The National Football League (NFL) records a variety of performance data for ind

Question

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 confenence (Conf), average number of passing yards pe 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 Arizona Cardinals Adanta Falcons Carolina Panthers Cincinnati Bengals yds/Att 0.044 Green Bay Packers Indianapois Colts Jacksonvilleaguars Minnesota Vikings New England Patriots New Orleans Saints Oakland Raiders San Francisco 49ers Tennessea Titans Washington Redskins a. compute R2 the average number of passing yards per attempt is the independent variable (to 3 decimals). Enter negative value as negative number. Yds/Att(to 2 decimals) Did the estimated regression equation that uses only the average nurnber of passing yards per attempt as the independent variable to predict the percentage of games won pravide a good fit? The input in the box below will not be graded, but may be reviewed and considered by your instructer. blank h. Compute R2 if the average number of passing yards per attempt and the numher of interceptions thrown per attempt are the independent variables (to 3 decimals). Enter negative value as negative number. Yds Att+ Int/Att (to 2 declmals) Discuss the benef t 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 coefficierit of determinativn increased to R and the adjusted coefficient of determination is Thus, using both independent variables provides much-Select your annver- | fit.

Explanation / Answer

a)

y=-54.49+15.84*Yds/Att

r^2=0.5137

Since FSTAT is in the rejection region, we can say that independent variable affects the dependent variable and hence the model is significant.

b)

y=1.007+12.07*Yds/Att-1071.4727*Int/Att

r^2=0.6944

Adj r^2=0.6474

As we use both the average number of passing yards per attempt and the number of interceptions thrown per attempt to predict the percentage of games won, more variability in the dependent variable is accounted for than just by using a single variable.

Thus, using both independent variables provides a much better fit.

SUMMARY OUTPUT Regression Statistics Multiple R 0.716726028 R Square 0.513696199 Adjusted R Square 0.478960214 Standard Error 16.93261956 Observations 16 ANOVA df SS MS F Significance F Regression 1 4240.089526 4240.089526 14.7885885 0.001782971 Residual 14 4013.990474 286.7136053 Total 15 8254.08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -54.48725577 28.43662881 -1.916094068 0.075999997 -115.4777587 6.503247139 Yds/Att 15.84428656 4.120114886 3.845593388 0.001782971 7.007519001 24.68105412

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