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 (USA Today website, January 7, 2004).

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 tried to acquire new players who would 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.

Proportion Proportion WonHR ERA Team WonHR ERA 420 196 5.058 512 144 4.027 410 24 4517 426 182 5.127 Philadelphia 531 166 4.072 463 163 4.664 128 4.904 621 180 3.734 525 196 4.642 Arizona Atlanta 519 52 3.857 623 235 4.106 Montreal 172 3.842 New York Cincinnati Colorado 457 198 5.269 ttsburgh 562 157 4059 San Diego 537 191 525 124 3.162 395 Houston Los Angeles 3.880 San Francisco6 St. Louis