Question

 Comparable number of bedrooms and house size effects Given the, the prediction equation between y = selling price and x1 = house size and x2 = number of bedrooms was yn = 60,102 + 63.0x1 + 15,170x2.

a. For fixed number of bedrooms, how much is the house selling price predicted to increase for each square foot increase in house size? Why?

b. For a fixed house size of 2000 square feet, how does the predicted selling price change for two, three, and

four bedrooms?

Answer 1

(a) $y(x_1, x_2) = 60102 + 63x_1 + 15170x_2$

$y(x_1+1, x_2) - y(x_1, x_2) = (60102 + 63(x_1+1) + 15170x_2)- (60102 + 63x_1 + 15170x_2)=63$

Therefore, the house selling price predicted to increase by 63.0 for each square foot increase in house size.

(Another way: $\frac{\partial}{\partial x_1}y(x_1, x_2) = \frac{\partial}{\partial x_1}(60102 + 63x_1 + 15170x_2)=63)$

Answer: 63 per square foot

(b) $y(2000,2) = 60102 + 63\cdot 2000 + 15170\cdot 2= 216442$

The house selling price predicted to increase by 15170 for each additional bedroom, therefore:

$y(2000,3) = y(2000,2)+15170= 216442+15170=231612$

$y(2000,4) = y(2000,3)+15170=231612+15170=246782$

Answer: 216,442 (with 2 bedrooms in a house), 231,612 (with 3 bedrooms in a house), 246,782(with 4 bedrooms in a house).