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 following data 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 one full season. (Let x1 represent Yds/Att, x2 represent Int/Att, and y represent Win%). Team Conf Yds/Att Int/Att Win%
Arizona Cardinals NFC 6.5 0.042 50.0
Atlanta Falcons NFC 7.1 0.022 62.5
Carolina Panthers NFC 7.4 0.033 37.5
Cincinnati Bengals AFC 6.2 0.026 56.3
Detroit Lions NFC 7.2 0.024 62.5
Green Bay Packers NFC 8.9 0.014 93.8
Houstan Texans AFC 7.5 0.019 62.5
Indianapolis Colts AFC 5.6 0.026 12.5
Jacksonville Jaguars AFC 4.6 0.032 31.3
Minnesota Vikings NFC 5.8 0.033 18.8
New England Patriots AFC 8.3 0.020 81.3
New Orleans Saints NFC 8.1 0.021 81.3
Oakland Raiders AFC 7.6 0.044 50.0
San Francisco 49ers NFC 6.5 0.011 81.3
Tennessee Titans AFC 6.7 0.024 56.3
Washington Redskins NFC 6.4 0.041 31.3
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. What proportion of variation in the sample values of proportion of games won (in %) does this model explain?
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. What proportion of variation in the sample values of proportion of games won (in %) does this model explain?
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. What proportion of variation in the sample values of proportion of games won (in %) does this model explain?
D) Suppose the average number of passing yards per attempt for a certain team was 6.1, and the team's number of interceptions thrown per attempt was 0.034. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the team.
Suppose for this season the team's record was 7 wins and 9 losses. Compare your prediction to the actual percentage of games won by the team.
1) The predicted value is lower than the actual value.
2) The predicted value is identical to the actual value.
3) The predicted value is higher than the actual value.
E) Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?
Based on the coefficient of determination from the two models using the average number of passing yards per attempt as the independent variable, the model using only the average number of passing yards per attempt as the independent variablethe best fit.