Question

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?

Answer 1

Regression equation is

E(Y) = 0.159 + 0.4 *E(x)             (E(e) = 0)

a) For x = 0.200

E(Y) = 0.159 + 0.4 * 0.200

        = 0.159 + 0.08

       = 0.239

If a player's batting average is 0.200 in his first year, we can predict that his second year's average batting average is 0.239

b) For x = 0.265

E(Y) = 0.159 + 0.4 * 0.265

        = 0.159 + 0.106

       = 0.265

If a player's batting average is 0.200 in his first year, we can predict that his second year's average batting average is 0.265

c) For x = 0.310

E(Y) = 0.159 + 0.4 * 0.310

        = 0.159 + 0.124

       = 0.283

If a player's batting average is 0.200 in his first year, we can predict that his second year's average batting average is 0.283