{"id":813,"date":"2025-07-29T20:24:36","date_gmt":"2025-07-30T00:24:36","guid":{"rendered":"https:\/\/literaciadigital.ufms.br\/?page_id=813"},"modified":"2025-10-11T16:47:52","modified_gmt":"2025-10-11T20:47:52","slug":"15-2","status":"publish","type":"page","link":"https:\/\/literaciadigital.ufms.br\/en\/data8\/15-0\/15-2\/","title":{"rendered":"Cap\u00edtulo 15.2"},"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\nimport numpy as np\r\npath_data = '..\/..\/..\/assets\/data\/'\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=\"a-linha-de-regress-o\" style=\"text-align: center\">A Linha de Regress\u00e3o<\/h1>\n<p style=\"text-align: justify\">O coeficiente de correla\u00e7\u00e3o r n\u00e3o apenas mede como os pontos em um gr\u00e1fico de dispers\u00e3o est\u00e3o agrupados em torno de uma linha reta. Ele tamb\u00e9m ajuda a identificar a linha reta em torno da qual os pontos est\u00e3o agrupados. Nesta se\u00e7\u00e3o, vamos refazer o caminho que Galton e Pearson percorreram para descobrir essa linha.<\/p>\n<p style=\"text-align: justify\">Como vimos, nosso conjunto de dados sobre as alturas dos pais e seus filhos adultos indica uma associa\u00e7\u00e3o linear entre as duas vari\u00e1veis. A linearidade foi confirmada quando nossas previs\u00f5es das alturas dos filhos com base nas alturas dos pais aproximadamente seguiram uma linha reta.<\/p>\n<pre><code><span style=\"color: black\">original = Table.read_table(path_data + 'family_heights.csv')\r\n\r\nheights = Table().with_columns(\r\n    'MidParent', original.column('midparentHeight'),\r\n    'Child', original.column('childHeight')\r\n    )<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">def predict_child(mpht):\r\n    \"\"\"Retorna uma previs\u00e3o da altura de um filho\r\n    cujos pais t\u00eam uma altura do meio dos pais de mpht.\r\n\r\n    A previs\u00e3o \u00e9 a altura m\u00e9dia dos filhos\r\n    cuja altura do meio dos pais est\u00e1 na faixa de mpht mais ou menos 0,5 polegadas.\r\n    \"\"\"\r\n\r\n    close_points = heights.where('MidParent', are.between(mpht-0.5, mpht + 0.5))\r\n    return close_points.column('Child').mean()   <\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_with_predictions = heights.with_column(\r\n    'Prediction', heights.apply(predict_child, 'MidParent')\r\n    )<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_with_predictions.scatter('MidParent')<\/span><\/code><\/pre>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-815\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-1.png\" alt=\"\" width=\"491\" height=\"349\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-1.png 491w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-1-300x213.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-1-450x320.png 450w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<h2 id=\"medindo-em-unidades-padr-o\">Medindo em Unidades Padr\u00e3o<\/h2>\n<p style=\"text-align: justify\">Vamos ver se conseguimos encontrar uma maneira de identificar esta linha. Primeiro, observe que a associa\u00e7\u00e3o linear n\u00e3o depende das unidades de medida \u2013 podemos muito bem medir ambas as vari\u00e1veis em unidades padr\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def standard_units(xyz):\r\n    \"Converta qualquer array de n\u00fameros em unidades padr\u00e3o.\"\r\n    return (xyz - np.mean(xyz))\/np.std(xyz)  <\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_SU = Table().with_columns(\r\n    'MidParent SU', standard_units(heights.column('MidParent')),\r\n    'Child SU', standard_units(heights.column('Child'))\r\n)\r\nheights_SU<\/span><\/code><\/pre>\n<pre><code><span style=\"color: black\">heights_SU = Table().with_columns(\r\n    'MidParent SU', standard_units(heights.column('MidParent')),\r\n    'Child SU', standard_units(heights.column('Child'))\r\n)\r\nheights_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\">MidParent SU<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Child