Bordeaux wine sold at auction. 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 of a certain vintage). The publishers of a newsletter titled Liquid Assets: The International Guide to Fine Wine used 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 the growing season and age of vintage. Consider the multiple regression results for hypothetical data collected for 30 vintages (years) shown at the bottom of the page.

a. Conduct a t-test for each of the beta parameters in the model. Interpret the results.

b. When the natural logarithm of y is used as a dependent variable, the antilogarithm of a beta coefficient minus 1 (i.e., eb - 1) represents the percentage change in y for every one-unit increase in the associated x value.*

Use this information to interpret each of the beta estimates.

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

Independent Variable Beta Estimate Standard Error x1 = Vintage year .03 .006 x2 = Average growing-season temperature (°C) .60 .120 x3 = Sept.-Aug. rainfall (cm) -.004 .001 x4 = Rainfall in months preceding vintage (cm) .0015 .0005 x5 = Average Sept. temperature (°C) .008 .550 R2 = .85, s = .30