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 multiple coefficient of determination is
A)0.32
B)0.42
C)0.68
D)0.50

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 multiple coefficient of determination is
A)0.32 
B)0.42 
C)0.68 
D)0.50

Quizplus · Accepted Answer

The multiple coefficient of determination is calculated as:

R-squared = 1 - (SSE / SST)
R-squared = 1 - (384 / 1200)
R-squared = 0.68

Therefore, the best choice is C, which corresponds to an R-squared value of 0.68. This means that 68% of the variability in yearly income can be explained by age and gender.

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