SU<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.45465<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.80416<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.45465<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.686005<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.45465<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.630097<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">3.45465<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.630097<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.47209<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.88802<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.47209<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.60848<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.47209<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.348285<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">2.47209<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">-0.348285<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.58389<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.18917<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">1.58389<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">0.350559<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Nesta escala, podemos calcular nossas previs\u00f5es exatamente como antes. Mas primeiro temos que descobrir como converter nossa antiga defini\u00e7\u00e3o de pontos &#8220;pr\u00f3ximos&#8221; para um valor na nova escala. Dissemos que as alturas dos pais m\u00e9dios eram &#8220;pr\u00f3ximos&#8221; se eles estivessem a 0,5 polegadas um do outro Como as unidades padr\u00e3o medem dist\u00e2ncias em unidades de SDs, temos que descobrir quantos SDs da altura do pai m\u00e9dio correspondem a 0,5 polegadas.<\/p>\n<p style=\"text-align: justify\">Um SD de altura dos pais m\u00e9dios tem cerca de 1,8 polegadas. Portanto, 0,5 polegadas equivale a cerca de 0,28 SDs.<\/p>\n<pre><code><span style=\"color: black\">sd_midparent = np.std(heights.column(0))\r\nsd_midparent<\/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\">1.8014050969207571<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<pre><code><span style=\"color: black\">0.5\/sd_midparent<\/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\">0.277561110965367<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify\">Agora estamos prontos para modificar nossa fun\u00e7\u00e3o de previs\u00e3o para fazer previs\u00f5es na escala de unidades padr\u00e3o. Tudo o que mudou \u00e9 que estamos usando a tabela de valores em unidades padr\u00e3o e definindo &#8220;close&#8221; como acima.<\/p>\n<pre><code><span style=\"color: black\">def predict_child_su(mpht_su):\r\n    \"\"\"Retornar uma previs\u00e3o da altura (em unidades padr\u00e3o) de uma crian\u00e7a\r\n    cujos pais t\u00eam uma altura midparent de mpht_su em unidades padr\u00e3o.\r\n    \"\"\"\r\n    close = 0.5\/sd_midparent\r\n    close_points = heights_SU.where('MidParent SU', are.between(mpht_su-close, mpht_su + close))\r\n    return close_points.column('Child SU').mean()   <\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_with_su_predictions = heights_SU.with_column(\r\n    'Prediction SU', heights_SU.apply(predict_child_su, 'MidParent SU')\r\n    )<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_with_su_predictions.scatter('MidParent SU')<\/span><\/code><\/pre>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-816\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-2.png\" alt=\"\" width=\"518\" height=\"345\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-2.png 518w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-2-300x200.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-2-480x320.png 480w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-2-350x233.png 350w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p style=\"text-align: justify\">Este gr\u00e1fico parece exatamente com o gr\u00e1fico desenhado na escala original. Apenas os n\u00fameros nos eixos mudaram. Isso confirma que podemos entender o processo de previs\u00e3o apenas trabalhando em unidades padr\u00e3o.<\/p>\n<h2 id=\"identificando-a-linha-em-unidades-padr-o\">Identificando a Linha em Unidades Padr\u00e3o<\/h2>\n<p style=\"text-align: justify\">O gr\u00e1fico de dispers\u00e3o acima tem uma forma <em>oval<\/em> &#8211; ou seja, \u00e9 aproximadamente oval como uma bola de futebol americano. Nem todos os gr\u00e1ficos de dispers\u00e3o s\u00e3o em forma de bola, nem mesmo aqueles que mostram associa\u00e7\u00e3o linear. Mas nesta se\u00e7\u00e3o trabalharemos apenas com gr\u00e1ficos de dispers\u00e3o em forma de bola. Na pr\u00f3xima se\u00e7\u00e3o, generalizaremos nossa an\u00e1lise para outras formas de gr\u00e1ficos.