# Question

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 of a certain 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 the growing season and age of vintage. Data collected for the vintages of 1952 to 1980 were used. Three models were fit to the data. The results of the regressions are summarized in the table.

a. For each model, conduct a t -test for each of the b parameters in the model. Interpret the results.

b. When the natural logarithm of y is used as a dependent variable, the antilogarithm of a b coefficient minus 1 (i.e., eβi – 1) represents the percentage change in y for every one-unit increase in the associated x value. * Use this information to interpret the b estimates of each model.

c. On the basis of the values of R2 and s shown, which of the three models would you use to predict red Bordeaux wine prices? Explain.

a. For each model, conduct a t -test for each of the b parameters in the model. Interpret the results.

b. When the natural logarithm of y is used as a dependent variable, the antilogarithm of a b coefficient minus 1 (i.e., eβi – 1) represents the percentage change in y for every one-unit increase in the associated x value. * Use this information to interpret the b estimates of each model.

c. On the basis of the values of R2 and s shown, which of the three models would you use to predict red Bordeaux wine prices? Explain.

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