Chapter 27
Inferences for Regression
497
Chapter 27 – Inferences for Regression
1. Ms. President?
a)
The equation of the line of best fit for these data points is
%
ˆ
..
(
)
Yes
Year
=−
+
5 583
0 999
,
where
Year
is measured in years since 1900.
According to the linear model, the percentage
of people willing to vote for a female candidate for president is increasing by about 1%
each year.
b)
H
0
: There has been no change in the percentage of people willing to vote for a female
candidate for president.
β
1
0
=
()
H
A
: There has been a change in the percentage of people willing to vote for a female
candidate for president.
1
0
≠
c)
Assuming the conditions have been met, the sampling distribution of the regression slope
can be modeled by a Student’s
t
model with (16 – 2) = 14 degrees of freedom.
We will use a
regression slope
t
test.
The value of
t
=
15.1.
The
P
value
≤
0.0001 means that the association we see in the data is
unlikely to occur by chance.
We reject the null hypothesis, and conclude that there is
strong evidence that the percentage of people willing to vote for a female presidential
candidate is increasing.
d)
94.2% of the variation in the percentage of people willing to vote for a female president is
explained by the year.
2. Drug use.
a)
The equation of the line of best fit for these data points is
%
ˆ
.
.
(%
)
OtherDrugs
Marijuana
+
3 068
0 615
.
According to the linear model, the percentage
of ninth graders in these countries who use other drugs increases by about 0.615% for each
additional 1% of ninth graders who use marijuana.
b)
H
0
: There is no linear relationship between marijuana use and use of other drugs.
1
0
=
H
A
: There is a linear relationship between marijuana use and use of other drugs.
1
0
≠
c)
Assuming the conditions have been met, the sampling distribution of the regression slope
can be modeled by a Student’s
t
model with (11 – 2) = 9 degrees of freedom.
We will use a
regression slope
t
test.
The value of
t
=
7.85.
The
P
value of 0.0001 means that the association we see in the data is
unlikely to occur by chance.
We reject the null hypothesis, and conclude that there is
strong evidence that the percentage of ninth graders who use other drugs is related to the
percentage of ninth graders who use marijuana.
Countries with a high percentage of ninth
graders using marijuana tend to have a high percentage of ninth graders using other drugs.
d)
87.3% of the variation in the percentage of ninth graders using other drugs can be
accounted for by the percentage of ninth graders using marijuana.
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Part VII
Inference When Variables are Related
e)
The use of other drugs is associated with marijuana use, but there is no proof of a
causeandeffect relationship between the two variables.
There may be lurking variables
present.
3. No opinion.
a)
H
0
: There has been no change in the percentage of people expressing no opinion about
their willingness to vote for a female candidate for president.
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 Spring '11
 Wells
 Statistics, Regression Analysis, Errors and residuals in statistics, coeff, linear relationship, regression slope

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