<\/p>\n<p style=\"text-align: justify\">Aqui est\u00e1 um gr\u00e1fico de dispers\u00e3o em forma de bola com ambas as vari\u00e1veis medidas em unidades padr\u00e3o. A linha de 45 graus est\u00e1 mostrada em vermelho.<\/p>\n<pre><code><span style=\"color: black\">r = 0.5\r\nx_demo = np.random.normal(0, 1, 10000)\r\nz_demo = np.random.normal(0, 1, 10000)\r\ny_demo = r*x_demo + np.sqrt(1 - r**2)*z_demo\r\nplots.figure(figsize=(6,6))\r\nplots.xlim(-4, 4)\r\nplots.ylim(-4, 4)\r\nplots.scatter(x_demo, y_demo, s=10)\r\n#plots.plot([-4, 4], [-4*0.6,4*0.6], color='g', lw=2)\r\nplots.plot([-4,4],[-4,4], color='r', lw=2)\r\n#plots.plot([1.5,1.5], [-4,4], color='k', lw=2)\r\nplots.xlabel('x in standard units')\r\nplots.ylabel('y in standard units');<\/span><\/code><\/pre>\n<p><img decoding=\"async\" class=\"alignnone size-full wp-image-817\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-3.png\" alt=\"\" width=\"440\" height=\"409\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-3.png 440w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-3-300x279.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-3-344x320.png 344w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p style=\"text-align: justify\">Mas a linha de 45 graus n\u00e3o \u00e9 a linha que separa os centros das faixas verticais. Voc\u00ea pode ver isso na figura abaixo, onde a linha vertical em 1,5 unidades padr\u00e3o \u00e9 mostrada em preto. Os pontos no gr\u00e1fico de dispers\u00e3o pr\u00f3ximos as todas as linhas pretas t\u00eam alturas aproximadamente na faixa de -2 a 3. A linha vermelha \u00e9 muito alta para ser destacada no centro.<\/p>\n<pre><code><span style=\"color: black\">r = 0.5\r\nx_demo = np.random.normal(0, 1, 10000)\r\nz_demo = np.random.normal(0, 1, 10000)\r\ny_demo = r*x_demo + np.sqrt(1 - r**2)*z_demo\r\nplots.figure(figsize=(6,6))\r\nplots.xlim(-4, 4)\r\nplots.ylim(-4, 4)\r\nplots.scatter(x_demo, y_demo, s=10)\r\n#plots.plot([-4, 4], [-4*0.6,4*0.6], color='g', lw=2)\r\nplots.plot([-4,4],[-4,4], color='r', lw=2)\r\nplots.plot([1.5,1.5], [-4,4], color='k', lw=2)\r\nplots.xlabel('x in standard units')\r\nplots.ylabel('y in standard units');<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-818\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-4.png\" alt=\"\" width=\"440\" height=\"409\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-4.png 440w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-4-300x279.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-4-344x320.png 344w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Portanto, a linha de 45 graus n\u00e3o \u00e9 o &#8220;gr\u00e1fico das m\u00e9dias&#8221;. Essa linha \u00e9 a verde mostrada abaixo.<\/p>\n<pre><code><span style=\"color: black\">r = 0.5\r\nx_demo = np.random.normal(0, 1, 10000)\r\nz_demo = np.random.normal(0, 1, 10000)\r\ny_demo = r*x_demo + np.sqrt(1 - r**2)*z_demo\r\nplots.figure(figsize=(6,6))\r\nplots.xlim(-4, 4)\r\nplots.ylim(-4, 4)\r\nplots.scatter(x_demo, y_demo, s=10)\r\nplots.plot([-4, 4], [-4*0.6,4*0.6], color='g', lw=2)\r\nplots.plot([-4,4],[-4,4], color='r', lw=2)\r\nplots.plot([1.5,1.5], [-4,4], color='k', lw=2)\r\nplots.xlabel('x in standard units')\r\nplots.ylabel('y in standard units');<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-819\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-5.png\" alt=\"\" width=\"440\" height=\"409\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-5.png 440w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-5-300x279.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-5-344x320.png 344w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p style=\"text-align: justify\">Ambas as linhas passam pela origem (0, 0). A linha verde passa pelos centros das faixas verticais (pelo menos aproximadamente) e \u00e9 <em>mais plana<\/em> do que a linha vermelha de 45 graus.<\/p>\n<p style=\"text-align: justify\">A inclina\u00e7\u00e3o da linha de 45 graus \u00e9 1. Portanto, a inclina\u00e7\u00e3o da linha verde &#8220;gr\u00e1fico das m\u00e9dias&#8221; \u00e9 um valor positivo, mas menor que 1.<\/p>\n<p style=\"text-align: justify\">Que valor poderia ser esse? Voc\u00ea adivinhou &#8211; \u00e9 r.<\/p>\n<h2 id=\"a-linha-de-regress-o-em-unidades-padronizadas\" style=\"text-align: justify\">A Linha de Regress\u00e3o, em Unidades Padronizadas<\/h2>\n<p style=\"text-align: justify\">A linha verde &#8220;gr\u00e1fico das m\u00e9dias&#8221; \u00e9 chamada de <em>linha de regress\u00e3o<\/em>, por um motivo que explicaremos em breve. Mas primeiro, vamos simular alguns gr\u00e1ficos de dispers\u00e3o em forma de bola de futebol com diferentes valores de r, e ver como a linha muda. Em cada caso, a linha vermelha de 45 graus foi desenhada para compara\u00e7\u00e3o.