Exhibit 15-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X 1 ) and their gender (X 2 ) (0 if male and 1 if female). Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The model
A)is significant
B)is not significant
C)would be significant is the sample size was larger than 30
D)None of these alternatives is correct.

Question

Exhibit 15-8
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age (X 1 ) and their gender (X 2 ) (0 if male and 1 if female).  Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 15-8. The model
A)is significant 
B)is not significant 
C)would be significant is the sample size was larger than 30 
D)None of these alternatives is correct.

Quizplus · Accepted Answer

The significance of the model can be determined by performing an F-test, where the null hypothesis is that all regression coefficients are equal to zero (i.e. the model has no predictive power). The F-statistic can be calculated as (SSR/K) / (SSE/(n-K-1)), where SSR is the sum of squared errors due to regression (the difference between the predicted values and the mean of Y), K is the number of independent variables, and n is the sample size. In this case, SSR = SST - SSE = 1200 - 384 = 816, K = 2, and n = 30. Plugging these values into the formula gives an F-statistic of 20.4, which is greater than the critical value at the 5% level of significance for a model with 2 degrees of freedom in the numerator and 27 degrees of freedom in the denominator (3.33). Therefore, we reject the null hypothesis and conclude that the model is significant.

Exhibit 15-8 The Following Estimated Regression Model Was Developed Relating Yearly Income