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 male individual is
A)$13.80
B)$13,800
C)$46,800
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 male individual is
A)$13.80 
B)$13,800 
C)$46,800 
D)$49,800

Quizplus · Accepted Answer

We can use the estimated regression model to estimate the yearly income of a 24-year-old male individual as follows:
Y = b0 + b1*X1 + b2*X2
where Y is the dependent variable (yearly income in $1,000s), X1 is the age of the individual, X2 is the gender (0 if male), and b0, b1, and b2 are the estimated regression coefficients.

Substituting X1 = 24 and X2 = 0 into the regression model, we get:
Y = -8.4 + 0.32*24 + 1.8*0
Y = -8.4 + 7.68
Y = -0.72

This estimate does not make sense because it is negative. This suggests that the estimated regression model may not be a good fit for the data, or that the relationship between income, age, and gender is not accurately captured by the model.

Alternatively, we can use the SST and SSE values to calculate the coefficient of determination (R-squared) as follows:
R-squared = 1 - SSE/SST
R-squared = 1 - 384/1200
R-squared = 0.68

This suggests that the model explains 68% of the total variation in income, and 32% of the variation is unexplained. However, we cannot use this information to estimate the income of a specific individual.

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