STAT 101  Agresti
Homework 8 Solutions
11/15/10
Chapter 9
9.13.
120
0.60
0.90
80
y
x
s
b
r
s
=
=
=
;
a
y
bx
=

= 500 – 0.90(480) = 68;
ˆ
y
a
bx
= +
= 68 + 0.90
x
.
9.18. (a) (i)
ˆ
y
= 30 + 0.60(100) = 90; (ii)
ˆ
y
= 30 + 0.60(50) = 60. (b)
(
29
x
y
r
b s
s
=
= 0.60(10/10) = 0.60.
(c)
r
= 1(10/10) = 1.0. (d)
r
= 0(10/10) = 0.
9.20. (a)
ˆ
y
= –0.105 + 0.546
x
; for each $1000 increase in GDP per person, the predicted annual oil
consumption per person increases by 0.55 barrels. (b)
r
= 0.847; there is a moderately strong positive
association between GDP per person and annual oil consumption per person. (c)
ˆ
y
=
–0.105 + 0.546(41) = 22.3;
ˆ
y
y

= 26 – 22.3 = 3.7; the predicted annual oil consumption per person
is
3.7 barrels higher than would be predicted by the regression line.
9.29. (a)
0
H
:
β
= 0 and
a
H
:
≠ 0,
t
=
b
/
se
= 0.294/0.0149 = 19.7,
P
< 0.001. There is extremely strong
evidence that number of years of mother’s education has a positive effect on number of years of
education. (b)
b
±
t
0.025
(
se
) = 0.294 ± 1.96(0.0149) = 0.265 to 0.323. We can be 95% confident that
falls between 0.265 and 0.323.
In the population, the mean number of years of education increases by
between 0.27 and 0.32 for each additional year of the mother’s education. (c) Since
r
= 0.37 is less than 1,
number of years of education is predicted to be fewer standard deviations from its mean than number of
years of mother’s education is from its mean.
9.32. (a)
P
= 0.0015. There is strong evidence of an association between number of hours spent in the
home on religious activity and political ideology, and the estimated slope shows that it is positive. In this
case, more hours spent in the home on religious activity is associated with being more conservative. (b)
While these results are statistically significant, the slope of 0.0064 is so close to 0 that it has no practical
significance.
For example, an increase in
x
of 10 hours a month corresponds to a
predicted change on the
political ideology scale of 0.064, which is extremely small because political ideology is on a scale from 1
to 7.
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View Full Document9.38. A correlation matrix follows.
Correlations
Food
Decor
Service
Cost
Food
Pearson Correlation
1
0.288(*)
0.616(**)
0.410(**)
Sig. (2tailed)
0.022
0.000
0.001
N
63
63
63
63
Decor
Pearson Correlation
0.288(*)
1
0.677(**)
0.820(**)
Sig. (2tailed)
0.022
0.000
0.000
N
63
63
63
63
Service
Pearson Correlation
0.616(**)
0.677(**)
1
0.718(**)
Sig. (2tailed)
0.000
0.000
0.000
N
63
63
63
63
Cost
Pearson Correlation
0.410(**)
0.820(**)
0.718(**)
1
Sig. (2tailed)
0.001
0.000
0.000
N
63
63
63
63
*
Correlation is significant at the 0.05 level (2tailed).
**
Correlation is significant at the 0.01 level (2tailed).
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 Fall '10
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 Standard Deviation, Mean

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