In a multiple regression model $y ^ { \prime } = - 14 + 2 x _ { 2 } + 11 x _ { 2 } + 7 x _ { 3 } + 5 x _ { 4 }$ if the value of $\mathrm { X } _ { 2 }$ increases by 6 and the value of x3 decreases by 3, then the predicted value for y will
A) increase by 87
B) decrease by 87
C) increase by 45
D) decrease by 45

Question

Quizplus · Accepted Answer

We need to calculate the change in predicted value for y when x2 increases by 6 and x3 decreases by 3.

The new values for x2 and x3 will be:

x2 = original value + 6 = 2 + 6 = 8

x3 = original value - 3 = 7 - 3 = 4

Substituting these values in the multiple regression equation, we get:

y' = -14 + 2(8) + 11(8) + 7(4) + 5(x4)

y' = -14 + 16 + 88 + 28 + 5(x4)

y' = 118 + 5(x4)

Therefore, the predicted value for y increases by 45 units (since the coefficient for x4 is 5) when x2 increases by 6 and x3 decreases by 3. Hence, the correct answer is C.

In a Multiple Regression Model y′=−14+2x2+11x2+7x3+5x4y ^ { \prime } = - 14 + 2 x _ { 2 } + 11 x _ { 2 } + 7 x _ { 3 } + 5 x _ { 4 }y′=−14+2x2​+11x2​+7x3​+5x4​

In a Multiple Regression Model $y ^ { \prime } = - 14 + 2 x _ { 2 } + 11 x _ { 2 } + 7 x _ { 3 } + 5 x _ { 4 }$