12.47 A real estate agent hypothesizes that in her town the selling price of a house in dollars (y) depends on its size in square feet of floor space 1x12, the lot size in square feet 1x22, the number of bedrooms 1x32, and the number of bathrooms 1x42. For a random sample of 20 house sales, the following least squares estimated model was obtained:

yn = 1998.5 + 22.352x1 + 1.4686x2 + 6767.3x3 + 2701.1x4 12.55432 11.44922 11820.82 11996.22 R2 = 0.9843 The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

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 onesided 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 4,700 square feet, 3 bedrooms, and 1 bathroom.