A multiple regression model involves 40 observations and 4 independent variables and produces SST = 2000 and SSR = 1608. The value of MSE is 11.2.

Question

Quizplus · Accepted Answer

Since MSE = SSR/(n-p) where n is the number of observations and p is the number of independent variables plus the intercept term, we can solve for n and p as follows:

11.2 = 1608/(n-4) 
11.2(n-4) = 1608 
n-4 = 143.57 
n = 147.57

Now we can solve for the degrees of freedom for error (dfE) and the degrees of freedom for regression (dfR):

dfE = n-p = 143 
dfR = p-1 = 3

Using these values, we can calculate the F-statistic as follows:

F = MSR/MSE = (SST-SSR)/(p-1) / MSE = (2000-1608)/3 / 11.2 = 10.36

Looking at an F-distribution table with 3 and 143 degrees of freedom, we can see that the critical value for a 5% significance level is 2.75. Since our calculated F-statistic is greater than this critical value, we reject the null hypothesis that all the regression coefficients are equal to zero and conclude that at least one of the independent variables is a significant predictor of the dependent variable. Therefore, the statement is true.

A Multiple Regression Model Involves 40 Observations and 4 Independent