Suppose that the sample regression equation of a model is $ = 10 + 4 x _ { 1 } + 3 x _ { 2 } - x _ { 1 } x _ { 2 }$ . If we examine the relationship between $x _ { 1 }$ and y for three different values of $x _ { 2 }$ , we observe that the:
A) three equations produced differ only in the intercept.
B) coefficient of $x _ { 2 }$ remains unchanged.
C) coefficient of $x _ { 1 }$ varies.
D) three equations produced differ not only in the intercept term but the coefficient of $x _ { 1 }$ , also varies.

Question

Suppose that the sample regression equation of a model is $ = 10 + 4 x _ { 1 } + 3 x _ { 2 } - x _ { 1 } x _ { 2 }$ . If we examine the relationship between $x _ { 1 }$ and y for three different values of $x _ { 2 }$ , we observe that the:
A) three equations produced differ only in the intercept. 
B) coefficient of $x _ { 2 }$ remains unchanged. 
C) coefficient of $x _ { 1 }$ varies. 
D) three equations produced differ not only in the intercept term but the coefficient of $x _ { 1 }$ , also varies.

Quizplus · Accepted Answer

The sample regression equation suggests that there is a linear relationship between y and the variables included in the model. If the coefficient of $x _ { 1 }$ varies when examining the relationship for different values of $x _ { 2 }$, this means that the slope of the regression line is changing. Therefore, the three equations produced differ not only in the intercept term but also in the coefficient of $x _ { 1 }$.

Suppose That the Sample Regression Equation of a Model Is =10+4x1+3x2−x1x2 = 10 + 4 x _ { 1 } + 3 x _ { 2 } - x _ { 1 } x _ { 2 }=10+4x1​+3x2​−x1​x2​

Suppose That the Sample Regression Equation of a Model Is $= 10 + 4 x _ { 1 } + 3 x _ { 2 } - x _ { 1 } x _ { 2 }$