{"id":3904,"date":"2023-07-14T20:50:46","date_gmt":"2023-07-14T20:50:46","guid":{"rendered":"https:\/\/statorials.org\/pt\/hipotese-linear-r\/"},"modified":"2023-07-14T20:50:46","modified_gmt":"2023-07-14T20:50:46","slug":"hipotese-linear-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/hipotese-linear-r\/","title":{"rendered":"Como usar a fun\u00e7\u00e3o linearhypothesis() em r"},"content":{"rendered":"

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Voc\u00ea pode usar a fun\u00e7\u00e3o LinearHypothesis()<\/strong> do pacote car<\/strong> em R para testar hip\u00f3teses lineares em um modelo de regress\u00e3o espec\u00edfico.<\/span><\/p>\n

Esta fun\u00e7\u00e3o usa a seguinte sintaxe b\u00e1sica:<\/span><\/p>\n

 linearHypothesis(fit, c(\" var1=0<\/span> \", \" var2=0<\/span> \"))<\/strong><\/pre>\n
 Este exemplo espec\u00edfico testa se os coeficientes de regress\u00e3o var1<\/strong> e var2<\/strong> no modelo denominado ajuste<\/strong> s\u00e3o conjuntamente iguais a zero.<\/span><\/p>\n
 O exemplo a seguir mostra como usar esta fun\u00e7\u00e3o na pr\u00e1tica.<\/span><\/p>\n
 Exemplo: como usar a fun\u00e7\u00e3o LinearHypothesis() em R<\/strong><\/span><\/h2>\n
 Suponha que temos o seguinte quadro de dados em R que mostra o n\u00famero de horas gastas estudando, o n\u00famero de exames pr\u00e1ticos realizados e a nota do exame final de 10 alunos em uma turma:<\/span><\/p>\n
 #create data frame\n<\/span>df <- data.frame(score=c(77, 79, 84, 85, 88, 99, 95, 90, 92, 94),\n                 hours=c(1, 1, 2, 3, 2, 4, 4, 2, 3, 3),\n                 prac_exams=c(2, 4, 4, 2, 4, 5, 4, 3, 2, 1))\n\n#view data frame\n<\/span>df\n\n   score hours prac_exams\n1 77 1 2\n2 79 1 4\n3 84 2 4\n4 85 3 2\n5 88 2 4\n6 99 4 5\n7 95 4 4\n8 90 2 3\n9 92 3 2\n10 94 3 1\n<\/strong><\/pre>\n
 Agora suponha que queiramos ajustar o seguinte modelo de regress\u00e3o linear m\u00faltipla em R:<\/span><\/p>\n
 Nota do exame = \u03b2 0<\/sub> + \u03b2 1<\/sub> (horas) + \u03b2 2<\/sub> (exames pr\u00e1ticos)<\/span><\/p>\n
 Podemos usar a fun\u00e7\u00e3o lm()<\/a> para adaptar este modelo:<\/span><\/p>\n
 #fit multiple linear regression model\n<\/span>fit <- lm(score ~ hours + prac_exams, data=df)\n\n#view summary of model\n<\/span>summary(fit)\n\nCall:\nlm(formula = score ~ hours + prac_exams, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-5.8366 -2.0875 0.1381 2.0652 4.6381 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 72.7393 3.9455 18.436 3.42e-07 ***\nhours 5.8093 1.1161 5.205 0.00125 ** \nprac_exams 0.3346 0.9369 0.357 0.73150    \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.59 on 7 degrees of freedom\nMultiple R-squared: 0.8004, Adjusted R-squared: 0.7434 \nF-statistic: 14.03 on 2 and 7 DF, p-value: 0.003553\n<\/strong><\/pre>\n
 Agora, suponha que queiramos testar se o coeficiente de horas<\/strong> e prac_exams<\/strong> s\u00e3o ambos zero.<\/span><\/p>\n
 Podemos usar a fun\u00e7\u00e3o LinearHypothesis()<\/strong> para fazer isso:<\/span><\/p>\n
 library<\/span> (car)\n\n#perform hypothesis test for hours=0 and prac_exams=0\n<\/span>linearHypothesis(fit, c(\" hours=0<\/span> \", \" prac_exams=0<\/span> \"))\n\nLinear hypothesis testing\n\nHypothesis:\nhours = 0\nprac_exams = 0\n\nModel 1: restricted model\nModel 2: score ~ hours + prac_exams\n\n  Res.Df RSS Df Sum of Sq F Pr(>F)   \n1 9 452.10                                \n2 7 90.24 2 361.86 14.035 0.003553 **\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n
 O teste de hip\u00f3tese retorna os seguintes valores:<\/span><\/p>\n