Question

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

Answer 1

A. Increase by 2

Explanation:

Given that a fitted multiple regression equation is

`Y = 28 + 5X_1 -4X_2 + 7X_3 + 2X_4`

This is a multiple regression line with dependent variable y and independent variables x1, x2, x3 and x4

The coefficients of independent variables represent the slope.

In other words the coefficients represent the rate of change of y when xi is changed by 1 unit.

Given that x3 and x4 remain unchanged and x1 increases by 2 and x2 by 2 units

Since slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in y

i.e. for 2 units change in x1, we expect 10 units change in Y

Similarly for 2 units change in x2, we expect -2(4) units change in Y

Put together we have

`10-8 =2` change in y

Since positive 2, there is an increase by 2

A. Increase by 2