In his best-selling book Moneyball, author Michael Lewis discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this analysis is that a team’s on-base percentage is the best predictor of winning percentage. The on-base percentage is the proportion of time a player reaches a base. For example, an on-base percentage of 0.3 would mean the player safely reaches bases 3 times out of 10, on average. For the 2010 baseball season, winning percentage, y, and on-base percentage, x,
are linearly related by the least-squares regression equation y-hat = 3.4722x - 0.6294.
(a) Interpret the slope.
(b) For 2010, the lowest on-base percentage was 0.298 and the highest on-base percentage was 0.350. Use this information to explain why it does not make sense to interpret the y-intercept.
(c) Would it be a good idea to use this model to predict the winning percentage of a team whose on-base percentage was 0.250? Why or why not?
(d) The 2010 World Series Champion San Francisco Giants had an on-base percentage of 0.321 and a winning percentage of 0.568. What is the residual for San Francisco? How would you interpret this residual?