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.

Transcribed Image Text:

X1 X2 Xз X4 y 0.3684 17.1167 600 160 0.6348 16.7333 690 80 30 0.1359 16.0000 578 74