14. A study has shown that a good model for the relationship between X and Y, the first and second year batting averages of a randomly chosen major league baseball player, is given by the equation Y = .159+.4X +e where e is a normal random variable with mean 0. That is, the model is a simple linear regression with a regression toward the mean.

a. If a player’s batting average is .200 in his first year, what would you predict for the second year?

b. If a player’s batting average is .265 in his first year, what would you predict for the second year?

c. If a player’s batting average is .310 in his first year, what would you predict for the second year?