DATA FOR THIS Q: https://docs.google.com/spreadsheets/d/1isLprxdzWhofCg7UozJkjuT-QtzZSomD0YvdQYZa5rk/edit?usp=sharing

You want to study the prices of different place/country's red wines, and you are needed to categorize the wines into commercial, semipremium, premium, and ultrapremium. The data for premium wines are stored in the file premium-wine; those for ultrapremium wines are in the file ultrapremium-wine. Your are concerned with the variables PRICE (bottle price, CPI adjusted), SCORE (score out of 100 given by the Wine Spectator Magazine), AGE (years of aging), and CASES (number of cases produced in thousands).

1. What signs would you expect on the coefficients (2,3,4) in the following model? Why?
2. PRICE = 1 + 2SCORE + 3AGE + 4CASES +
3. Estimate separate equations for premium and ultrapremium wine, and discuss the results. Do the coefficients have the expected signs? If not is there an alternative explanation? Is SCORE more important for premium wines or ultrapremium wines? Is AGE more important for premium wines or ultrapremium wines?
4. Find point and 95% interval estimates for
5. i. [E[PRICE | SCORE = 90, AGE = 2, CASES = 2] for premium wines, and
6. ii. E[PRICE | SCORE = 93, AGE = 3, CASES = 1] for ultrapremium wines.]
7. Do the intervals overlap, or is there a clear price distinction between the two classes?
8. Suppose that you are a wine producer choosing between producing 1000 cases of ultra- premium wine that has to be aged three years and is likely to get a score of 93, and 2000 cases of premium wine that is aged two years and is likely to get a score of 90. Which choice gives the higher expected bottle price? Which choice gives the higher expected revenue? (There are 12 bottles in a case of wine.)