For the multiple regression model $\hat { y }$ = 75 + 25x1 - 15 x2 + 10 x3, if $x _ { 2 }$ were to increase by 5, holding $x _ { 1 }$ and $x _ { 3 }$ constant, the value of y would:
A)increase by 5.
B)increase by 75.
C)decrease on average by 5.
D)decrease on average by 75.

Question

Quizplus · Accepted Answer

Given the model, a 5 unit increase in $x_2$ (while holding $x_1$ and $x_3$ constant) would result in a decrease in $\hat{y}$ because the coefficient for $x_2$ is -15. Thus, a 5 unit increase in $x_2$ would lead to a decrease of $5 \times -15 = -75$ in the predicted value of $y$.

For the Multiple Regression Model y^\hat { y }y^​ = 75 + 25x1 - 15 X2 + 10 X3

For the Multiple Regression Model $\hat { y }$ = 75 + 25x1 - 15 X2 + 10 X3