# Question: In baseball an earned run is any run that the

In baseball, an earned run is any run that the opposing team scores off the pitcher except for runs scored as a result of errors. The earned run average (ERA), the statistic most often used to compare the performance of pitchers, is computed as follows:

Note that the average number of earned runs per inning pitched is multiplied by nine, the number of innings in a regulation game. Thus, ERA represents the average number of runs the pitcher gives up per nine innings. For instance, in 2008, Roy Halladay, a pitcher for the Toronto Blue Jays, pitched 246 innings and gave up 76 earned runs; his ERA was (76/246)9 = 2.78. To investigate the relationship between ERA and other measures of pitching performance, data for 50 Major League Baseball pitchers for the 2008 season appear in the data set named MLB Pitching (MLB website, February 2009). Descriptions for variables which appear on the data set follow:

W Number of games won

L Number of games lost

WPCT Percentage of games won

H/9 Average number of hits given up per nine innings

HR/9 Average number of home runs given up per nine innings

BB/9 Average number of bases on balls given up per nine innings

a. Develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings.

b. Develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings, the average number of home runs given up per nine innings, and the average number of bases on balls given up per nine innings.

c. At the .05 level of significance, test whether the two independent variables added in part (b), the average number of home runs given up per nine innings and the average number of bases on ball given up per nine innings, contribute significantly to the estimated regression equation developed in part (a).

Note that the average number of earned runs per inning pitched is multiplied by nine, the number of innings in a regulation game. Thus, ERA represents the average number of runs the pitcher gives up per nine innings. For instance, in 2008, Roy Halladay, a pitcher for the Toronto Blue Jays, pitched 246 innings and gave up 76 earned runs; his ERA was (76/246)9 = 2.78. To investigate the relationship between ERA and other measures of pitching performance, data for 50 Major League Baseball pitchers for the 2008 season appear in the data set named MLB Pitching (MLB website, February 2009). Descriptions for variables which appear on the data set follow:

W Number of games won

L Number of games lost

WPCT Percentage of games won

H/9 Average number of hits given up per nine innings

HR/9 Average number of home runs given up per nine innings

BB/9 Average number of bases on balls given up per nine innings

a. Develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings.

b. Develop an estimated regression equation that can be used to predict the earned run average given the average number hits given up per nine innings, the average number of home runs given up per nine innings, and the average number of bases on balls given up per nine innings.

c. At the .05 level of significance, test whether the two independent variables added in part (b), the average number of home runs given up per nine innings and the average number of bases on ball given up per nine innings, contribute significantly to the estimated regression equation developed in part (a).

## Relevant Questions

A study provided data on variables that may be related to the number of weeks a manufacturing worker has been jobless. The dependent variable in the study (Weeks) was defined as the number of weeks a worker has been jobless ...Write a multiple regression equation that can be used to analyze the data for a randomized block design involving three treatments and two blocks. Define all variables. Lower prices for color laser printers make them a great alternative to inkjet printers. PC World reviewed and rated 10 color laser printers. The following data show the printing speed for color graphics in pages per minute ...A study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. a. ...Data on quantities of three items sold in 1995 and 2009 are given here along with the sales prices of the items in 1995. Compute a weighted aggregate quantity index for 2009.Post your question