The following table presents data on the ratings of quarterbacks for the 2004 Na
ID: 3390209 • Letter: T
Question
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 6.71Explanation / Answer
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
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