Chapter 12, Problem 12.171ACI

State casket sales restrictions Refer to the Journal of Law and Economics (February 2008) study of the impact of lifting casket sales restrictions on the cost of a funeral, Exercise 12.123 (p. 779). Recall that data collected for a sample of 1,437 funerals were used to fit the model, E (y) = 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:

     $\begin{array}{l}\hat{y}=1,432+793x_1-252x_2+261x_1{x}_2,R^2=.78\\ (70)(134)(109)\end{array}$

(70)(134)(109)

1. a. Interpret the reported value of R².
2. b. Use the value of R² to compute the F-statistic for testing the overall adequacy of the model. Test at α = .05.
3. c. Compute the predicted price of a direct burial with a basic wooden casket for a funeral home in a restrictive state.
4. 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.
5. 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.
6. 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.