Professor Orley Ashenfelter of Princeton University is a pioneer in the field of wine economics. He claims that, contrary to old orthodoxy, the quality of wine can be explained mostly in terms of weather conditions. Wine romantics accuse him of undermining the whole wine-tasting culture. In an interesting co-authored paper that appeared in Chance magazine in 1995, he ran a multiple regression model where quality, measured by the prices that wines fetch at auctions, is used as the response variable y. The explanatory variables used in the analysis were the average temperature in Celsius x1, the amount of winter rain x2, the amount of harvest rain x3, and the years since vintage x4. A portion of the data is shown in the accompanying table.

a. Estimate the linear model: y = β0 + β1 x1 + β2 x2 + β3 x 3 + β4 x4 + ε. What is the predicted price if x1 = 16, x2 = 600, x3 = 120, and x4 = 20?
b. Estimate the exponential model: ln(y) = β0 + β1 x1 + β2 x2 + β3 x3 + β4 x4 + ε. What is the predicted price if x1 = 16, x2 = 600, x3 = 120, and x4 = 20?
c. Use R 2 to select the appropriate model for

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Winter Harvest 17.12 1.8870 16.73 Price Temperature Rain 600 690 Rain Vintage 160 き鄭 1.4448 31 30 1.145716.00 578 74 3