Bordeaux wine sold at auction. The vineyards in the

QUESTION:

Problem 23E

Bordeaux wine sold at auction. The vineyards in the Bordeaux region of France are known for producing excellent red wines. However, the uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some Bordeaux vineyards produce better wines than others encourage speculation concerning the value of a case of wine produced by a certain vineyard during a certain year (or vintage). As a result, many wine experts attempt to predict the auction price of a case of Bordeaux wine. The publishers of a newsletter titled Liquid Assets: The International Guide to Fine Wine discussed a multiple regression approach to predicting the London auction price of red Bordeaux wine in Chance (Fall 1995). The natural logarithm of the price y (in dollars) of a case containing a dozen bottles of red wine was modeled as a function of weather during growing season and age of vintage using data collected for the vintages of 1952–1980. Three models were fit to the data. The results of the regressions are summarized in the table on the next page.

a. For each model, conduct a t-test (at α = .05) for each of the β parameters in the model. Interpret the results.

b. When the natural log of y is used as a dependent variable, the antilogarithm of α β coefficient minus 1—that is eβi - 1 - represents the percentage change in y for every 1-unit increase in the associated x value. Use this information to interpret the b estimates of each model.

c. Based on the values of R2 and s, which of the three models would you recommend for predicting Bordeaux wine prices? Explain.