Consider the following multiple linear regression models with the associated RSS
ID: 3289847 • Letter: C
Question
Consider the following multiple linear regression models with the associated RSS. (a) Suppose that you want to test the null hypothesis that X_4 has no effect on Y. You have a sample size of 65. Conduct a test at the 5% level. Write down the null and alternative hypothesis, the test statistic, the degrees of freedom, the critical value, and the result of the test. (b) Suppose that you want to test the null hypothesis that X_2, X_3, and X_4 don't have an effect on Y. You have a sample size of 65. Conduct a test at the 5% level. Write down the null and alternative hypothesis, the test statistic, the degrees of freedom, the critical value, and the result of the test.Explanation / Answer
a) Reduced model - B
Unreduced model - A
TS =((SSR_r - SSR_ur)/q)/(SSR_ur)/(n-k-1))
= ((355 - 320)/1) /(320/(65 -4-1)
=6.5625
df1 = q = 1
df2 = n-k-1= 65 -4-1 = 60
critical value = 4
since TS > critical value ,we reject the null and conclude that X4 is significant
b) here q= 3
reduced model - D
Unreduced model - A
TS =((SSR_r - SSR_ur)/q)/(SSR_ur)/(n-k-1))
= ((410- 320)/3) /(320/(65 -4-1) =5.625
df1 = 3 ,df2 = 60
hence critical value = 2.77
since TS >critical value ,the variables are jointly significant
Please rate my solution