In: Statistics and Probability
DATAfile: NFLPassing
A statistical program is recommended.
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.
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. (Round your numerical values to one decimal place. Let x1 represent Yds/Att and y represent Win%.)
ŷ =
(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. (Round your numerical values to the nearest integer. Let x2 represent Int/Att, and y represent Win%.)
ŷ =
(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. (Round your numerical values to the nearest integer. Let x1 represent Yds/Att, x2 represent Int/Att, and y represent Win%.)
ŷ =
(d)
The average number of passing yards per attempt for a certain team was 6.1 and the 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. (Round your answer to one decimal place.)
______%
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.
The predicted value is higher than the actual value.
The predicted value is identical to the actual value.
The predicted value is lower than the actual value.
using excel>data>data analysis>Regression
we have
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.759693 | |||||
R Square | 0.577133 | |||||
Adjusted R Square | 0.546928 | |||||
Standard Error | 15.87319 | |||||
Observations | 16 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 4814.254 | 4814.254 | 19.10735 | 0.000639 | |
Residual | 14 | 3527.416 | 251.9583 | |||
Total | 15 | 8341.67 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -58.7703 | 26.17541 | -2.24525 | 0.041423 | -114.911 | -2.62964 |
Yds/Att | 16.39063 | 3.749689 | 4.371195 | 0.000639 | 8.348341 | 24.43291 |
(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.
ŷ =-58.8+16.4 x1
using excel
we have
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.661739 | |||||
R Square | 0.437898 | |||||
Adjusted R Square | 0.397748 | |||||
Standard Error | 18.3008 | |||||
Observations | 16 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 1 | 3652.8 | 3652.8 | 10.90651 | 0.005236 | |
Residual | 14 | 4688.87 | 334.9193 | |||
Total | 15 | 8341.67 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | 97.53825 | 13.86182 | 7.03647 | 5.9E-06 | 67.80762 | 127.2689 |
Int/Att | -1600.49 | 484.63 | -3.3025 | 0.005236 | -2639.92 | -561.063 |
(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. (Round your numerical values to the nearest integer. Let x2 represent Int/Att, and y represent Win%.)
ŷ =97.5 -1600.5 x2
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.867461 | |||||
R Square | 0.752489 | |||||
Adjusted R Square | 0.71441 | |||||
Standard Error | 12.60237 | |||||
Observations | 16 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 2 | 6277.014 | 3138.507 | 19.76145 | 0.000114 | |
Residual | 13 | 2064.656 | 158.8197 | |||
Total | 15 | 8341.67 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -5.76328 | 27.1468 | -0.2123 | 0.835165 | -64.4104 | 52.88381 |
Yds/Att | 12.94936 | 3.18567 | 4.064877 | 0.001338 | 6.067136 | 19.83158 |
Int/Att | -1083.79 | 357.1165 | -3.03483 | 0.009575 | -1855.29 | -312.285 |
(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. (Round your numerical values to the nearest integer. Let x1 represent Yds/Att, x2 represent Int/Att, and y represent Win%.)
ŷ = -6 +13 x1 -1084 x2
(d)
The average number of passing yards per attempt for a certain team was 6.1 and the 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. (Round your answer to one decimal place.)
36.4%
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.
The predicted value is higher than the actual value.