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  NFL teams for a season

Team	Conf	Yds/Att	Int/Att	Win%
Arizona Cardinals	NFC	6.7	0.043	50.0
Atlanta Falcons	NFC	7.0	0.023	62.7
Carolina Panthers	NFC	7.2	0.033	37.4
Cincinnati Bengals	AFC	6.0	0.028	56.4
Detroit Lions	NFC	7.3	0.023	62.4
Green Bay Packers	NFC	8.9	0.013	93.8
Houstan Texans	AFC	7.3	0.020	62.6
Indianapolis Colts	AFC	5.7	0.025	12.3
Jacksonville Jaguars	AFC	4.4	0.034	31.0
Minnesota Vikings	NFC	5.7	0.034	18.6
New England Patriots	AFC	8.5	0.019	81.4
New Orleans Saints	NFC	8.1	0.021	81.4
Oakland Raiders	AFC	7.7	0.045	49.9
San Francisco 49ers	NFC	6.4	0.013	81.5
Tennessee Titans	AFC	6.8	0.026	56.4
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.

    

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.

    

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.

      

d. The average number of passing yards per attempt for the Kansas City Chiefs was  and the number of interceptions thrown per attempt was . 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  wins and  losses.) Compare your prediction to the actual percentage of games won by the Kansas City Chiefs (to whole number).

Predicted percentage		Actual percentage
	- Select your answer -<>=Item 9

Answer 1

a)

using excel data analysis tool for regression,following o/p is obtained

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.740304094
R Square	0.548050151
Adjusted R Square	0.515768019
Standard Error	16.47902495
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4610.214315	4610.214315	16.97688835	0.001040086
Residual	14	3801.815685	271.5582632
Total	15	8412.03
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-51.6928	26.0583	-1.9837	0.0673	-107.5823	4.1967
Yds/Att	15.3928	3.7358	4.1203	0.0010	7.3802	23.4054

Win% = -51.7 +15.4*Yds/Att

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b)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.660631241
R Square	0.436433636
Adjusted R Square	0.396178896
Standard Error	18.4017413
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	3671.29284	3671.29284	10.84179485	0.005339404
Residual	14	4740.73716	338.6240829
Total	15	8412.03
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	97.96	14.03	6.98	0.00	67.87	128.05
Int/Att	-1586.83	481.93	-3.29	0.01	-2620.46	-553.20

Win% = 98.0 - 1586.8*Int/Att

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c)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.849522219
R Square	0.721688001
Adjusted R Square	0.678870771
Standard Error	13.41975835
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	2	6070.861116	3035.430558	16.8550836	0.000245164
Residual	13	2341.168884	180.0899141
Total	15	8412.03
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.63933685	28.30204765	0.057922906	0.954690912	-59.50351982	62.78219352	-59.50351982	62.78219352
Yds/Att	11.94979754	3.273698557	3.650243702	0.002935963	4.877401789	19.0221933	4.877401789	19.0221933
Int/Att	-1077.038815	378.1842556	-2.84792082	0.013711504	-1894.056228	-260.021403	-1894.056228	-260.021403

Win % = 1.6 +11.9*Yds/Att - 1077.0*Int/Att

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