Question

Suppose you are a rabid football fan and you get into a discussion about the importance of offense (yards made) versus defense (yards allowed) in terms of winning a game. You decide to look at football statistics to provide evidence of which variable is a stronger predictor of wins.

Part a) Develop a simple linear regression that compares wins to yards made. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part b) Develop a simple linear regression that compares wins against yards allowed. Perform the following diagnostics on this regression: 1) test of significance on the slope; 2) assess the fit of the line using the appropriate statistics; 3) interpret the slope of the equation if the slope is significant. Part c) Which explanatory variable provides a better prediction of the response variable? Support your answer briefly by citing the appropriate diagnostics. Note: Use an alpha of .05 for both tests of significance. Be sure to show ALL steps of the hypothesis testing procedure

EXCEL DATA TO USE.

Team	Win	Rush	Pass	Yds Allowed	Yds Made
Arizona Cardinals	62.50	93.40	251.00	346.40	344.40
Atlanta Falcons	56.30	117.21	223.19	348.90	340.40
Baltimore Ravens	56.30	137.51	213.69	305.00	351.20
Buffalo Bills	37.50	116.71	157.19	340.60	273.90
Carolina Panthers	50.00	156.16	174.94	315.80	331.10
Chicago Bears	43.80	93.24	217.06	337.80	310.30
Cincinnati Bengals	62.50	128.48	180.63	301.40	309.10
Cleveland Browns	31.30	130.45	129.75	389.30	260.20
Dallas Cowboys	68.80	131.46	267.94	315.90	399.40
Denver Broncos	50.00	114.71	226.69	315.00	341.40
Detroit Lions	12.50	101.00	198.00	392.10	299.00
Green Bay Packers	68.80	117.85	261.25	284.40	379.10
Houston Texans	56.30	92.23	290.88	324.90	383.10
Indianapolis Colts	87.50	80.91	282.19	339.20	363.10
Jacksonville Jaguars	53.80	126.85	209.75	352.30	336.60
Kansas City Chiefs	25.00	120.58	182.63	388.20	303.20
Miami Dolphins	43.80	139.48	198.13	349.30	337.60
Minnesota Vikings	75.00	119.85	259.75	305.50	379.60
New England Patriots	62.50	120.05	277.25	320.20	397.30
New Orleans Saints	81.30	131.61	272.19	357.80	403.80
New York Giants	50.00	114.81	251.19	324.90	366.00
New York Jets	56.30	172.25	148.75	252.30	321.00
Oakland Raiders	31.30	106.29	159.81	361.90	266.10
Philadelphia Eagles	68.80	102.34	255.56	321.10	357.90
Pittsburgh Steelers	56.30	112.05	259.25	305.30	371.30
Saint Louis Rams	6.30	111.50	167.88	327.00	279.38
San Diego Chargers	81.30	88.94	271.13	326.40	360.06
San Francisco 49ers	50.00	100.00	190.75	356.40	290.75
Seattle Seahawks	31.30	97.86	218.94	372.80	316.80
Tampa Bay Buccaneers	18.80	101.69	185.81	365.60	287.50
Tennessee Titans	50.00	161.96	189.44	365.60	351.40
Washington Redskins	25.00	94.38	218.13	319.70	312.50

Answer 1

A.1)  Regression Analysis: Win versus Yds Made

The regression equation is
Win = - 79.0 + 0.386 Yds Made

the t.test for the Coefficient is given below

Predictor	Coefficient	SE Coef	T	P.Value
Constant	-79.03	19.7	-4.01	0.0000
Yds Made	0.38603	0.05838	6.61	0.0000

A. 2)  R-Sq and R-Sq(adj) are given below which explain how best the regression line fits the data.

R-Sq = 59.3% R-Sq(adj) = 58.0%

Here we have R-Sq = 59.3% which imply that 60% of variation in win (dependent variable) is explained by the Yds Made (independent variable).

A. 3) Since the Coefficient = 0.38603 is significant as calculated p.value = 0.0000 is less then 0.05 significance level. Here we have Coefficient = 0.38603, which imply that a unit change in Yds Made (independent variable) will result 0.38603 in win (dependent variable).

B.1) Regression Analysis: Win versus Yds Allowed

The regression equation is
Win = 151 - 0.300 Yds Allowed

Predictor	Coefficient	SE Coef	T	P.Value
Constant	151.01	35.05	4.31	0.0000
Yds Made	-0.3003	0.1041	-2.88	0.0070

B. 2)  R-Sq and R-Sq(adj) are given below which explain how best the regression line fits the data.

R-Sq = 21.7% R-Sq(adj) = 19.1%

Here we have R-Sq = 21.7% which imply that 22% of variation in win (dependent variable) is explained by the Yds Allowed (independent variable).

B. 3) Since the Coefficient = -0.3003 is significant as calculated p.value = 0.0070 is less then 0.05 significance level. Here we have Coefficient = -0.3003, which imply that a unit change in Yds Allowed (independent variable) will result -0.3003 in win (dependent variable).

C.1) The explanatory variable (Yds Made) provides a better prediction of the response variable (Win) as R-sq corresponding to first model (Win = - 79.0 + 0.386 Yds Made) is R-Sq = 59.3% and R-sq corresponding to Second model (Win = 151 - 0.300 Yds Allowed) is R-Sq = 21.7%.