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. (Let x₁ represent Yds/Att, x₂ represent Int/Att, and y represent Win%.)

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 three decimal places.)

=

What proportion of variation in the sample values of proportion of games won (in %) does this model explain? (Round your answer to two decimal places.)

%

(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 three decimal places.)

=

What proportion of variation in the sample values of proportion of games won (in %) does this model explain? (Round your answer to two decimal places.)

%

(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 three decimal places.)

=

What proportion of variation in the sample values of proportion of games won (in %) does this model explain? (Round your answer to two decimal places.)

%

(d)

Suppose the average number of passing yards per attempt for a certain team was 6.1, and the team's 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.)

%

Suppose 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 identical to the actual value. The predicted value is lower than the actual value.

(e)

Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?

Based on the coefficient of determination from the two models using the average number of passing yards per attempt as the independent variable, the model using only the average number of passing yards per attempt as the independent variable ---Select--- is is not the best fit.