Exhibit 15-2
A regression model between sales (Y in $1,000), unit price (X 1 in dollars) and television advertisement (X 2 in dollars) resulted in the following function: For this model SSR = 3500, SSE = 1500, and the sample size is 18.
-Refer to Exhibit 15-2. To test for the significance of the model, the p-value is
A)less than 0.01
B)between 0.01 and 0.025
C)between 0.025 and 0.05
D)between 0.05 and 0.10

Question

Exhibit 15-2
A regression model between sales (Y in $1,000), unit price (X 1 in dollars) and television advertisement (X 2 in dollars) resulted in the following function:  For this model SSR = 3500, SSE = 1500, and the sample size is 18.
-Refer to Exhibit 15-2. To test for the significance of the model, the p-value is
A)less than 0.01 
B)between 0.01 and 0.025 
C)between 0.025 and 0.05 
D)between 0.05 and 0.10

Quizplus · Accepted Answer

To test for the significance of the model, we need to perform an F-test with the null hypothesis being that all regression coefficients are zero (i.e. the model is not significant) and the alternative hypothesis being that at least one coefficient is non-zero (i.e. the model is significant). The p-value for this F-test is less than 0.01, as SSR/SSE = 2.33 and F(2, 15) = 4.64, which exceeds the critical F-value of 3.68 at alpha = 0.01. Therefore, we reject the null hypothesis and conclude that the model is significant.

Exhibit 15-2 A Regression Model Between Sales (Y in $1,000), Unit Price