Chapter 15.3, Problem 18E

R² in Predicting Baseball Pitcher Performance. Refer to exercise 10, where Major League Baseball (MLB) pitching statistics were reported for a random sample of 20 pitchers from the American League for one full season.

1. a. In part (c) of exercise 10, an estimated regression equation was developed relating the average number of runs given up per inning pitched given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched. What are the values of R² and $R_{\text{a}}^2$?
2. b. Does the estimated regression equation provide a good fit to the data? Explain.
3. c. Suppose the earned run average (ERA) is used as the dependent variable in part (c) instead of the average number of runs given up per inning pitched. Does the estimated regression equation that uses the ERA provide a good fit to the data? Explain.

10. Baseball Pitcher Performance. Major League Baseball (MLB) consists of teams that play in the American League and the National League. MLB collects a wide variety of team and player statistics. Some of the statistics often used to evaluate pitching performance are as follows:

ERA: The average number of earned runs given up by the pitcher per nine innings. An earned run is any run that the opponent scores off a particular pitcher except for runs scored as a result of errors.

SO/IP: The average number of strikeouts per inning pitched.

HR/IP: The average number of home runs per inning pitched.

R/IP: The number of runs given up per inning pitched.

The following data show values for these statistics for a random sample of 20 pitchers from the American League for a full season.

1. a. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched.
2. b. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of home runs per inning pitched.
3. c. Develop an estimated regression equation that can be used to predict the average number of runs given up per inning given the average number of strikeouts per inning pitched and the average number of home runs per inning pitched.
4. d. A. J. Burnett, a pitcher for the New York Yankees, had an average number of strikeouts per inning pitched of .91 and an average number of home runs per inning of .16. Use the estimated regression equation developed in part (c) to predict the average number of runs given up per inning for A. J. Burnett. (Note: The actual value for R/IP was .6.)
5. e. Suppose a suggestion was made to also use the earned run average as another independent variable in part (c). What do you think of this suggestion?