<\/p>\n<p style=\"text-align: justify\">A fun\u00e7\u00e3o que realiza a simula\u00e7\u00e3o \u00e9 chamada <code>regression_line<\/code> e recebe r como argumento.<\/p>\n<pre><code><span style=\"color: black\">\r\ndef regression_line(r):\r\n    x = np.random.normal(0, 1, 10000)\r\n    z = np.random.normal(0, 1, 10000)\r\n    y = r*x + (np.sqrt(1-r**2))*z\r\n    plots.figure(figsize=(6, 6))\r\n    plots.xlim(-4, 4)\r\n    plots.ylim(-4, 4)\r\n    plots.scatter(x, y)\r\n    plots.plot([-4, 4], [-4*r,4*r], color='g', lw=2)\r\n    if r &gt;= 0:\r\n        plots.plot([-4,4],[-4,4], lw=2, color='r')\r\n    else:\r\n        plots.plot([-4,4], [4,-4], lw=2, color='r')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">regression_line(0.95)<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-820\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-6.png\" alt=\"\" width=\"418\" height=\"387\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-6.png 418w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-6-300x278.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-6-346x320.png 346w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<pre><code><span style=\"color: black\">regression_line(0.6)<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-821\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-7.png\" alt=\"\" width=\"418\" height=\"387\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-7.png 418w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-7-300x278.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-7-346x320.png 346w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p style=\"text-align: justify\">Quando r est\u00e1 pr\u00f3ximo de 1, o gr\u00e1fico de dispers\u00e3o, a linha de 45 graus e a linha de regress\u00e3o est\u00e3o todas muito pr\u00f3ximas umas das outras. Mas para valores mais moderados de r, a linha de regress\u00e3o \u00e9 perceptivelmente mais plana.<\/p>\n<h2 id=\"o-efeito-de-regress-o\" style=\"text-align: justify\">O Efeito de Regress\u00e3o<\/h2>\n<p style=\"text-align: justify\">Em termos de previs\u00e3o, isso significa que para pais cuja altura m\u00e9dia dos pais est\u00e1 em 1,5 unidades padr\u00e3o, nossa previs\u00e3o da altura do filho \u00e9 um pouco <em>menor<\/em> do que 1,5 unidades padr\u00e3o. Se a altura m\u00e9dia dos pais for de 2 unidades padr\u00e3o, prevemos que a altura do filho ser\u00e1 um pouco menor do que 2 unidades padr\u00e3o.<\/p>\n<p style=\"text-align: justify\">Em outras palavras, prevemos que o filho ser\u00e1 um pouco mais pr\u00f3ximo da m\u00e9dia do que os pais. Isso \u00e9 chamado de &#8220;regress\u00e3o \u00e0 m\u00e9dia&#8221; e \u00e9 como o nome <em>regress\u00e3o<\/em> surge.<\/p>\n<p style=\"text-align: justify\">A regress\u00e3o \u00e0 m\u00e9dia tamb\u00e9m funciona quando a altura m\u00e9dia dos pais \u00e9 abaixo da m\u00e9dia. Filhos cuja altura m\u00e9dia dos pais foi abaixo da m\u00e9dia acabaram sendo um pouco mais altos em rela\u00e7\u00e3o \u00e0 sua gera\u00e7\u00e3o, em m\u00e9dia.<\/p>\n<p style=\"text-align: justify\">Em geral, indiv\u00edduos que est\u00e3o afastados da m\u00e9dia em uma vari\u00e1vel esperam-se que estejam um pouco menos afastados da m\u00e9dia em outra. Isso \u00e9 chamado de <em>efeito de regress\u00e3o<\/em>.<\/p>\n<p style=\"text-align: justify\">Lembre-se de que o efeito de regress\u00e3o \u00e9 uma afirma\u00e7\u00e3o sobre m\u00e9dias. Por exemplo, ele diz que se voc\u00ea pegar todos os filhos cuja altura m\u00e9dia dos pais \u00e9 de 1,5 unidades padr\u00e3o, ent\u00e3o a altura m\u00e9dia dessas crian\u00e7as \u00e9 um pouco menos que 1,5 unidades padr\u00e3o. N\u00e3o diz que todas essas crian\u00e7as ser\u00e3o um pouco menos que 1,5 unidades padr\u00e3o em altura. Algumas ser\u00e3o mais altas e outras mais baixas. A <em>m\u00e9dia<\/em> dessas alturas ser\u00e1 menor que 1,5 unidades padr\u00e3o.