In baseball, an earned run is any run that the opposing team scores off the pitcher exceptfor runs scored as a result of errors. The earned run average (ERA), the statistic mostoften used to compare the performance of pitchers, is computed as follows:ERA 5 Searned runs given upinnings pitched D9Note that the average number of earned runs per inning pitched is multiplied by nine, thenumber of innings in a regulation game. Thus, ERA represents the average number ofruns the pitcher gives up per nine innings. For instance, in 2008, Roy Halladay, a pitcherfor 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 ofpitching performance, data for 50 Major League Baseball pitchers for the 2008 seasonappear in the data set named MLBPitching (MLB website, February 2009). Descriptionsfor variables which appear on the data set follow:W Number of games wonL Number of games lostWPCT Percentage of games wonH/9 Average number of hits given up per nine inningsHR/9 Average number of home runs given up per nine inningsBB/9 Average number of bases on balls given up per nine inningsa. Develop an estimated regression equation that can be used to predict the earned runaverage given the average number hits given up per nine innings.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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:
ERA 5 S
earned runs given up
innings pitched D9
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 MLBPitching (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.
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