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 the 2011 season (NFL web site, February 12, 2012).

Click on the datafile logo to reference the data.

Team	Conference	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

Let x₁ represent Yds/Att.
Let x₂ represent Int/Att.

The average number of passing yards per attempt for the Pittsburgh Steelers during the 2011 season was 8, and the team’s number of interceptions thrown per attempt was 0.028. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Pittsburgh Steelers during the 2011 season. (Note: For the 2011 the 2011 season, the Pittsburgh Steelers' record was 7 wins and 9 loses.)

If required, round your answer to one decimal digit. Do not round intermediate calculations. 67.5%(correct)

Compare your prediction to the actual percentage of games won by the Pittsburgh Steelers. If required, round your answer to one decimal digit.

Q. The Pittsburgh Steelers performed worse than what we predicted by ? %.

Answer 1

result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.867461188
R Square	0.752488913
Adjusted R Square	0.714410284
Standard Error	12.60236794
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6277.014191	3138.507096	19.76144986	0.000114384
Residual	13	2064.655809	158.8196776
Total	15	8341.67
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-5.763283816	27.1467994	-0.212300674	0.835165005	-64.41037837
Yds/Att	12.94935632	3.185669555	4.064877446	0.001338458	6.067135667
Int/Att	-1083.787956	357.1165398	-3.034829909	0.009575422	-1855.291335

y^= -5.7633 + 12.9494 yds/att -1083.787956* int/Att

= -5.7633 + 12.9494 *8 -1083.787956* 0.028

= 67.4858

= 67.5 %

7 wins and 9 loses

hence actual % = 7/(7+9) *100 % = 43.75%

hence worse by 67.5 - 43.8%

= 23.7 %