<\/p>\n<h2 id=\"a-equa-o-da-linha-de-regress-o\" style=\"text-align: justify\">A Equa\u00e7\u00e3o da Linha de Regress\u00e3o<\/h2>\n<p style=\"text-align: justify\">Na regress\u00e3o, usamos o valor de uma vari\u00e1vel (que chamaremos de x) para prever o valor de outra (que chamaremos de y). Quando as vari\u00e1veis x e y s\u00e3o medidas em unidades padr\u00e3o, a linha de regress\u00e3o para prever y com base em x tem inclina\u00e7\u00e3o r e passa pela origem. Assim, a equa\u00e7\u00e3o da linha de regress\u00e3o pode ser escrita como:<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">estimativa de y = r \u22c5 x quando ambas as vari\u00e1veis s\u00e3o medidas em unidades padr\u00e3o<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Nas unidades originais dos dados, isso se torna<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\"><sup>(estimativa de y &#8211; m\u00e9dia de y)<\/sup>\u2044(<sub>SD de y)<\/sub> = r \u00d7 <sup>(o dado x &#8211; m\u00e9dia de x)<\/sup>\u2044<sub>(SD de x)<\/sub><\/div>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-826 aligncenter\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-regLine.png\" alt=\"\" width=\"766\" height=\"625\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-regLine.png 766w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-regLine-300x245.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-regLine-392x320.png 392w\" sizes=\"(max-width: 766px) 100vw, 766px\" \/><\/p>\n<p>A inclina\u00e7\u00e3o e o intercepto da linha de regress\u00e3o em unidades originais podem ser derivados do diagrama acima.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\"><strong>inclina\u00e7\u00e3o da linha de regress\u00e3o<\/strong> = r \u22c5 <sup>(SD de y)<\/sup>\u2044<sub>(SD de x)<\/sub><\/div>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\"><strong>intercepto da linha de regress\u00e3o<\/strong> = m\u00e9dia de y &#8211; inclina\u00e7\u00e3o \u22c5 m\u00e9dia de x<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">As tr\u00eas fun\u00e7\u00f5es abaixo calculam a correla\u00e7\u00e3o, a inclina\u00e7\u00e3o e o intercepto. Todas elas recebem tr\u00eas argumentos: o nome da tabela, o r\u00f3tulo da coluna contendo x, e o r\u00f3tulo da coluna contendo y.<\/p>\n<pre><code><span style=\"color: black\">def correlation(t, label_x, label_y):\r\n    return np.mean(standard_units(t.column(label_x))*standard_units(t.column(label_y)))\r\n\r\ndef slope(t, label_x, label_y):\r\n    r = correlation(t, label_x, label_y)\r\n    return r*np.std(t.column(label_y))\/np.std(t.column(label_x))\r\n\r\ndef intercept(t, label_x, label_y):\r\n    return np.mean(t.column(label_y)) - slope(t, label_x, label_y)*np.mean(t.column(label_x))<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<h2 id=\"a-linha-de-regress-o-nas-unidades-dos-dados\">A linha de Regress\u00e3o nas Unidades dos Dados<\/h2>\n<p>A correla\u00e7\u00e3o entre a altura dos pais m\u00e9dios e a altura da crian\u00e7a \u00e9 de 0,32:<\/p>\n<pre><code><span style=\"color: black\">family_r = correlation(heights, 'MidParent', 'Child')\r\nfamily_r<\/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\">0.32094989606395924<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Tamb\u00e9m podemos encontrar a equa\u00e7\u00e3o da linha de regress\u00e3o para prever a altura da crian\u00e7a com base na altura dos pais m\u00e9dios.<\/p>\n<pre><code><span style=\"color: black\">family_slope = slope(heights, 'MidParent', 'Child')\r\nfamily_intercept = intercept(heights, 'MidParent', 'Child')\r\nfamily_slope, family_intercept<\/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\">(0.637360896969479, 22.63624054958975)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>A equa\u00e7\u00e3o da linha de regress\u00e3o \u00e9<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">estimativa da altura da crian\u00e7a = 0.64 \u22c5 altura m\u00e9dia dos pais + 22.64<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Isso tamb\u00e9m \u00e9 conhecido como <em>equa\u00e7\u00e3o de regress\u00e3o.<\/em> O principal uso da equa\u00e7\u00e3o de regress\u00e3o \u00e9 prever y com base em x.<\/p>\n<p style=\"text-align: justify\">Por exemplo, para uma altura m\u00e9dia dos pais de 70.48 polegadas, a equa\u00e7\u00e3o de regress\u00e3o prev\u00ea que a altura da crian\u00e7a seja de 67.56 polegadas.<\/p>\n<pre><code><span style=\"color: black\">family_slope * 70.48 + family_intercept<\/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\">67.55743656799862<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Nossa previs\u00e3o original, criada tomando a altura m\u00e9dia de todas as crian\u00e7as que tinham alturas dos pais m\u00e9dios pr\u00f3ximas de 70,48, ficou bem pr\u00f3xima: 67,63 polegadas em compara\u00e7\u00e3o com a previs\u00e3o da linha de regress\u00e3o de 67,55 polegadas.