Question

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the data in the Excel Online file below show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for a season. Construct a spreadsheet to answer the following questions. Open spreadsheet a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt (to 1 decimal). Win% = bo + bı Yds/Att bo = bi = b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Win% = bo + b · Int/Att bo =

Answer 1

Solution:

a. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt to 1 decimal). Win% = bo + b . Yds/Att bo = -57.1 b1 = 16.3 SUMMARY OUTPUT Regression Statistics Multiple R 0.7480 R Square 0.5595 Adjusted R Square 0.5280 Standard Error 16.1813 Observations 16 ANOVA df F Significance F 0.0009 Regression Residual Total 17.7795 M S 4655.2755 261.8346 1 14 15 SS 4655.2755 3665.6845 8320.96 Lower 95% Intercept Yds/Att Coefficients -57.0583 16.2940 Standard Error 26.7060 3.8643 Stat -2.1365 4.2166 2.2165 P-value 0.0508 0.0009 0.0508 -114.3370 UPDEC.95% 3.8643 Upper 95% 0.2204 24.5820 8.0059

b. Develop the estimated regression equation that could be used to predict the percentage of games won given the number of interceptions thrown per attempt (to 1 decimal). Win% = bo +b Int/Att bo = 98.4 bi = -1645.3 SUMMARY OUTPUT Regression Statistics Multiple R 0.6648 R Square 0.4419 Adjusted R Square 0.4021 Standard Error 18.2123 Observations 16 ANOVA df F 11.0868 Significance F 0.0050 Regression Residual Total MS 3677.3488 331.6865 1 14 15 3677.3488 4643.6112 8320.96 Intercept Int/Att Coefficients 98.3649 -1645.3094 Standard Error 14.0095 494.1332 tStat 7.0213 -3.3297 P-value 0.0000 0.0050 Lower 95% 68.3176 -2705.1198 Upper 95% 128.4122 -585.4990 Activate

C. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt and the number of interceptions thrown per attempt (to 1 decimal). Win% = bo + b1 · Yds/Att + b2 · Int/Att bo = -2.5 bi = 12.7 b2 = -1121.2 d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For this season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number). Predicted percentage Actual percentage 36% 44% SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.859 0.738 0.697 12.958 16 ANOVA df F 18.2767 Significance F 0.0002 Regression Residual Total MS 3069.0082 167.9187 2 13 15 SS 6138.0163 2182.9437 8320.96 Intercept Yds/Att Int/Att Coefficients -2.5331 12.7129 -1121.1782 Standard Error 28.1795 3.3210 377.3042 tStat -0.0899 3.8280 -2.9715 P-value 0.9297 0.0021 0.0108 Lower 95% -63.4112 5.5383 -1936.2943 Upper 95% 58.3449 19.8874 -306.0621