Chapter 7 Recommended Homework Solutions
78.
a)
Estimated Effects and Coefficients for charge
Term
Coef
StDev Coef
T
P
Constant
1.000
0.4462
2.24
0.055
method
2.797
0.4462
6.27
0.000
position
0.640
0.4462
1.43
0.189
method*position
0.610
0.4462
1.37
0.209
b)
0.0
2.5
5.0
position
Mean
Interaction Plot for charge
The interaction plot does not indicate a significant interaction between Method and Position.
c) The tratios are given in the output shown in part a.
The tratios indicate that only Method is significant at
the
α
= 0.05 level.
d) The 95% confidence intervals are given by effect estimate
±
2(s.e.(effect))
where s.e.(effect) = 2[s.e.(coefficient)].
The s.e.(coefficient) is given in the Minitab output of part a.
Method: s.e.(effect) = 2(0.4462) = 0.8924
Approximate 95% confidence interval on the the effect of Method:

5.593
±
2(0.8924)
(

7.38,

0.3.81)
Position: s.e.(effect) = 2(0.4462) = 0.8924
Approximate 95% confidence interval for the effect of Position:

1.28
±
2(0.8924)
(

3.065, 0.505)
Method*Position: s.e.(effect)
= 2(0.4462) = 0.8924
Approximate 95% confidence interval for the effect of Method*Position:

1.22
±
2(0.8924)
(

3.005, 0.565)
e)
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The regression equation is
charge =  1.00  2.80 method  0.640 position  0.610 meth*pos
Predictor
Coef
StDev
T
P
Constant
1.0000
0.4462
2.24
0.055
method
2.7967
0.4462
6.27
0.000
position
0.6400
0.4462
1.43
0.189
meth*pos
0.6100
0.4462
1.37
0.209
Based on the regression analysis, only Method appears to be the significant factor.
This result is
equivalent to that obtained in part c.
The regression analysis and final model are
The regression equation is
charge =  1.00  2.80 method
Predictor
Coef
StDev
T
P
Constant
1.0000
0.4873
2.05
0.067
method
2.7967
0.4873
5.74
0.000
S = 1.688
RSq = 76.7%
RSq(adj) = 74.4%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
1
93.856
93.856
32.94
0.000
Error
10
28.490
2.849
Total
11
122.347
Unusual Observations
Obs
method
charge
Fit
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 Fall '06
 andersonrowland
 Normal Distribution, Normal probability plot, 74.4%, 76.7%, 72.2%

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