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 (Win96) for a random sample of 16 NFL teams for a season Conf NFC NFC NFC AFC NFC NFC AFC AFC AFC NFC AFC NFC AFC NFC AFC NFC Yds/Att Team Arizona Cardinals Atlanta Falcons Carolina Panthers Cincinnati Bengals Detroit Lions Green Bay Packers Houstan Texans Indianapolis Colts Jacksonville Jaguars Minnesota Vikings New England Patriots New Orleans Saints Oakland Raiders San Francisco 49ers Tennessee Titans Washington Redskins Int/Att 0.044 0.021 0.032 0.027 0.023 0.015 0.018 0.025 0.033 0.032 0.021 0.021 0.043 0.010 0.023 0.041 Win% 49.9 62.7 37.7 56.2 62.3 93.8 62.7 12.5 31.0 18.7 81.0 81.4 49.9 81.4 56.1 31.2 7.3 7.5 6.3 7.7 4.7 8.4 7.4 6.7 6.6 6.6 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 1 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 1 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% 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 percentagee .Yds/Att Int/Att Actual percentage Select your answer

Answer 1

Answer:

a).

win% = -60.6+16.5*yds/att

b).

win%= 94.2 +(-1487.8)*Int/Att

c). win% = -14.4+13.3*yds/Att +(-889.9)*int/Att

d).

predicted percentage 36 < actual percentage 44

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	r²	0.603	n	16
	r	0.776	k	1
	Std. Error of Estimate	15.398	Dep. Var.	winn%
Regression output						confidence interval
variables		coefficients	std. error	t (df=14)	p-value	95% lower	95% upper
Intercept	a =	-60.597
ydsatt	b =	16.514	3.582	4.610	.0004	8.832	24.197
ANOVA table
Source	SS	df	MS	F	p-value
Regression	5,039.831	1	5,039.831	21.26	.0004
Residual	3,319.473	14	237.105
Total	8,359.304	15
Regression Analysis
	r²	0.393	n	16
	r	-0.627	k	1
	Std. Error of Estimate	19.036	Dep. Var.	winn%
Regression output						confidence interval
variables		coefficients	std. error	t (df=14)	p-value	95% lower	95% upper
Intercept	a =	94.173
intatt	b =	-1,487.807	494.088	-3.011	.0093	-2,547.521	-428.093
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,285.905	1	3,285.905	9.07	.0093
Residual	5,073.399	14	362.386
Total	8,359.304	15
Regression Analysis
	R²	0.721
	Adjusted R²	0.678	n	16
	R	0.849	k	2
	Std. Error of Estimate	13.402	Dep. Var.	winn%
Regression output						confidence interval
variables		coefficients	std. error	t (df=13)	p-value	95% lower	95% upper
Intercept	a =	-14.384
ydsatt	b1 =	13.301	3.406	3.905	.0018	5.942	20.660
intatt	b2 =	-889.874	380.047	-2.341	.0358	-1,710.916	-68.833
ANOVA table
Source	SS	df	MS	F	p-value
Regression	6,024.500	2	3,012.250	16.77	.0003
Residual	2,334.805	13	179.600
Total	8,359.304	15
Predicted values for: winn%
			95% Confidence Interval		95% Prediction Interval
ydsatt	intatt	Predicted	lower	upper	lower	upper	Leverage
6.2	0.036	36.047	25.730	46.363	5.311	66.782	0.127