Question

In: Statistics and Probability

DATAfile: NFLPassing A statistical program is recommended. The National Football League (NFL) records a variety of...

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.

Solutions

Expert Solution

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.


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