Determine the estimated regression equation that could be used to predict the proportion of games…

Determine the estimated regression equation that could be used to predict the proportion of games…

In baseball, a team’s success is often thought to be a function of the team’s hitting and pitching performance. One measure of hitting performance is the number of home runs the team hits, and one measure of pitching performance is the earned run average for the team’s pitching staff. It is generally believed that teams that hit more home runs and have a lower earned run average will win a higher percentage of the games played. The following data show the proportion of games won, the number of team home runs (HR), and the earned run average (ERA) for the 16 teams in the National League for the 2003 Major League Baseball season

 

Proportion

 

 

 

Proportion

 

 

Team

Won

HR

ERA

Team

Won

HR

ERA

Arizona

0.519

152

3.857

Milwaukee

0.420

196

5.058

Atlanta

0.623

235

4.106

Montreal

0.512

144

4.027

Chicago

0.543

172

3.842

New York

0.410

124

4.517

Cincinnati

0.426

182

5.127

Philadelphia

0.531

166

4.072

Colorado

0.457

198

5.269

Pittsburgh

0.463

163

4.664

Florida

0.562

157

4.059

San Diego

0.395

128

4.904

Houston

0.537

191

3.880

San Francisco

0.621

180

3.734

Los Angeles

0.525

124

3.162

St. Louis

0.525

196

4.642

a. Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs.

b. Determine the estimated regression equation that could be used to predict the proportion of games won given the earned run average for the team’s pitching staff.

c. Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs and the earned run average for the team’s pitching staff.

d. For the 2003 season San Diego won only 39.5% of the games they played, the lowest in the National League. To improve next year’s record, the team is trying to acquire new players who will increase the number of team home runs to 180 and decrease the earned run average for the team’s pitching staff to 4.0. Use the estimated regression equation developed in part (c) to estimate the percentage of games San Diego will win if they have 180 team home runs and have an earned run average of 4.0.

 

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