This problem extends the home prices example used previously to 76 homes (Sec tion 6.1

This problem extends the home prices example used previously to 76 homes (Sec tion 6.1 contains a complete case study of these data). We wish to model the relationship between the price of a single-family home (Y, in $ thousands) and the following predictors:

X1 = floor size (thousands of square feet)

X 2 = lot size category (from l to I I-see page 78)

x 3 = number of bathrooms (with half-bathrooms counting as “0.1”)

Xi = number of bedrooms (between 2 and 6)

Xs = age (standardized: (year built – 1970)/ l 0)

X6 = garage size (0, l ,2, or 3 cars)

D 1 = indicator for “active listing” (reference: pending or sold)

D 8 = indicator for Edison Elementary (reference: Edgewood Elementary)

D 9 = indicator for Harris Elementary (reference: Edgewood Elementary)

Consider the following model, which includes an interaction between X3 and Xi:

E(Y ) = bo+b1X1 + biX2 +b3X3 +b4XJ +bsX3XJ

+ b s +h? X f +b s +b9D1 + b1oDs +b 1 1 D9 .

The regression results for this model are:

Predictor variable

Parameter estimate

1vo tail p-value

56.72

0.05

9.92

O.Ql

-98.16

0.02

-78.91

0.01

X3XJ

30.39

0.01

3.30

0.30 x2

l.64

0.03

13.12

0.12

27.42

0.02

67.06

o.oo

47.27

0.00

Test whether the relationship between home price (Y) and number of bathrooms (X3) depends on number of bedrooms (Xi), all else equal (significance level 5% ).

(b) Does the association between number of bathrooms and home price vary with number of bedrooms? We can investigate this by isolating the parts of the model involving just X3: the “X3 effect” is given by b3X3 + b5X3XJ = (bJ + bsXi )X3. For example, when Xi =2, this effect is estimated to be (-98.16+30.39(2))X3 =

-37.38X3. Thus, for two-bedroom homes, there is a negative relationship between number of bathrooms and home price (for each additional bathroom, price drops by $37,380, all else being equal-perhaps adding extra bathrooms to two-bedroom homes is considered a waste of space and so has a negative impact on price). Use a similar calculation to show the relationship between number of bathrooms and home price for three-bedroom homes, and also for four-bedroom homes.

Hint: Understanding the example on page 142 will help you solve this part.