<\/p>\n<pre><code><span style=\"color: black\">heights_with_predictions.where('MidParent', are.equal_to(70.48)).show(3)<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">MidParent<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Child<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Prediction<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.48<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">74<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">67.6342<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.48<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">67.6342<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.48<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">67.6342<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>Aqui est\u00e3o todas as linhas da tabela, juntamente com as nossas previs\u00f5es originais e as novas previs\u00f5es de regress\u00e3o das alturas das crian\u00e7as.<\/p>\n<pre><code><span style=\"color: black\">heights_with_predictions = heights_with_predictions.with_column(\r\n    'Regression Prediction', family_slope * heights.column('MidParent') + family_intercept\r\n)\r\nheights_with_predictions<\/span><\/code><\/pre>\n<table style=\"font-family: monospace;border-collapse: collapse;width: auto;margin-left: 1em\" border=\"1\">\n<thead>\n<tr style=\"background-color: #f0f0f0;border-bottom: 2px solid #ddd\">\n<th style=\"text-align: left;padding: 4px 8px\">MidParent<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Child<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Prediction<\/th>\n<th style=\"text-align: left;padding: 4px 8px\">Regression Prediction<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.2<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">75.43<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.1<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.7124<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.4158<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.4158<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">65.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.4158<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">73.66<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">65.5<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">70.4158<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">69.5842<\/td>\n<\/tr>\n<tr>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.06<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">71<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5025<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5645<\/td>\n<\/tr>\n<tr style=\"background-color: #f8f8f8\">\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">72.06<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5025<\/td>\n<td style=\"padding: 4px 8px;border: 1px solid #ddd\">68.5645<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">heights_with_predictions.scatter('MidParent')<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-822\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-8.png\" alt=\"\" width=\"573\" height=\"349\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-8.png 573w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-8-300x183.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-8-525x320.png 525w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p style=\"text-align: justify\">Os pontos cinza mostram as previs\u00f5es de regress\u00e3o, todos na linha de regress\u00e3o. Observe como a linha est\u00e1 muito pr\u00f3xima do gr\u00e1fico dourado das m\u00e9dias. Para estes dados, a linha de regress\u00e3o faz um bom trabalho de aproximar os centros das faixas verticais.<\/p>\n<h2 id=\"valores-ajustados\">Valores Ajustados<\/h2>\n<p style=\"text-align: justify\">As previs\u00f5es est\u00e3o todas na linha e s\u00e3o conhecidas como &#8220;valores ajustados&#8221;. A fun\u00e7\u00e3o <code>fit<\/code> recebe o nome da tabela e os r\u00f3tulos de x e y, e retorna uma matriz de valores ajustados, um para cada ponto no gr\u00e1fico de dispers\u00e3o.<\/p>\n<pre><code><span style=\"color: black\">def fit(table, x, y):\r\n    \"\"\"Retorna a altura da linha de regress\u00e3o em cada valor de x.