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 yearly income of a 24-year-old female individual is
A)$19.80
B)$19,800
C)$49.80
D)$49,800

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 yearly income of a 24-year-old female individual is
A)$19.80 
B)$19,800 
C)$49.80 
D)$49,800

Quizplus · Accepted Answer

The regression model is Y = b0 + b1X1 + b2X2, where X1 is age and X2 is gender (0 for male and 1 for female). From the model, we can see that the coefficient b1 represents the change in yearly income associated with a one-year increase in age, while the coefficient b2 represents the difference in yearly income between females and males, holding age constant.

To predict the yearly income of a 24-year-old female individual, we plug in X1 = 24 and X2 = 1 into the regression model: Y = b0 + b1(24) + b2(1) = 16.80 + 0.50(24) + 2.50(1) = 19.80.

However, note that the question asks for the yearly income in thousands of dollars, so the answer is $19,800 (option D).

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