12.32 In a study of revenue generated by national lotteries, the following regression equation was fitted to data from 29 countries with lotteries:

y = -31.323 + 0.4045x1 10.007552

+ 0.8772x2 10.31072

- 365.01x3 1263.882

- 9.9298x4 13.45202 R2 = .51 where y = dollars of net revenue per capita per year generated by the lottery x1 = mean per capita personal income of the country x2 = number of hotel, motel, inn, and resort rooms per thousand persons in the country x3 = spendable revenue per capita per year generated by pari-mutuel betting, racing, and other legalized gambling x4 = percentage of the nation’s border contiguous with a state or states with a lottery The numbers in parentheses under the coefficients are the estimated coefficient standard errors.

a. Interpret the estimated coefficient on x1.

b. Find and interpret a 95% confidence interval for the coefficient on x2 in the population regression.

c. Test the null hypothesis that the coefficient on x3 in the population regression is 0 against the alternative that this coefficient is negative. Interpret your findings.