| | Take me out to the ball game. |
| | In baseball a teams 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 that team hits, and one measure of pitching performance is the earned run average for the teams 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 games played. The following data show the proportion of games won, the number of home runs (HR), and the earned run average (ERA) for the 16 teams in the National League for the 2003 Major League Baseball season. |
| | | | Team | Won | HR | ERA |
| | | | Arizona | 0.519 | 152 | 3.857 |
| | | | Atlanta | 0.623 | 235 | 4.106 |
| | | | Chicago | 0.543 | 172 | 3.842 |
| | | | Cincinnati | 0.426 | 182 | 5.127 |
| | | | Colorado | 0.457 | 198 | 5.269 |
| | | | Florida | 0.562 | 157 | 4.059 |
| | | | Houston | 0.537 | 191 | 3.880 |
| | | | Los Angeles | 0.525 | 124 | 3.162 |
| | | | Milwaukee | 0.420 | 196 | 5.058 |
| | | | Montreal | 0.512 | 144 | 4.027 |
| | | | New York | 0.410 | 124 | 4.517 |
| | | | Philadelphia | 0.531 | 166 | 4.072 |
| | | | Pittsburgh | 0.463 | 163 | 4.664 |
| | | | San Diego | 0.395 | 128 | 4.904 |
| | | | San Francisco | 0.621 | 180 | 3.734 |
| | | | St Louis | 0.525 | 196 | 4.642 |
| | 1 | Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs. |
| | 2 | 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.. |
| | 3 | 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.. |
| | 4 | Use the estimated regression equation developed in part (3) 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. |
| | 5 | What is the multiple coefficient of determination which measures the goodness of fit for the estimated multiple regression equation. |
| | 6 | Setup the hypothesis test for the multiple regression problem. |