In: Statistics and Probability
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 a season
Team | Conf | Yds/Att | Int/Att | Win% |
---|---|---|---|---|
Arizona Cardinals | NFC | 6.7 | 0.044 | 49.8 |
Atlanta Falcons | NFC | 7.3 | 0.022 | 62.7 |
Carolina Panthers | NFC | 7.4 | 0.033 | 37.7 |
Cincinnati Bengals | AFC | 6.0 | 0.026 | 56.4 |
Detroit Lions | NFC | 7.0 | 0.023 | 62.6 |
Green Bay Packers | NFC | 8.9 | 0.013 | 93.8 |
Houstan Texans | AFC | 7.5 | 0.018 | 62.2 |
Indianapolis Colts | AFC | 5.4 | 0.028 | 12.7 |
Jacksonville Jaguars | AFC | 4.5 | 0.032 | 31.4 |
Minnesota Vikings | NFC | 5.6 | 0.035 | 18.5 |
New England Patriots | AFC | 8.3 | 0.022 | 81.0 |
New Orleans Saints | NFC | 8.0 | 0.020 | 81.5 |
Oakland Raiders | AFC | 7.6 | 0.043 | 49.7 |
San Francisco 49ers | NFC | 6.3 | 0.013 | 81.4 |
Tennessee Titans | AFC | 6.6 | 0.023 | 56.4 |
Washington Redskins | NFC | 6.3 | 0.041 | 31.4 |
a. Compute R2 if the average number of passing yards per attempt is the independent variable (to 3 decimals). Enter negative value as negative number.
y^=_____ + _____ Yds/Att (to 2 decimals)
R2=_____
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?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
b. Compute R2 if the average number of passing yards per attempt and the number of interceptions thrown per attempt are the independent variables (to 3 decimals). Enter negative value as negative number.
y^=_____ + _____ Yds/Att + _____ Int/Att (to 2 decimals)
R2=_____
Discuss the benefit of using both the average number of passing yards per attempt and the number of interceptions thrown per attempt to predict the percentage of games won.
The value of the coefficient of determination increased to R2=_____ , and the adjusted coefficient of determination is R2a=_____ . Thus, using both independent variables provides a much - Select your answer -better -OR-worse fit.
Team | Conf | Yds/Att | Int/Att | Win% |
---|---|---|---|---|
Arizona Cardinals | NFC | 6.7 | 0.044 | 49.8 |
Atlanta Falcons | NFC | 7.3 | 0.022 | 62.7 |
Carolina Panthers | NFC | 7.4 | 0.033 | 37.7 |
Cincinnati Bengals | AFC | 6.0 | 0.026 | 56.4 |
Detroit Lions | NFC | 7.0 | 0.023 | 62.6 |
Green Bay Packers | NFC | 8.9 | 0.013 | 93.8 |
Houstan Texans | AFC | 7.5 | 0.018 | 62.2 |
Indianapolis Colts | AFC | 5.4 | 0.028 | 12.7 |
Jacksonville Jaguars | AFC | 4.5 | 0.032 | 31.4 |
Minnesota Vikings | NFC | 5.6 | 0.035 | 18.5 |
New England Patriots | AFC | 8.3 | 0.022 | 81.0 |
New Orleans Saints | NFC | 8.0 | 0.020 | 81.5 |
Oakland Raiders | AFC | 7.6 | 0.043 | 49.7 |
San Francisco 49ers | NFC | 6.3 | 0.013 | 81.4 |
Tennessee Titans | AFC | 6.6 | 0.023 | 56.4 |
Washington Redskins | NFC | 6.3 | 0.041 | 31.4 |
A -
ŷ = - 50.81 + 15.37* Yds/Att
R squared = 0.748
The model provides a good fit as the variance explained (R squared value) for Win% is 74.8%
B -
ŷ = 5.34 + 11.78 * Yds/Att - 1158.68 * Int/Att
R squared = 0.766
Adjusted R squared = 0.73
The R squared value has increased, hence we have a better fit using both independent variables