In a multiple regression model y' = -11 + 4x₁ + 11x₂ + 7x₃ + 3x₄, if the value of x₂ increases by 2 and the value of x₃ decreases by 5, then the predicted value for y will A) decrease by 57. B) increase by 57. C) decrease by 13. D) increase by 13.

Question

Quizplus · Accepted Answer

If x₂ increases by 2 and x₃ decreases by 5, then the new coefficients will be 11+2=13 for x₂ and 7-5=2 for x₃. Plugging these new coefficients into the original equation: y' = -11 + 4x₁ + 13x₂ + 2x₃ + 3x₄ Now we can see that the coefficient for x₃ has decreased by 5, which means that its effect on y will also decrease. Thus, the predicted value for y will decrease by 2*(-5) = -10. Therefore, the answer is (C) decrease by 13.

In a Multiple Regression Model Y' = -11 + 4x1

In a Multiple Regression Model Y' = -11 + 4x₁