A real estate economist collects information on 1000 house price sales from two

Question

A real estate economist collects information on 1000 house price sales from two similar neighborhoods: University Towns, which borders a large state university and University Far Town which is about three miles from the state university.

PRICE: house price in $1,000
SQRT: number of hundreds of square feet of living space
AGE: house age in years
UTOWN (binary variable): location of homes
1 = for homes near the university
0 = otherwise
POOL (binary variable): whether or not house has a pool
1 = if pool is present
0 = otherwise
FPLACE (binary variable): whether or not house has a fireplace
1 = if house has a fireplace
0 = otherwise
The economist specifies the regression equation as:
PRICE = ?0 + ?1UTOWN + ?2SQRT + ?3(SQRT*UTOWN) + ?4AGE + ?5POOL + ?6FPLACE + u
The estimated regression function for houses are
^price= 24.5 + 27.5UTOWN + 7.6SQRT + 1.3(SQRT*UTOWN) - 0.19AGE + 4.4POOL + 1.6FPLACE
a. What is the estimated regression function for houses near the university?
b. What is the estimated regression function for houses in other areas?
c. Interpret the UTOWN coefficient, i.e., the location premium for houses near the university (Hint: price is in $1,000)?
d. By how much do all houses depreciate by per year?
e. By how much does a pool increase the value of a home?

Explanation / Answer

^price= 24.5 + 27.5UTOWN + 7.6SQRT + 1.3(SQRT*UTOWN) - 0.19AGE + 4.4POOL + 1.6FPLACE

a)  regression function for houses near the university = 24.5 + 27.5*1 + 7.6SQRT + 1.3(SQRT*1) - 0.19AGE + 4.4POOL + 1.6FPLACE

= 52+ 8.9SQRT - 0.19AGE + 4.4POOL + 1.6FPLACE

b)  regression function for houses in other areas =

24.5 + 27.5*0 + 7.6SQRT + 1.3(SQRT*0) - 0.19AGE + 4.4POOL + 1.6FPLACE

= 24.5+ 7.6SQRT - 0.19AGE + 4.4POOL + 1.6FPLACE

c)  UTOWN is positively correalted to price.

difference between houses near the university and far from university = 52+ 8.9SQRT - 0.19AGE + 4.4POOL + 1.6FPLACE - (24.5+ 7.6SQRT - 0.19AGE + 4.4POOL + 1.6FPLACE)

= 27.5 +1.3SQRT

UTOWN has an interaction effect with SQRT.If house is near university, the SQRT has higher effect on price

d. ^price= 24.5 + 27.5UTOWN + 7.6SQRT + 1.3(SQRT*UTOWN) - 0.19AGE + 4.4POOL + 1.6FPLACE

dPrice/dAge =  - 0.19

all houses depreciate by $0.19 per year

e. pool increase the value of a home by $4.4

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