Question: A real state agent hypothesizes that in her own town the selling price of a house in dollars (y) depends on its size in square feet of floor space (x1), the lot size in square feet (x2), the number of bedrooms (x3), and the number of bathrooms (x4). For a random sample of 20 house sales the following least squares estimated model was obtained:

yˆ ?1998.5?22.352x1 ?1.4686x2 ?6767.3x3 ?2710.1x4

(2.5543) (1.4492) (1820.8) (1996.2)

The numbers in parentheses under the coefficients are the estimated coefficient standard errors. R2 = 0.9843.

a) Interpret in the context of this model the estimated coefficient on x2.

b) Interpret the coefficient of determination.

c) Assuming that the model is correctly specified, test at the 5% level against the appropriate one-sided alternative the null hypothesis that, all else being equal, selling price does not depend on number of bathrooms.

d) Estimate the selling price of a house with 1,250 square feet of floor space, a lot of 4,500 square feet, 3 bedrooms, and 1 bathroom.