Question

In: Statistics and Probability

The National Football League (NFL) records a variety of performance data for individuals and teams. To...

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.

Solutions

Expert Solution

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


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