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 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 *x*_{1} 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 *x*_{2} 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 *x*_{1} represent Yds/Att,
*x*_{2} represent Int/Att, and *y* represent
Win%.)

*ŷ* =

(d)

The average number of passing yards per attempt for a certain team was 6.3 and the number of interceptions thrown per attempt was 0.034. 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.)

Answer #1

Regression analysis

We solve the problem in Excel. We go to Data > Data Analysis > Regression to get the regression equations.

a. Taking Yds/Att as the independent variable we get:

Thus we get the required equation as:

b. Taking Int/Att as the independent variable we get:

Thus the required equation is:

c. Taking both as the independent variables we get:

Hence the required equation is:

d. Putting 6.3 and 0.034 in the equation we get:

Thus the predicted Win% is 45.0.

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...

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
6.7...

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.
Excel File
https://drive.google.com/file/d/1pfIsW3U477qRB8nj0fv_PD1fnRHV68Xx/view?usp=sharing
(a)
Using Excel Regression Analysis, write...

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 average number of passing yards per attempt
(yds/att) and the percentage of games won (WinPct) for a random
sample of 10 NFL teams for the 2011 season (NFL website, February
12, 2012). Team YDS/ATT WinPct Ariziona Cardinals 6.1 19 Atlanta
Falcons 6.6 27 Carinlona Panthers...

In exercise 24 an estimated regression equation was developed
relating the percentage of games won by a team in the national foot
ball league for the 2011 season (y) given the average number of
passing yards obtained per game on offense (x1) and the
average number of yards given up per game on defense
(x2) The estimated regression equation was
y=60.5+.319x1-.241x2
Team
OffPassYds/G
DefYds/G
Win%
Arizona
222.9
355.1
50.0
Atlanta
262.0
333.6
62.5
Baltimore
213.9
288.9
75.0
St Louis
179.4...

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