Question

For the multiple regression model Y with hat on top equals 40 plus 15 X subscript 1 minus 10 X subscript 2 plus 5 X subscript 3, if X subscript 1 and X subscript 2 were to decrease by 4 units, holding X subscript 3 constant, the value of Y would be expected to

Answer 1

Answer:

When x1 and x2 decrease 4 units, y decreases by 20 units

Step-by-step explanation:

The regression model is

$y=40+15x_1-10x_2+5x_3$

We have to calculate y for a decrease of 4 units in x1 and x2. For this we have to calculate the variation of y in function of x1 and x2.

As it is a linear regression model, we have:

$\Delta y=15\Delta x_1-10\Delta x_2$

For a variation in 4 units of x1 and x2, we have

$\Delta y=15\Delta x_1-10\Delta x_2\\\\\Delta y=15(-4)-10(-4)=-60+40=-20$