Recall that data collected for a sample of 1,437 funerals were used to fit the model, E(y) = β0 + β1x1 + β2x2 + β3x1x2, where y is the price (in dollars) of a direct burial, x1= {1 if funeral home is in a restricted state, 0 if not), and x2 = {1 if price includes a basic wooden casket, 0 if no casket}. The estimated equation (with standard errors in parentheses) is:
y = 1,432 + 793x1 - 252x2 + 261x1x2, R2 = -78
(70) (134) (109)
a. Interpret the reported value of R2.
b. Use the value of R2 to compute the F-statistic for testing the overall adequacy of the model. Test at α = .05.
c. Compute the predicted price of a direct burial with a basic wooden casket for a funeral home in a restrictive state.
d. Estimate the difference between the mean price of a direct burial with a basic wooden casket and the mean price of a burial with no casket for a funeral home in a restrictive state.
e. Estimate the difference between the mean price of a direct burial with a basic wooden casket and the mean price of a burial with no casket for a funeral home in a nonrestrictive state.
f. Is there sufficient evidence to indicate that the difference between the mean price of a direct burial with a basic wooden casket and the mean price of a burial with no casket depends on whether the funeral home is in a restrictive state? Test using α=.05.
For Information: Refer to the Journal of Law and Economics (Feb. 2008) study of the impact of lifting casket sales restrictions on the cost of a funeral. Exercise 12.121.