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

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?

Y.159+4X+e