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). = 30 + 0.7x 1 + 3x 2
Also provided are SST = 1,200 and SSE = 384.
-In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see
A)a horizontal band of points centered near zero
B)a widening band of points
C)a band of points having a slope consistent with that of the regression equation
D)a parabolic band of points

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).  = 30 + 0.7x 1 + 3x 2 
Also provided are SST = 1,200 and SSE = 384.
-In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see
A)a horizontal band of points centered near zero 
B)a widening band of points 
C)a band of points having a slope consistent with that of the regression equation 
D)a parabolic band of points

Quizplus · Accepted Answer

In a residual plot that does not suggest we should challenge the assumptions of our regression model, we would expect to see a horizontal band of points centered near zero. This indicates that the residuals are randomly scattered around zero and have constant variance, which is a key assumption of linear regression. Choices B, C, and D suggest patterns in the residuals that would indicate violations of the assumptions of linear regression.

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