Question

House price y is estimated as a function of the square footage of a house x; a dummy variable d that equals 1 if the house has ocean views and 0 otherwise; and the interaction variable xd. The estimated house price, measured in $1,000s, is given by yˆy^ = 80 + 0.12x + 40d + 0.01xd.

a. Compute the predicted price of a house with ocean views and square footage of 2,000 and 3,000, respectively. (Enter your answers in thousands.)

b. Compute the predicted price of a house without ocean views and square footage of 2,000 and 3,000, respectively. (Enter your answers in thousands.)

Answer 1

(A) Regression equation is y = 80 + 0.12x + 40d + 0.01xd

setting x = 2000 and d = 1 because it is with ocean views

y = 80 + 0.12x + 40d + 0.01xd

= 80 + (0.12*2000) + (40*1) + (0.01*2000*1)

= 80+240 + 40 +20

= 380 (in $1000s)

And with square footage 3000

setting x = 3000 and d = 1 because it is with ocean views

y = 80 + 0.12x + 40d + 0.01xd

= 80 + (0.12*3000) + (40*1) + (0.01*3000*1)

= 80+360 + 40 +30

= 510 (in $1000s)

(B) Regression equation is y = 80 + 0.12x + 40d + 0.01xd

setting x = 2000 and d = 0 because it is without ocean views

y = 80 + 0.12x + 40d + 0.01xd

= 80 + (0.12*2000) + (40*0) + (0.01*2000*0)

= 80+240 + 0 +0

= 320 (in $1000s)

And with square footage 3000

setting x = 3000 and d = 0 because it is without ocean views

y = 80 + 0.12x + 40d + 0.01xd

= 80 + (0.12*3000) + (40*0) + (0.01*3000*0)

= 80+360 + 0 +0

= 440 (in $1000s)