47. a.
95 PI is 20.21, 43.69, no
b.
28.53, 51.92, at least 90
49.
431.3, 628.5
51. a.
45 is closer to
b.
46.28, 46.78
c.
47.56, 49.84
53.
a narrower than b, c narrower than d, a narrower than c, b narrower than d
57.
If, for example, 18 is the minimum age of eligibility, then for most people
.
59. a.
.966
b.
The percent dry fiber weight for the first specimen tends to be larger than for the second.
c.
No change
d.
93.3
e.
, so there does appear to be such a relationship.
61. a.
. Using either , yes.
b.
.560 56, same
63.
, yet ; so
cannot be rejected.
65. a.
.481
b.
, so at level .01, no linear associ- ation.
c.
At level .01, no positive linear association, but at level .05, there does appear to be positive linear association.
t 5 1.98, P-value 5 .07
H : r 5 0
t 5 2.44 , 2.776
r 5 .773
or .01 a 5
.05 r 5
.748, t 5 3.9, P-value 5 .001 t 5
14.9, P-value 0 y
x 2 18 x 5
45.18
67. a.
Reject H
b.
No. , which
indicates only a weak relationship. c.
Yes, but very large , so no practical
significance.
69. a.
95 CI: .888, 1.086
b.
95 CI: 47.730, 49.172
c.
95 PI: 45.378, 51.524
d.
Narrower for , since 25 is closer to
e.
.981
71. a.
, so don’t reject H
b.
.970
73. a.
.507
b.
.712
c.
, so reject
and conclude that there is a useful linear relationship.
d.
A 95 CI is 1.056, 1.275.
e.
1.0143, .2143
75. a. y
1.69 ⫹ .0805x b. y ⫽ ⫺20.40 ⫹ 12.2254x c. .984
for both regressions.
77. a.
A substantial linear relationship
b. c.
98.3
d. e.
Yes;
f.
.0394, .0499
g.
.762, .858
81. b.
.573
87.
, so it is plausible that .
b
1
5 g
1
t 5 2 1.14
t 5 19.96
.7702, 2.0902 y 5 2
.08259 1 .044649x H
: b
1
5 P
-value 5 .0013 , .01 5 a t 5 2
1.24 . 22.201 x
x 5 25
n 1 r .022
P -value 5 .00032 1 z 3.6 1 r .16
1. a.
6.32, 8.37, 8.94, 8.37, and 6.32
b.
7.87, 8.49, 8.83, 8.94, and 2.83
c.
The deviation is likely to be much smaller for the x values of part b.
3. a.
Yes.
b. ⫺
.31, ⫺.31, .48, 1.23, ⫺1.15, .35, ⫺.10, ⫺
1.39, .82, ⫺.16, .62, .09, 1.17, ⫺1.50, .96, .02, .65, ⫺2.16, ⫺
.79, 1.74. Here ee ranges between .57 and .65, so e is close to es.
c.
No.
5. a.
About 98 of observed variation in thickness is explained by the relationship.
b.
A nonlinear relationship
7. a.
.776
b.
Perhaps not, because of curvature.
c.
Substantial curvature rather than a linear pattern, implying inadequacy of the linear model. A parabola
quadratic regression provides a significantly better fit.
9.
For set 1, simple linear regression is appropriate. A quad- ratic regression is reasonable for set 2. In set 3, 13, 12.74
appears very inconsistent with the remaining data. The esti- mated slope for set 4 depends largely on the single observa-
tion 19, 12.5, and evidence for a linear relationship is not compelling.
11. c.
increases, and decreases.
13.
t with ;
.02
15. a.
A curved pattern
b.
A linear pattern
c. d.
A 95 PI is 3.06, 6.50.
e.
One standardized residual, corresponding to the third observation, is a bit large. There are only two positive
standardized residuals, but two others are essentially 0. The patterns in a standardized residual plot and normal
probability plot are marginally acceptable.
17. a. c.
, so don’t reject H
.
d.
, so reject H .
19. a.
No
b.
, where so .
c. d.
using transformed values,
, so don’t reject H .
21. a. b.
yˆ 5 15.17
mˆ
Y x
5 18.14 2 1485x
f 5 .33 , 8.68 5 F
.01,1,15
SSE 5 1.39587, SSPE 5 1.36594 aˆ 5
3.70034 10
2 5
, yˆr 5 6.7748, yˆ 5 875.5 bˆ 5 bˆ
1
5 3735.45, bˆ
5 2 10.2045
Y 5 ae
b t
P Y
r 5 ln Y, Y
r 5 b 1 b
1
1t 1 Pr H
: b 5 1, t 5 24.30 t 5 2
1.07 bˆ 5
1.254 bˆ
5 2 .468, aˆ 5 .626,
18.109, gy
i
r
2
5 16.572, bˆ
1
5 1.254,
gxr
i
y r
i
5 gxr
i
5 15.501,
gyr
i
5 13.352,
gxr
i 2
5 20.228,
Y 5 ax
b
P n 2
2 df V
Y
i
2 Yˆ
i
V Yˆ
i
Chapter 13
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
23.
For the exponential model, , which does
depend on x. A similar result holds for the power model.
25.
The z ratio for b
1
is highly significant, indicating that the like- lihood of a level being acceptable does decrease as the level
increases. We estimate that for each 1 dBA increase in noise level, the odds of acceptability decreases by a factor of .70.
27. b.
52.88, .12
c.
.895
d.
No
e.
48.54, 57.22
f.
42.85, 62.91
29. a. b.
c.
