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 average vintage price relative to 1961, is used as the response variable y. The explanatory variables were the average temperature x1 (in degrees Celsius), the amount of winter rain x2 (in millimeters), the amount of harvest rain x3 (in millimeters), and the years since vintage x4. A portion of the data is shown in the accompanying table.
a. Estimate the linear model: y = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε. What is the predicted price if x1 = 16, x2 = 600, x3 = 120, and x4 = 20?
b. Estimate the exponential model: ln(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 + ε. What is the predicted price if x1 = 16, x2 = 600, x3 = 120, and x4 = 20?
c. Use R2 to select the appropriate model for prediction.
