The ultimate goal in any sport (besides having fun) is to win. One measure of how well a team does is the winning percentage. In baseball, a lot of effort goes into guring out the variable that best predicts a team's winning percentage. The following data represent the winning percentages of teams in the National League along with potential explanatory variables based on the 2010 season. Team Batting Winning Home Batting On Base Average Team Team Percentage Runs Runs Average Percentage Against ERA ' Philadelphia 0.599 772 166 0.260 0.332 0.254 3.67 Atlanta 0.562 0.258 0.339 0.246 3.56 San Francisco 0.568 0.257 0.321 0.236 3.36 ' Chicago Cubs 0.463 0.257 0.320 0.255 4.18 ' Florida 0.494 719 152 0.254 0.321 0.261 4.08 LA Dodgers 0.494 667 120 0.252 0.322 0.244 4.01 Washington 0.426 655 149 0.250 0.318 0.266 4.13 Arizona 0.401 713 180 0.250 0.325 0.271 4.81 I NY Mets 0.488 656 128 0.249 0.314 0.260 3.70 Houston 0.469 0.247 0.303 0.261 San Diego 0.556 0.317 0.240 3.39 I Pittsburgh 0.352 0.304 0.282 5.00 Source: espn.com (a) Using the regression analysis tool built in Excel spreadsheet to estimate a regression equation that predicts winning percentage. Consider all available independent variables in the model. Show the summary output table. (2 marks) (b) Comment on the overall model performance. (4 marks) (c) At 10% level of signicance, are there any independent variables that appear to be unnecessary? Justify your answer. (6 marks) (d) Based on your discussion in part (c), re-develop the regression model, and show the summary output table. (2 marks) (e) Compare the two regressions developed in part (a) and (d), decide which model has a better t to the data? (3 marks) (t) Using the model developed in part (d), estimate the winning percentage for a team with Runs = 648 Home Runs = 123 Team Batting Average = 0.246 On Base Percentage = 0.325 Batting Average Against = 0.257 Team ERA = 3.56