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 data in the Excel Online file below 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 (Win96) for a random sample of 16 NFL teams for a season. Construct a spreadsheet to answer the following questions. Open spreadsheet 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) win% = h + bi . Yds/Att bo 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) 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) win%- bo + bi , Yds/Att + b2 . Int/Att bo b2 = 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 this 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 Conf NFC NFC NFC AFC NFC NFC AFC AFC AFC NFC AFC NFC AFC NFC AFC NFC Int/Att Win% Yds/Att leam 49.9 62.2 37.6 56.1 62.5 93.6 62.5 12.3 31.2 18.5 81.3 81.1 49.9 81.1 56.4 31.4 6.6 6.9 7.5 6.0 7.0 9.0 7.3 5.7 4.5 5.8 8.2 7.9 7.7 6.5 6.6 6.5 0.042 0.023 0.033 0.027 0.024 0.014 0.019 0.027 0.032 0.032 0.020 0.020 0.043 0.010 0.024 0.042 Arizona Cardinals Atlanta Falcons Carolina Panthers Cincinnati Bengals Detroit Lions Green Bay Packers Houstan Texans Indianapolis Colts Jacksonville Jaguars Minnesota Vikings New England Patriots New Orleans Saints Oakland Raiders San Francisco 49ers Tennessee Titans Washington Redskins

Answer 1

9261565325319144 9276232218119161 4635696131884853 3758297565 3 6676797545877666

Y-51.7786 + 15.4609 X1 ANOVA table F P-value Source DF Sum of Mean Squares Square Statisticue Regression (between 1 4292.9802 4292.9802 14.8667 0.001748 ýi and yi) Residual (between 14 40427098 288.7650 yi and yi) Total (between 15 8335.6900 555.7127 yi and y) lower upper Stand 025(4) 0.975(14) Coeff P-value VIF Coeff SEt-stat X1 15.4609 4.0098 3.8557 6.8606 24.0611 0.7176 0.001748 1.000

9261565325319144 9276232218119161 4635696131884853 2337449722 4232211233224124 3 42

y 98.0262 - 1622.2683 X1 ANOVA table Source DF Sum of Mean P-value Squares Square Statistic Regression (between 1 3805.5170 3805.5170 11.7605 0.004068 yi and yi) Residual (between |530.1730 3235838 yi and yi) Total (between 15 8335.6900 555.7127 yi and y) upper Stand SE t-stat ower Coeff 0.0254 to.9754 Coeff P-value VIF b 98.0262 13.5410 |7.2392 68.9837 127.0688 0.000 0.000004295 X11-1622.2683|473.05241-3.4294-2636.86481-607.671 0.675기0.004068 1.000

9261565325319144 9276232218119161 4635696131884853 3 42 2337449722 4232211233224124 9 6676797545877666

y = 3.8090 + 12.0717 XI - 1198 . 1723 X2 Correlation matrix X1 0.7176 1.000-0.3152 X2-0.6757 -0.3152 1.000 ANOVA table Source DF Sum of Mean P-value Squares Square Statistic Regression (between 2 6162.5939 3081,2969 18.4331 0.0001603 ýi and y) Residual (between 13 2173.0961 167.1612 yi and ý) Total (between 15 8335.6900 555.7127 yi and yi coefficient Table Iteration 1 (adiusted R-squared = 0.699 lower upper Stand SE t-stat Coeff 97513) Coeff P-Value VIIF b|3.8090 X1| 12.0717 3.2148 3.7551 5.1266 26.9121 0.1415 -54.3310 61.9490 0.000 0.8896 19.0168 0.5603 0.002404 1.1103 1198.1723 358.2706 -3.3443 -1972.1688-424.1758 -0.4990 0.0052781.1103

Given, 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. The predicted value of the percentage of games won is, 3.809012.0717 (x)-1198.1723 (x2) 3.8090 +12.0717 (6.2)- 1198.1723 (0.036) -27.9 The predicted percentages of games won is 27.9%.