Problem 4.5: This problem extends the home prices example used previously to 76

homes (Section 6.1 contains a complete case study of these data). We wish to

model the association between the price of a single-family home (Price in $

thousands) and the following predictors:

Floor = floor size (thousands of square feet)

Lot = lot size category (from 1 to 11see page 89)

Bath = number of bathrooms (with half-bathrooms counting as "0.1")

Bed = number of bedrooms (between 2 and 6)

Age = age (standardized: (year built 1970)/10)

Gar = garage size (0, 1, 2, or 3 cars)

DAc = indicator for "active listing" (rather than pending or sold)

DEd = indicator for proximity to Edison Elementary

DHa = indicator for proximity to Harris Elementary

Consider the following model, which includes an interaction between Bath and Bed:

E(Price) = b0 + b1Floor + b2Lot + b3Bath + b4Bed + b5BathBed + b6Age + b7Age2

+ b8Gar + b9DAc + b10DEd + b11DHa.

The regression results for this model are:

________________________________________

Predictor Parameter Two tail

variable estimate p-value

_________________________________________

Intercept 332.47 0.00

Floor 56.72 0.05

Lot 9.92 0.01

Bath -98.15 0.02

Bed -78.91 0.01

BathBed 30.39 0.01

Age 3.30 0.30

Age2

1.64 0.03

Gar 13.12 0.12

DAc 27.43 0.02

DEd 67.06 0.00

DHa 47.27 0.00

_________________________________________

Hint: Understanding the SALES1 example beginning on page 159 will help

you solve this problem.

a. Test whether the linear association between home price (Price) and number

of bathrooms (Bath) depends on number of bedrooms (Bed), all else equal

(use significance level 5%).

b. Does the linear association between Price and Bath vary with Bed? We can

investigate this by isolating the part of the model involving just Bath: the

"Bath effect" on Price is given by b3Bath + b5BathBed = (b3 + b5Bed)Bath.

For example, when Bed = 2, this effect is estimated to be (98.15 +

30.39(2))Bath = 37.37Bath. Thus, for two-bedroom homes, there is a

negative linear association between home price and number of bathrooms

(for each additional bathroom, the sale price drops by $37,370, all else

being equalperhaps adding extra bathrooms to two-bedroom homes is

considered a waste of space and so has a negative impact on price). Use

similar calculations to show the linear association between Price and Bath

for three-bedroom homes, and also for four-bedroom homes.