Exhibit 13-8
The following estimated regression model was developed relating yearly income Y in $1,000s) of 30 individuals with their age X1) and their gender X2) 0 if male and 1 if female).
$\hat { Y }$ =30+0.7X1+3X2
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. 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 13-8
The following estimated regression model was developed relating yearly income Y in $1,000s) of 30 individuals with their age X1) and their gender X2) 0 if male and 1 if female).
 $\hat { Y }$ =30+0.7X1+3X2
Also provided are SST = 1,200 and SSE = 384.
-Refer to Exhibit 13-8. 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 the F-test. The F-statistic is calculated using the formula: F = (SST - SSE) / (k) / (SSE / (n - k - 1)), where k is the number of predictors and n is the sample size. Here, SST = 1200, SSE = 384, k = 2, and n = 30. The F-statistic is significant if it is greater than the critical value from the F-distribution table for the given degrees of freedom. Given the large difference between SST and SSE, the model is likely significant.

Exhibit 13-8 the Following Estimated Regression Model Was Developed Relating Y^\hat { Y }Y^

Exhibit 13-8
the Following Estimated Regression Model Was Developed Relating $\hat { Y }$