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 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 0.042 50.2 Atlanta Falcons NFC 7.1 0.024 62.4 Carolina Panthers NFC 7.6 0.035 37.5 Cincinnati Bengals AFC 6.4 0.027 56.0 Detroit Lions NFC 7.1 0.023 62.4 Green Bay Packers NFC 9.1 0.014 93.9 Houstan Texans AFC 7.7 0.020 62.3 Indianapolis Colts AFC 5.5 0.027 12.4 Jacksonville Jaguars AFC 4.6 0.032 31.2 Minnesota Vikings NFC 5.8 0.033 19.0 New England Patriots AFC 8.2 0.020 81.1 New Orleans Saints NFC 7.9 0.023 81.3 Oakland Raiders AFC 7.7 0.046 50.2 San Francisco 49ers NFC 6.4 0.013 81.0 Tennessee Titans AFC 6.6 0.025 56.2 Washington Redskins NFC 6.4 0.040 31.1

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%= ____+____* Yrds/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%= ____+____*Yrd/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 .036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

Predicted percentage < > = ??? Actual percentage

Answer 1

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%= ____+____* Yrds/Att

1. Put the values in excel as shown below.

2. We use the regression option under the Data analysis tab.

3. Input the data as shown below.

4. The output will be generated as following

5. We formulate the regression equation using the output (highlighted in yellow)

reqression equation

Win%= (-52.7)+ 15.5 * Yrds/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

In the similar manner we find the regression with Int/Att as the independent variable

Win%= 98.6 + (-1597.5)*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%= ____+____*Yrd/Att +____ *Int/Att

In the similar manner we find the regression with both Yrd/Att and Int/Att as the independent variables

Win%= 0.2 + 12.3 *Yrd/Att + (-1127.3) *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 .036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs. Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

Yrds/Att= 6.2 and Int/Att =0.036

Model 1 : Win%= (-52.7)+ 15.5 * Yrds/Att
Win%= (-52.7)+ 15.5 * (6.2) = 43.32

Model 2 : Win%= 98.6 + (-1597.5)*Int/Att
Win%= 98.6 + (-1597.5)*(0.036)=41.083

Model 3 : Win%= 0.2 + 12.3 *Yrd/Att + (-1127.3) *Int/Att

Win%= 0.2 + 12.3 *(6.2) + (-1127.3) *0.036) = 36.23