Question

# 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

 Yds/Att Int/Att Win% Team Conf Arizona Cardinals NFC 6.4 0.044 50.0 Atlanta Falcons NFC 7.3 0.023 62.6 Carolina Panthers NFC 7.3 0.033 37.4 Cincinnati Bengals AFC 6.1 0.027 56.3 Detroit Lions NFC 7.2 0.024 62.3 Green Bay Packers NFC 8.9 0.014 93.8 Houstan Texans AFC 7.3 0.018 62.6 Indianapolis Colts AFC 5.6 0.025 12.4 Jacksonville Jaguars AFC 4.8 0.031 31.0 Minnesota Vikings NFC 5.6 0.034 18.7 New England Patriots AFC 8.1 0.022 81.3 New Orleans Saints NFC 8.3 0.021 81.1 Oakland Raiders AFC 7.6 0.046 49.7 San Francisco 49ers NFC 6.7 0.011 81.4 Tennessee Titans AFC 6.9 0.023 56.4 Washington Redskins NFC 6.5 0.042 31.4

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 (to 1 decimal). Enter negative value as negative number.

Win%=____+______.Yds/Att

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 (to 1 decimal). Enter negative value as negative number.

Win%=____+____.Int / Att

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 (to 1 decimal). Enter negative value as negative number.

Win=___+____.Yds/Att +____.Int/Att

d. The average number of passing yards per attempt for the Kansas City Chiefs was 6.2 and the number of interceptions thrown per attempt was 0.036 . Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. (Note: For a season the Kansas City Chiefs' record was 7 wins and 9 losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

a)

using excel data analysis tool for regression,steps are: write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

 Regression Statistics Multiple R 0.7928 R Square 0.6285 Adjusted R Square 0.6020 Standard Error 14.9013 Observations 16 ANOVA df SS MS F Significance F Regression 1 5258.9 5258.9 23.68 0.0002 Residual 14 3108.7 222.0 Total 15 8367.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -66.1151 25.0170 -2.6428 0.0193 -119.7712 -12.4591 X 17.4163 3.5787 4.8666 0.0002 9.7407 25.0919

Win%= -66.1 + 17.4*Yds/Att

b)

 Regression Statistics Multiple R 0.6169 R Square 0.3805 Adjusted R Square 0.3363 Standard Error 19.2418 Observations 16 ANOVA df SS MS F Significance F Regression 1 3184.1 3184.1 8.60 0.0109 Residual 14 5183.5 370.2 Total 15 8367.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 93.0661 14.0752 6.6121 0.0000 62.8778 123.2545 X -1417.0266 483.2027 -2.9326 0.0109 -2453.3934 -380.6599

Win% = 93.1 -1417.0 * Int/Att

c)

 SUMMARY OUTPUT Regression Statistics Multiple R 0.873337 R Square 0.762717 Adjusted R Square 0.726212 Standard Error 12.35841 Observations 16 ANOVA df SS MS F Significance F Regression 2 6382.116 3191.058 20.89342 8.69E-05 Residual 13 1985.494 152.7303 Total 15 8367.61 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -21.1787 26.55292 -0.7976 0.439427 -78.5428 36.18539 -78.5428 36.18539 Yds/Att 14.46541 3.161222 4.575892 0.00052 7.636005 21.29481 7.636005 21.29481 Int/Att -896.381 330.5452 -2.71183 0.017788 -1610.48 -182.282 -1610.48 -182.282

Win= -21.2 + 14.5*Yds/Att - 896.4 * Int/Att

d)

predicted Win= -21.2 + 14.5*6.2 - 896.4 * 0.036 = 36.24 %

actual percentage = 7/16 = 43.75

predicted percentage < actual