The following table presents data on the ratings of quarterb

The following table presents data on the ratings of quarterbacks for the 2004 National Football League season (source: The Sports Network).

Player D. Culpepper, MIN D. McNabb, PHI B. Griese, TAM M. Bulger, STL B. Favre, GBP J. Delhomme, CAR K. Warner, NYG M. Hasselbeck, SEA7.14 A. Brooks, NOS T. Rattay, SFX M. Vick, ATL J. Harrington, DET V. Testaverde, DAL P. Ramsey, WAS J. McCown, ARI P. Manning, IND D. Brees, SDC B. Roethlisberger, PIT8.88 T. Green, KAN T. Brady, NEP C. Pennington, NYJ B. Volek, TEN J. Plummer, DEN D. Carr, HOU B. Leftwich, JAC C. Palmer, CIN Yards per Attempt Rating points 8.61 8.26 7.83 8.17 7.57 7.29 7.42 110.9 104.7 97.5 93.7 92.4 87.3 86.5 83.1 79.5 78.1 78.1 77.5 76.4 74.8 74.1 121.1 104.8 98.1 95.2 92.6 91 87.1 84.5 83.5 82.2 77.3 7.03 6.67 7.21 6.23 7.14 6.12 6.15 9.17 7.9 8.26 7.79 7.22 6.96 7.85 7.58 6.67 6.71

Solution

Regression Analysis

r²

0.787

n

30

r

0.887

k

1

Std. Error

5.713

Dep. Var.

rating (y)

ANOVA table

Source

SS

df

MS

F

p-value

Regression

3,378.5262

1  

3,378.5262

103.53

6.55E-11

Residual

913.7205

28  

32.6329

Total

4,292.2467

29  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=28)

p-value

99% lower

99% upper

Intercept

-5.5576

9.1594

-0.607

.5489

-30.8674

19.7522

number of yards

12.6519

1.2434

10.175

6.55E-11

9.2160

16.0878

Predicted values for: rating (y)

99% Confidence Interval

99% Prediction Interval

number of yards

Predicted

lower

upper

lower

upper

Leverage

8.8

105.7793

99.9292

111.6293

88.9449

122.6136

0.137

It is suspected that the rating (y) is related to the average number of yards gained per pass attempt (x).

Y=-5.5576+12.6519 x

A 99.00% confidence interval of intercept is: (-30.8674, 19.7522)

A 99.00% confidence interval of slope is: (9.2160, 16.0878)

Mean rating when x = 8.8 is:
A 99.00% prediction interval on the rating when the x₀ = 8.8 is : (88.9449, 122.6136)

Regression Analysis
	r²	0.787	n	30
	r	0.887	k	1
	Std. Error	5.713	Dep. Var.	rating (y)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,378.5262	1	3,378.5262	103.53	6.55E-11
Residual	913.7205	28	32.6329
Total	4,292.2467	29
Regression output				confidence interval
variables	coefficients	std. error	t (df=28)	p-value	99% lower	99% upper
Intercept	-5.5576	9.1594	-0.607	.5489	-30.8674	19.7522
number of yards	12.6519	1.2434	10.175	6.55E-11	9.2160	16.0878
Predicted values for: rating (y)
		99% Confidence Interval	99% Prediction Interval
number of yards	Predicted	lower	upper	lower	upper	Leverage
8.8	105.7793	99.9292	111.6293	88.9449	122.6136	0.137