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 | 6.4 | 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).
Predicted percentage | Actual percentage | |
- Select your answer -<>=Item 9 |
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
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