A fitted multiple regression equation is Y = 28 + 5X₁ - 4X₂ + 7X₃ + 2X₄. When X₁ increases 2 units and X₂ increases 2 units as well, while X₃ and X₄ remain unchanged, what change would you expect in your estimate of Y? A)Increase by 2 B)Decrease by 4 C)Increase by 4 D)No change in Y

Question

Quizplus · Accepted Answer

When $X_1$ increases by 2 units, the change in $Y$ due to $X_1$ is $2 \times 5 = 10$. When $X_2$ increases by 2 units, the change in $Y$ due to $X_2$ is $2 \times (-4) = -8$. The net change in $Y$ is $10 - 8 = 2$, indicating an increase by 2. $X_3$ and $X_4$ remain unchanged, so they do not contribute to the change in $Y$.

A Fitted Multiple Regression Equation Is Y = 28