\"\"\"\r\n    a = slope(table, x, y)\r\n    b = intercept(table, x, y)\r\n    return a * table.column(x) + b<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<p>\u00c9 mais f\u00e1cil ver a linha no gr\u00e1fico abaixo do que no acima.<\/p>\n<pre><code><span style=\"color: black\">heights.with_column('Fitted', fit(heights, 'MidParent', 'Child')).scatter('MidParent')<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-823\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-9.png\" alt=\"\" width=\"461\" height=\"349\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-9.png 461w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-9-300x227.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-9-423x320.png 423w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/p>\n<p>Outra maneira de tra\u00e7ar a linha \u00e9 usar a op\u00e7\u00e3o <code>fit_line=True<\/code> com o m\u00e9todo Table <code>scatter<\/code>.<\/p>\n<pre><code><span style=\"color: black\">heights.scatter('MidParent', fit_line=True)<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-824\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-10.png\" alt=\"\" width=\"367\" height=\"346\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-10.png 367w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-10-300x283.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-10-339x320.png 339w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<h2 id=\"unidades-de-medida-da-inclina-o\">Unidades de Medida da Inclina\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify\">A inclina\u00e7\u00e3o \u00e9 uma raz\u00e3o, e vale a pena dedicar um momento para estudar as unidades em que ela \u00e9 medida. Nosso exemplo vem do conjunto de dados familiar sobre m\u00e3es que deram \u00e0 luz em um sistema hospitalar. O gr\u00e1fico de dispers\u00e3o dos pesos da gravidez versus alturas se parece com uma bola de futebol que foi usada em muitos jogos, mas \u00e9 pr\u00f3xima o suficiente de uma bola de futebol para que possamos justificar colocar nossa linha ajustada nela. Nas se\u00e7\u00f5es posteriores veremos como tornar essas justificativas mais formais.<\/p>\n<pre><code><span style=\"color: black\">baby = Table.read_table(path_data + 'baby.csv')<\/span><\/code><\/pre>\n<p>&nbsp;<\/p>\n<pre><code><span style=\"color: black\">baby.scatter('Maternal Height', 'Maternal Pregnancy Weight', fit_line=True)<\/span><\/code><\/pre>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-825\" src=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-11.png\" alt=\"\" width=\"376\" height=\"342\" srcset=\"https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-11.png 376w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-11-300x273.png 300w, https:\/\/literaciadigital.ufms.br\/files\/2025\/07\/15-2-11-352x320.png 352w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<pre><code><span style=\"color: black\">slope(baby, 'Maternal Height', 'Maternal Pregnancy Weight')<\/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\">3.572846259275056<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A inclina\u00e7\u00e3o da linha de regress\u00e3o \u00e9 de <strong>3,57 libras por polegada<\/strong>. Isso significa que, para duas mulheres que t\u00eam 1 polegada de diferen\u00e7a na altura, nossa previs\u00e3o do peso durante a gravidez ser\u00e1 diferente em 3,57 libras. Para uma mulher que \u00e9 2 polegadas mais alta do que outra, nossa previs\u00e3o do peso durante a gravidez ser\u00e1<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\">2 \u00d7 3.57 = 7.14<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">libras a mais do que nossa previs\u00e3o para a mulher mais baixa.<\/p>\n<p style=\"text-align: justify\">Observe que as faixas verticais sucessivas no gr\u00e1fico de dispers\u00e3o est\u00e3o separadas por uma polegada, porque as alturas foram arredondadas para a polegada mais pr\u00f3xima. Outra maneira de pensar na inclina\u00e7\u00e3o \u00e9 pegar duas faixas consecutivas (que est\u00e3o necessariamente a 1 polegada de dist\u00e2ncia), correspondendo a dois grupos de mulheres separados por 1 polegada de altura. A inclina\u00e7\u00e3o de 3,57 libras por polegada significa que o peso m\u00e9dio durante a gravidez do grupo mais alto \u00e9 cerca de 3,57 libras maior do que o do grupo mais baixo.