The file cocaine contains 56 observations on variables related to sales of cocaine powder in northeastern California over the period 1984-1991. The data are a subset of those used in the study Caulkins, J. P. and R. Padman (1993), "Quantity Discounts and Quality Premia for Illicit Drugs," Journal of the American Statistical Association, 88, 748-757. The variables are

a. What signs would you expect on the coefficients \(\beta_{2}, \beta_{3}\), and \(\beta_{4}\) ?

b. Use your computer software to estimate the equation. Report the results and interpret the coefficient estimates. Have the signs turned out as you expected?

c. What proportion of variation in cocaine price is explained jointly by variation in quantity, quality, and time?

d. It is claimed that the greater the number of sales, the higher the risk of getting caught. Thus, sellers are willing to accept a lower price if they can make sales in larger quantities. Set up \(H_{0}\) and \(H_{1}\) that would be appropriate to test this hypothesis. Carry out the hypothesis test.

e. Test the hypothesis that the quality of cocaine has no influence on expected price against the alternative that a premium is paid for better-quality cocaine.

f. What is the average annual change in the cocaine price? Can you suggest why price might be changing in this direction?

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PRICE = price per gram in dollars for a cocaine sale QUANT = number of grams of cocaine in a given sale QUAL=quality of the cocaine expressed as percentage purity TREND = a time variable with 1984 = 1 up to 1991 = 8 Consider the regression model