# Question

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

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.

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.

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