PS11-Multiple Regression Practice Problems. Required: all. 6. In baseball, a tea

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PS11-Multiple Regression Practice Problems. Required: all. 6. 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 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). is the earned run Proportion Won HR ERA Team Team Arizona Atlanta Chicago Proportion Won HR ERA 0.519 0.623 0.543 152 3.857 Milwaukee 235 4.106 Montreal 172 3.842 New York 182 5.127 Philadelphia 198 5.269 Pittsburgh 157 4.059 San Diego 191 3.88 San Francisco 196 5.058 144 4.027 124 4.517 166 4072 163 4.664 128 4.904 180 3.734 0.525196 4642 0.420 0.512 0.410 0.531 Colorado 0.457 0.562 0.537 0.525 124 3.162 St. Louis 0.395 0,621 Houston Los Angeles Determine the estimated regression equation that could be used to predict the proportion of games won given the number of team home runs 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 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 For the 2003 season San Diego won only 39.S% of the games they played. 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. a. b. c. d. SUMMARY OUTPUT Regression Saristics - Multiple R R Square Adjusted R Square Standard Error 0.391 0.067 16 ANOVA MS Significance F 0.011 Residual 0.004 Coefficients Standard Error 0.096 0,001 Stat P-valve 0.354 3.691 HR

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Data Analysis>Regression

in excel select Y as Proportion Won and X as HR

SUMMARY OUTPUT Regression Statistics Multiple R 0.391 R Square 0.153 Adjusted R Square 0.093 Standard Error 0.067 Observations 16.000 ANOVA df SS MS F Significance F Regression 1.000 0.011 0.011 2.532 0.134 Residual 14.000 0.062 0.004 Total 15.000 0.073 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.354 0.096 3.691 0.002 0.148 0.560 HR 0.001 0.001 1.591 0.134 0.000 0.002

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