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	6.3	0.041	49.7
Atlanta Falcons	NFC	7.1	0.021	62.4
Carolina Panthers	NFC	7.6	0.033	37.6
Cincinnati Bengals	AFC	6.1	0.028	56.4
Detroit Lions	NFC	7.4	0.024	62.3
Green Bay Packers	NFC	9.1	0.016	93.7
Houstan Texans	AFC	7.4	0.021	62.2
Indianapolis Colts	AFC	5.7	0.025	12.2
Jacksonville Jaguars	AFC	4.5	0.034	31.3
Minnesota Vikings	NFC	6.0	0.033	18.6
New England Patriots	AFC	8.1	0.022	81.3
New Orleans Saints	NFC	8.2	0.020	81.1
Oakland Raiders	AFC	7.7	0.045	49.8
San Francisco 49ers	NFC	6.5	0.011	81.0
Tennessee Titans	AFC	6.5	0.026	56.3
Washington Redskins	NFC	6.5	0.040	31.4

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.

Win%= ----------- + ---------. Yds/Att

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.

Win%= ----------- + ---------. Int/Att

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.

Win%= ----------- + ---------. Yds/Att + ---------. Int/Att

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
	(</>/=)

Answer 1

a)

using excel data analysis tool for regression,steps are:

write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	0.7135
R Square	0.5091
Adjusted R Square	0.4740
Standard Error	17.0943
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4242.37	4242.37	14.5180	0.0019
Residual	14	4091.02	292.22
Total	15	8333.39
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-48.8415	27.3805	-1.7838	0.0961	-130.3489	32.6659
X	14.8940	3.9089	3.8102	0.0019	3.2577	26.5303

Win%= -48.8 + 14.9*Yds/Att

b)

using excel data analysis tool for regression,steps are:

write data>menu>data>data analysis>regression>enter required labels>ok> and following o/p is obtained

Regression Statistics
Multiple R	-0.6384
R Square	0.4076
Adjusted R Square	0.3653
Standard Error	18.7780
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3396.78	3396.78	9.6331	0.0078
Residual	14	4936.61	352.61
Total	15	8333.39
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	97.9249	14.8476	6.5954	0.0000	53.7261	######
X	-1589.7693	512.2131	-3.1037	0.0078	-3114.5473	######

Win%= 97.9 - 1589.8 *  Int/Att

c)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.829471
R Square	0.688023
Adjusted R Square	0.640026
Standard Error	14.14167
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	2	5733.562	2866.781	14.33486	0.000515
Residual	13	2599.827	199.9867
Total	15	8333.389
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	3.751268	29.73262	0.126167	0.90153	-60.4822	67.98469	-60.4822	67.98469
Yds/Att	11.73849	3.434027	3.418287	0.004579	4.319725	19.15725	4.319725	19.15725
Int/Att	-1118.57	409.6356	-2.73065	0.017161	-2003.53	-233.607	-2003.53	-233.607

Win%= 3.8 + 11.7 *Yds/Att - 1118.6 * Int/Att

d)

actual win percentage=7/16=43.75%

predicted win % = 3.8 + 11.7 *6.2 - 1118.6*0.036 = 36.07%

so, predicted percentage < actual percentage