<\/p>\n<h2 id=\"exemplo\">Exemplo<\/h2>\n<p style=\"text-align: justify\">Suponha que nosso objetivo seja usar regress\u00e3o para estimar a altura de um basset hound com base em seu peso, usando uma amostra que parece consistente com o modelo de regress\u00e3o. Suponha que a correla\u00e7\u00e3o observada r seja 0,5, e que as estat\u00edsticas resumidas para as duas vari\u00e1veis sejam conforme a tabela abaixo:<\/p>\n<table style=\"width: 80%;margin-left: auto;margin-right: auto\">\n<thead>\n<tr>\n<th style=\"text-align: right\"><\/th>\n<th style=\"text-align: center\"><strong>m\u00e9dia<\/strong><\/th>\n<th style=\"text-align: center\"><strong>SD<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: right\">altura<\/td>\n<td style=\"text-align: center\">14 polegadas<\/td>\n<td style=\"text-align: center\">2 polegadas<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: right\">peso<\/td>\n<td style=\"text-align: center\">50 libras<\/td>\n<td style=\"text-align: center\">5 libras<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Para calcular a equa\u00e7\u00e3o da linha de regress\u00e3o, precisamos da inclina\u00e7\u00e3o e do intercepto.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">inclinacao = <sup>(r \u22c5 SD de y)<\/sup>\u2044<sub>(SD de x)<\/sub> = <sup>(0.5 \u22c5 2 polegadas)<\/sup>\u2044<sub>5 libras<\/sub> = 0.2 polegadas por libra<\/div>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 1.6em\">intercepto = m\u00e9dia de y &#8211; inclinacao \u22c5 m\u00e9dia de x = 14 polegadas &#8211; 0.2 polegadas por libra \u22c5 50 libras = 4 polegadas<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A equa\u00e7\u00e3o da linha de regress\u00e3o nos permite calcular a altura estimada, em polegadas, com base em um peso dado em libras:<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;font-family: serif;font-size: 2.2em\">altura estimada = 0.2 \u22c5 peso dado + 4<\/div>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A inclina\u00e7\u00e3o da linha mede o aumento na altura estimada por unidade de aumento no peso. A inclina\u00e7\u00e3o \u00e9 positiva, e \u00e9 importante notar que isso n\u00e3o significa que achamos que os basset hounds ficam mais altos se ganharem peso. A inclina\u00e7\u00e3o reflete a diferen\u00e7a nas alturas m\u00e9dias de dois grupos de c\u00e3es que est\u00e3o a 1 libra de dist\u00e2ncia no peso. Especificamente, considere um grupo de c\u00e3es cujo peso seja w libras, e o grupo cujo peso seja w+1 libras. Estima-se que o segundo grupo seja em m\u00e9dia 0,2 polegadas mais alto. Isso \u00e9 verdade para todos os valores de w na amostra.<\/p>\n<p style=\"text-align: justify\">Em geral, a inclina\u00e7\u00e3o da linha de regress\u00e3o pode ser interpretada como o aumento m\u00e9dio em y por unidade de aumento em x. Note que se a inclina\u00e7\u00e3o for negativa, ent\u00e3o para cada unidade de aumento em x, a m\u00e9dia de y diminui.<\/p>\n<h2 id=\"nota-final\" style=\"text-align: justify\">Nota Final<\/h2>\n<p style=\"text-align: justify\">Mesmo que n\u00e3o estabele\u00e7amos a base matem\u00e1tica para a equa\u00e7\u00e3o de regress\u00e3o, podemos ver que ela fornece previs\u00f5es bastante boas quando o gr\u00e1fico de dispers\u00e3o tem a forma de uma bola de futebol. \u00c9 um fato matem\u00e1tico surpreendente que, independentemente da forma do gr\u00e1fico de dispers\u00e3o, a mesma equa\u00e7\u00e3o fornece o &#8220;melhor&#8221; entre todas as linhas retas. Esse \u00e9 o tema da pr\u00f3xima se\u00e7\u00e3o.<\/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\/15-1\/\">\u2190 Cap\u00edtulo 15.1 &#8211; Correla\u00e7\u00e3o<\/a><\/td>\n<td align=\"right\"><a class=\"next-page-link\" href=\"https:\/\/literaciadigital.ufms.br\/data8\/15-0\/15-3\/\">Cap\u00edtulo 15.3 &#8211; M\u00e9todo dos M\u00ednimos Quadrados \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-813","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/813","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=813"}],"version-history":[{"count":4,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/813\/revisions"}],"predecessor-version":[{"id":1074,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/pages\/813\/revisions\/1074"}],"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=813"}],"wp:term":[{"taxonomy":"author","embeddable":true,"href":"https:\/\/literaciadigital.ufms.br\/en\/wp-json\/wp\/v2\/coauthors?post=813"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}