0, observed values for Area are also below the regression line, so this prediction is probably an
overestimate.
4.
The residual plot for Model I: Log (Area)
vs.
Time shows a random scatter of
points on either side of the line residuals = 0, suggesting a good fit.
5.
Model I:
log Area
0.34057
0.115582 Time
, so for 5.5 seconds,
0.97627
2
log Area
0.34057
0.115582
5.5
log Area
0.97627
Area
10
9.47 cm .
598
The Practice of Statistics, 4/e Chapter 12
© 2011 BFW Publishers
Test 12A
Part I
1.
d
―SE Coef‖ stands for standard error of the coefficient—
slope in this case.
This is the
estimate (from the sample) of standard deviation of the sample distribution of slope.
2.
e
S = 145.851 is the standard deviation of the residuals, and thus measures how far, on
average, observed word counts are from word counts predicted by the regression
equation.
3.
a
The
P

value for this test is on the line ―File size‖ and is therefore 0.022.
A
P
value less
than the level of significance provides enough evidence against
H
0
to reject it.
4.
d
Statement I is not a condition required for regression inference.
The Normality condition
requires that the value of the response variable be Normally distributed at each value of
the explanatory variable.
Statements II a
nd III are the ―Equal variance‖ and ―Linear‖
conditions.
5.
b
0.092498 is the slope of the sample regression line, and thus estimates the change in the
predicted value of the response variable for a oneunit change in the explanatory variable.
6.
c
Margin of error is
(
critical value)*(standard error of estimate).
The critical
t
for 90%
confidence and 40
–
2 = 38 degrees of freedom is not in table B, but must be slightly
larger than the critical
t
for 40 degrees of freedom, which is 1.684, thus the correct choice
must be
1.686 0.0106
.
7.
d
Statement I is the appropriate interpretation of a ―U

shaped‖ pattern in residuals.
Statement II is true because the residuals near x = 1982 are all below the regression line,
so the line overestimates observed values.
Without the scatterplot, we cannot determine
whether number of employees increases or decreases with year, so we don’t know if
Statement III is correct.
8.
b
If
, then log
log
log
x
y
ab
y
a
b x
, so the relationship between log
y
and
x
is linear
with slope log
b
and intercept log
a
.
9.
b
The ―Coef‖ column provides the slope and intercept of the regression equation for the
transformed variables.
This regression is for log
y
vs.
x¸
so the equation is
log
449.7
0.228
y
x
.
10. c
ln
5.36
3.216 ln12
5.36
3.216 2.4849
2.632
W
, so
2.632
13.894
W
e
Part II
11.
(a)
L
inear: the scatterplot shows a weak linear relationship between sleep and GPA, and the
residual plot shows a random scatter of points about the line residual = 0.
I
ndependent:
Study
time and score for randomlyselected students should be independent.
We are sampling without
replacement, but there are more than
10 10
100
students in the class.
N
ormal
:
The Normal
probability plot of the residuals is roughly linear, which suggests that test scores are roughly
Normally distributed for each value study time.
E
qual variance: the small sample size makes