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 | 6.7 | 0.042 | 50.1 |

Atlanta Falcons | NFC | 7.3 | 0.024 | 62.7 |

Carolina Panthers | NFC | 7.5 | 0.034 | 37.5 |

Cincinnati Bengals | AFC | 6.0 | 0.026 | 56.1 |

Detroit Lions | NFC | 7.0 | 0.025 | 62.3 |

Green Bay Packers | NFC | 8.9 | 0.014 | 93.9 |

Houstan Texans | AFC | 7.6 | 0.019 | 62.6 |

Indianapolis Colts | AFC | 5.7 | 0.027 | 12.2 |

Jacksonville Jaguars | AFC | 4.7 | 0.031 | 31.3 |

Minnesota Vikings | NFC | 5.9 | 0.035 | 18.5 |

New England Patriots | AFC | 8.1 | 0.020 | 81.1 |

New Orleans Saints | NFC | 8.1 | 0.021 | 81.2 |

Oakland Raiders | AFC | 7.8 | 0.043 | 50.2 |

San Francisco 49ers | NFC | 6.6 | 0.010 | 81.3 |

Tennessee Titans | AFC | 6.6 | 0.025 | 56.2 |

Washington Redskins | NFC | 6.2 | 0.043 | 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.

**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.

**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.

**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 a 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 | |

- Select your answer -<>=Item 9 |

Answer #1

Consider the variables

Y : Percentage of games won

X1 : Average number of passing yards per attempt

X2 : Number of interaction thrown per attempt.

**a)** We have to obtain regression equation that
could be used to predict the percentage of games won given average
number of passing yards per attempt.

i.e. We have to obtain simple linear equation Y on X1

By using R

>
y=c(50.1,62.7,37.5,56.1,62.3,93.9,62.6,12.2,31.3,18.5,81.1,81.2,50.2,81.3,56.2,31.2)

>
x1=c(6.7,7.3,7.5,6,7,8.9,7.6,5.7,4.7,5.9,8.1,8.1,7.8,6.6,6.6,6.2)

> a=lm(y~x1)

> a

Call:

lm(formula = y ~ x1)

Coefficients:

(Intercept) x1

**-57.78 16.20**

From R-output

The regression equation Y on X1 is

**Y = -57.78 + 16.20 * X1.**

**b)** We have to obtain regression equation that
could be used to predict the percentage of games won given number
of interaction thrown per attempt.

i.e. We have to obtain simple linear equation Y on X2

by using R

>
y=c(50.1,62.7,37.5,56.1,62.3,93.9,62.6,12.2,31.3,18.5,81.1,81.2,50.2,81.3,56.2,31.2)

>
x2=c(0.042,0.024,0.034,0.026,0.025,0.014,0.019,0.027,0.031,0.035,0.02,0.021,0.043,0.01,0.025,0.043)

> b=lm(y~x2)

> b

Call:

lm(formula = y ~ x2)

Coefficients:

(Intercept) x2

**99.08 -1633.15**

From R -output

The line of regression Y on X2 is

**Y = 99.08 - 1633.15 * X2**

**c)** We have to obtain regression equation that
could be used to predict the percentage of games won given average
number of passing yards per attempt and number of interaction
thrown per attempt.

i.e. We have to obtain multiple linear regression Y on X1 and X2.

Y is dependent variable and X1 and X2 are independent variables.

By using R

>
y=c(50.1,62.7,37.5,56.1,62.3,93.9,62.6,12.2,31.3,18.5,81.1,81.2,50.2,81.3,56.2,31.2)

>
x1=c(6.7,7.3,7.5,6,7,8.9,7.6,5.7,4.7,5.9,8.1,8.1,7.8,6.6,6.6,6.2)

>
x2=c(0.042,0.024,0.034,0.026,0.025,0.014,0.019,0.027,0.031,0.035,0.02,0.021,0.043,0.01,0.025,0.043)

> d=data.frame(y,x1,x2)

> d

y x1 x2

1 50.1 6.7 0.042

2 62.7 7.3 0.024

3 37.5 7.5 0.034

4 56.1 6.0 0.026

5 62.3 7.0 0.025

6 93.9 8.9 0.014

7 62.6 7.6 0.019

8 12.2 5.7 0.027

9 31.3 4.7 0.031

10 18.5 5.9 0.035

11 81.1 8.1 0.020

12 81.2 8.1 0.021

13 50.2 7.8 0.043

14 81.3 6.6 0.010

15 56.2 6.6 0.025

16 31.2 6.2 0.043

> c=glm(data=d,y~x1+x2)

> c

Call: glm(formula = y ~ x1 + x2, data = d)

Coefficients:

(Intercept) x1 x2

**-0.2792 12.5391 -1173.6054**

Degrees of Freedom: 15 Total (i.e. Null); 13 Residual

Null Deviance: 8383

Residual Deviance: 1976 AIC: 130.5

From R-output

**Y = -0.2792 + 12.5391 * X1 - 1173*6054 * X2**

**d)** Given

X1 : 6.2 and X2 = 0.036

Predicted percentage of won = -0.2792 + 12.5391 * (6.2) - 1173.6054*0.036 = 35.24

**Predicted Percentage = 35.24**

Since Total number of games = 9+ 7= 16

number of wins = 7

**Actual percentage of win = 7 / 16 * 100 =
43.75**

**The difference between actual and predicted percentage
(error) = 43.75 - 35.24 = 8.51.**

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 one full season.
Team
Conf
Yds/Att
Int/Att
Win%
Arizona Cardinals
NFC...

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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