Suppose that you estimate a model of house prices to determine the impact of having beach frontage on the value of a house. You do some research, and you decide to use the size of the lot instead of the size of the house for a number of theoretical and data availability reasons. Your results (standard errors in parentheses) are:

Where:

PRICE_i = the price of the ith house (in thousands of dollars)

LOT_i = the size of the lot of the ith house (in thousands of square feet)

AGE_i = the age of the ith house in years

BED_i = the number of bedrooms in the ith house

FIRE_i = a dummy variable for a fireplace (1 = yes for the ith house)

BEACH_i = a dummy for having beach frontage (1 = yes for the ith house)

a. You expect the variables LOT, BED, and BEACH to have positive coefficients. Create and test the appropriate hypotheses to evaluate these expectations at the 5-percent level.

b. You expect AGE to have a negative coefficient. Create and test the appropriate hypotheses to evaluate these expectations at the 10-percent level.

c. At first you expect FIRE to have a positive coefficient, but one of your friends says that fireplaces are messy and are a pain to keep clean, so you’re not sure. Run a two-sided t-test around zero to test these expectations at the 5-percent level.

d. What problems appear to exist in your equation?

e. Which of the problems that you outlined in part d is the most worrisome? Explain your answer.

f. What explanation or solution can you think of for this problem?