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 one full season. Team Conf Yds/Att Int/Att Win% Arizona Cardinals NFC 6.5 0.042 50.0 Atlanta Falcons NFC 7.1 0.022 62.5 Carolina Panthers NFC 7.4 0.033 37.5 Cincinnati Bengals AFC 6.2 0.026 56.3 Detroit Lions NFC 7.2 0.024 62.5 Green Bay Packers NFC 8.9 0.014 93.8 Houstan Texans AFC 7.5 0.019 62.5 Indianapolis Colts AFC 5.6 0.026 12.5 Jacksonville Jaguars AFC 4.6 0.032 31.3 Minnesota Vikings NFC 5.8 0.033 18.8 New England Patriots AFC 8.3 0.020 81.3 New Orleans Saints NFC 8.1 0.021 81.3 Oakland Raiders AFC 7.6 0.044 50.0 San Francisco 49ers NFC 6.5 0.011 81.3 Tennessee Titans AFC 6.7 0.024 56.3 Washington Redskins NFC 6.4 0.041 31.3
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 one full season. Team Conf Yds/Att Int/Att Win% Arizona Cardinals NFC 6.5 0.042 50.0 Atlanta Falcons NFC 7.1 0.022 62.5 Carolina Panthers NFC 7.4 0.033 37.5 Cincinnati Bengals AFC 6.2 0.026 56.3 Detroit Lions NFC 7.2 0.024 62.5 Green Bay Packers NFC 8.9 0.014 93.8 Houstan Texans AFC 7.5 0.019 62.5 Indianapolis Colts AFC 5.6 0.026 12.5 Jacksonville Jaguars AFC 4.6 0.032 31.3 Minnesota Vikings NFC 5.8 0.033 18.8 New England Patriots AFC 8.3 0.020 81.3 New Orleans Saints NFC 8.1 0.021 81.3 Oakland Raiders AFC 7.6 0.044 50.0 San Francisco 49ers NFC 6.5 0.011 81.3 Tennessee Titans AFC 6.7 0.024 56.3 Washington Redskins NFC 6.4 0.041 31.3
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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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 one full season.
| Team | Conf | Yds/Att | Int/Att | Win% |
|---|---|---|---|---|
| Arizona Cardinals | NFC | 6.5 | 0.042 | 50.0 |
| Atlanta Falcons | NFC | 7.1 | 0.022 | 62.5 |
| Carolina Panthers | NFC | 7.4 | 0.033 | 37.5 |
| Cincinnati Bengals | AFC | 6.2 | 0.026 | 56.3 |
| Detroit Lions | NFC | 7.2 | 0.024 | 62.5 |
| Green Bay Packers | NFC | 8.9 | 0.014 | 93.8 |
| Houstan Texans | AFC | 7.5 | 0.019 | 62.5 |
| Indianapolis Colts | AFC | 5.6 | 0.026 | 12.5 |
| Jacksonville Jaguars | AFC | 4.6 | 0.032 | 31.3 |
| Minnesota Vikings | NFC | 5.8 | 0.033 | 18.8 |
| New England Patriots | AFC | 8.3 | 0.020 | 81.3 |
| New Orleans Saints | NFC | 8.1 | 0.021 | 81.3 |
| Oakland Raiders | AFC | 7.6 | 0.044 | 50.0 |
| San Francisco 49ers | NFC | 6.5 | 0.011 | 81.3 |
| Tennessee Titans | AFC | 6.7 | 0.024 | 56.3 |
| Washington Redskins | NFC | 6.4 | 0.041 | 31.3 |
(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. (Round your numerical values to one decimal place. Let x1 represent Yds/Att and y represent Win%.)
ŷ =
(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. (Round your numerical values to the nearest integer. Let x2 represent Int/Att, and y represent Win%.)
ŷ =
(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. (Round your numerical values to the nearest integer. Let x1 represent Yds/Att, x2 represent Int/Att, and y represent Win%.)
ŷ =
(d)
The average number of passing yards per attempt for a certain team was 6.2 and the number of interceptions thrown per attempt was 0.038. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the team. (Round your answer to one decimal place.)
%
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