6. In baseball, a team's success is often thought to be a function of the team's hitting and pitch- ing 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 pitch- ing 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 (http://www.usatoday.com, January 7, 2004). Team Proportion Won Proportion 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 propor- tion of games won given the number of team home runs.

b. Determine the estimated regression equation that could be used to predict the propor- tion 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 propor- tion 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.