472<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1448<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">O diagrama de dispers\u00e3o das pontua\u00e7\u00f5es em matem\u00e1tica versus pontua\u00e7\u00f5es em leitura cr\u00edtica est\u00e1 fortemente agrupado em torno de uma linha reta; a correla\u00e7\u00e3o \u00e9 pr\u00f3xima de 0,985.<\/p>\n<pre><code><span style=\"color: black\">sat2014.scatter('Critical Reading', 'Math')<\/span><\/code><\/pre>\n<p style=\"text-align: justify\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-808\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-16.png\" alt=\"\" width=\"376\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-16.png 376w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-16-300x273.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-16-352x320.png 352w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<pre><code><span style=\"color: black\">correlation(sat2014, 'Critical Reading', 'Math')<\/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\">0.9847558411067434<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Isso \u00e9 uma correla\u00e7\u00e3o extremamente alta. Mas \u00e9 importante observar que isso n\u00e3o reflete a for\u00e7a da rela\u00e7\u00e3o entre as pontua\u00e7\u00f5es de Matem\u00e1tica e Leitura Cr\u00edtica dos <em>estudantes<\/em>.<\/p>\n<p style=\"text-align: justify\">Os dados consistem em pontua\u00e7\u00f5es m\u00e9dias em cada estado. Mas os estados n\u00e3o fazem os testes &#8211; os estudantes sim. Os dados na tabela foram criados agrupando todos os estudantes de cada estado em um \u00fanico ponto nas m\u00e9dias das duas vari\u00e1veis naquele estado. Mas nem todos os estudantes no estado estar\u00e3o nesse ponto, pois os estudantes variam em seu desempenho. Se voc\u00ea plotar um ponto para cada estudante em vez de apenas um para cada estado, haver\u00e1 uma nuvem de pontos em torno de cada ponto na figura acima. A imagem geral ser\u00e1 mais difusa. A correla\u00e7\u00e3o entre as pontua\u00e7\u00f5es de Matem\u00e1tica e Leitura Cr\u00edtica dos estudantes ser\u00e1 <em>menor<\/em> do que o valor calculado com base nas m\u00e9dias estaduais.<\/p>\n<p style=\"text-align: justify\">Correla\u00e7\u00f5es baseadas em agrega\u00e7\u00f5es e m\u00e9dias s\u00e3o chamadas de <em>correla\u00e7\u00f5es ecol\u00f3gicas<\/em> e s\u00e3o frequentemente relatadas. Como acabamos de ver, elas devem ser interpretadas com cuidado.<\/p>\n<h2 id=\"s-rio-ou-ir-nico-\" style=\"text-align: justify\">S\u00e9rio ou ir\u00f4nico?<\/h2>\n<p style=\"text-align: justify\">Em 2012, um <a href=\"http:\/\/www.biostat.jhsph.edu\/courses\/bio621\/misc\/Chocolate%20consumption%20cognitive%20function%20and%20nobel%20laurates%20%28NEJM%29.pdf\">artigo<\/a> no respeitado New England Journal of Medicine examinou a rela\u00e7\u00e3o entre o consumo de chocolate e os Pr\u00eamios Nobel em um grupo de pa\u00edses. A <a href=\"http:\/\/blogs.scientificamerican.com\/the-curious-wavefunction\/chocolate-consumption-and-nobel-prizes-a-bizarre-juxtaposition-if-there-ever-was-one\/\">Scientific American<\/a> respondeu seriamente, enquanto <a href=\"http:\/\/www.reuters.com\/article\/2012\/10\/10\/us-eat-chocolate-win-the-nobel-prize-idUSBRE8991MS20121010#vFdfFkbPVlilSjsB.97\">outros<\/a> foram mais descontra\u00eddos. Voc\u00ea \u00e9 livre para tomar sua pr\u00f3pria decis\u00e3o! O seguinte gr\u00e1fico, fornecido no artigo, deve motiv\u00e1-lo a ir dar uma olhada.<\/p>\n<pre><code><span style=\"color: black\">from IPython.display import Image\r\nImage(\"..\/..\/..\/images\/chocoNobel.png\")<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-809\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-17.png\" alt=\"\" width=\"725\" height=\"635\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-17.png 725w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-17-300x263.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-1-17-365x320.png 365w\" sizes=\"(max-width: 725px) 100vw, 725px\" \/><\/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\/\">\u2190 Cap\u00edtulo 15 &#8211; Previs\u00e3o<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-2\/\">Cap\u00edtulo 15.2 &#8211; Linha de Regress\u00e3o \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-791","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/791","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=791"}],"version-history":[{"count":7,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/791\/revisions"}],"predecessor-version":[{"id":1073,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/791\/revisions\/1073"}],"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=791"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}