Yes. from Minitab
d.
individual confidence levels 96:
level 1
joint confidence 98
t 5 2 6.55, P-value 5 .003
R
2
5 .995
SSE 5 16.8, s 5 2.048 V
Y|x 5 a
2
e
2bx
s
2
55. a.
The dependent variable is , and the predictors are
and ; .
b.
Now regress against and .
c.
1.24, 5.78
57. k
R
2
adj. R
2
C
k
1 .676
.647 138.2
2 .979
.975 2.7
3 .9819
.976 3.2
4 .9824
4
a.
The model with
b.
No
59.
The model with predictors x
1
, x
3
, and x
5
61.
No. All R
2
values are much less than .9.
63.
The impact of these two observations should be further investigated. Not entirely. The elimination of observation 6
followed by re-regressing should also be considered.
65. a.
The two distributions have similar amounts of variability, are both reasonably symmetric, and contain no outliers. The
main difference is that the median of the crack values is about 840, whereas it is about 480 for the no-crack values.
A 95 t CI for the difference between means is 132, 557.
b.
for the simple linear regression model, , but one standardized
residual is Including an indicator for crack–no
crack does not improve the fit, nor does including an indicator and interaction predictor.
67. a.
When gender, weight, and heart rate are held fixed, we esti- mate that the average change in VO
2
max associated with a 1-minute increase in walk time is
.
b.
When weight, walk time, and heart rate are held fixed, the esti-
mate of average difference between VO
2
max for males and females is .6566.
c. d.
.706
e.
, so there does appear to be a useful relationship.
69. a.
No. There is substantial curvature in the scatter plot.
b.
Cubic regression yields and a 95 PI of
261.98, 295.62, and the cubic predictor appears to be important .
A regression
of y
versus has
, but there is a very large standardized resid- ual and the standardized residual plot is not satisfactory.
71. a.
. pH is a candi- date for deletion. Note that there is one extremely large
standardized residual.
b.
, adjusted
c.
, don’t reject . The group of second-order predictors does not
appear to be useful.
d.
, and now all six predictors are judged important the largest P-value for any
t -ratio is .016; the importance of pH
2
was masked in the test of c. Note that there are two rather large standardized
residuals. R
2
5 .871, f 5 28.50, P-value 5 .000
b
20
5 H
: b
6
5 c 5 f 5
1.08, P-value . .10 R
2
5 .774, f 5 6.29, P-value 5 .002
R
2
5 .920
R
2
5 .802, f 5 21.03, P-value 5 .000
r
2
5 .991
lnx P-value 5 .001
R
2
5 .998
f 5 9.0 4.89 5 F
.01,4,15
3.669, 2.519 2
.0996 2
4.11 P
-value for model utility 5 0 r
2
5 .577
k 5 2
x
2
5 b x
1
5 a lnq
.1815, aˆ 5 4.7836, qˆ 5 18.27 gˆ 5 bˆ
2
5 bˆ 5 bˆ
1
5 .9450,
x
2
5 lnb
x
1
5 lna
lnq
.671,3.706, .00498, ⫺.00135 e.
69.531, 76.186, 66.271, 79.446, using software
31. a.
.980
b.
.747, much less than .977 for the cubic model.
c.
Yes, since .
d.
6.31, 6.57, 6.06, 6.81
e. t ⫽ ⫺
5.6, P-value ⫽ 0
33. a.
.9671, .9407
b. c.
, so the cubic term should be deleted.
d.
Identical
e.
.987, .994, yes
35. 37. a.
4.9
b.
When number of deliveries is held fixed, the average change in travel time associated with a 1-mile
increase in distance traveled is .060 hr. When distance trav- eled is held fixed, the average change in travel time associ-
ated with one extra delivery is .900 hr.
c.
.9861
39. a.
77.3
b.
40.4
41.
, so P-value . The
cho- sen model appears to be useful.
43. a.
48.31, 3.69
b.
No. If x
1
increases, either x
3
or x
2
must change.
c.
Yes, since P
-value
d.
Yes, using , since
and P-value .
45. a.
, so there does appear to be a use- ful linear relationship between y and at least one of the
predictors.
b.
.935
c.
9.095, 11.087
47. b.
, so conclude that the model is useful.
c.
, so reject ;
garbage does appear to provide additional useful information.
d.
1479.8, 1531.1, reasonable precision
e.
A 95 PI is 1435.7, 1575.2.
49. a. b .
, s o reject H
and conclude that the model is useful. c. 78.28,
115.38
d.
38.50, 155.16
e.
46.91, 140.66
f.
No. , so
cannot be rejected.
51. a.
No
b.
. There does appear to be a useful linear relationship.
c.
6.16, 3.304, 16.67, 31.91
d.
, so
cannot be rejected. The quad- ratic terms can be deleted.
H : b
3
5 b
4
5 b
5
5 f 5
3.44 , 4.07 5 F
.05,3,8
f 5 5.04 3.69 5 F
.05,5,8
H : b
1
5 P
-value 5 .208 f 5
14.9 8.02 5 F
.05,2,9
96.8303, 25.8303 H
: b
3
5 P
-value 5 .034 .05 5 a P
-value 5 .000 f 5
87.6, P-value 5 0 5
.003 t 5
3.496 a 5
.01 5
.001. f 5
18.924, ,
.001 f 5
24.4 . 5.12 5 F
.001,6,30
yˆ 5 7.6883e
.1799x2.0022x
2
t 5 2 , 3.182 5 t
.025,3
.96034944 .0000492x
3
2 .000446058x
2
1 .007290688x 1
t 5 14.18, P-value 5 0
2
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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