The uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some 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). 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. 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. Consider the multiple regression results for hypothetical data collected for 30 vintages (years) shown below.

a. Conduct a t-test (at α = .05) for each of the b parameters in the model. Interpret the results.

b. When the natural log of y is used as a dependent variable, the antilogarithm of a 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 each of the β estimates.

c. Interpret the values of R2 and s. Do you recommend using the model for predicting Bordeaux wine prices? Explain.

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Independent Variables x1 = Vintage year Beta Estimate Standard Error .03 .60 .006 .120 .001 .0005 x2 = Average growing season temperature(°C) Sept./Aug. rainfall (cm) Rainfall in months preceding vintage (cm) -.004 .0015 .008 x5 = Average Sept. temperature (°C) 550 R² = .85 s = .30