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 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 6.1 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.)

___________ %

For this season the team's record was 7 wins and 9 losses. Compare your prediction to the actual percentage of games won by the team.

_____The predicted value is higher than the actual value.

_____The predicted value is lower than the actual value.    

_____The predicted value is identical to the actual value.

Answer 1

Linear Regression

We use Excel to solve the problem.

Data > data analysis > regression

a. Using yds/att as the independent variable we get the output as:

so the estimated equation is:

b. Using int/att as the independent variable we get the output as:

so the estimated equation is:

c. Using both as the independent variables we get:

So the estimated equation is:

d. When yds/att is 6.1 and int/att is 0.038, we get from the equation i.e. .

Thus the team is predicted to win 32.1% of games.

In practice the team won {7/(7+9)}*100%= 44%.

Hence the predicted value is lower than the actual value.