1.
There is some evidence that drinking moderate amounts of wine helps prevent heart
attacks. The table below gives data on yearly wine consumption (liters of alcohol
from drinking wine, per person) and yearly deaths from heart disease (deaths per
100,000 people) in 19 developed nations. (Data from M. H. Criqui, University of
California, San Diego, reported in the
New York Times
, December 28, 1994.)
Country
Alcohol
from wine
Heart disease
deaths
Country
Alcohol
from wine
Heart disease
deaths
Australia
2.5
211
Netherlands
1.8
167
Austria
3.9
167
New Zealand
1.9
266
Belgium
2.9
131
Norway
0.8
227
Canada
2.4
191
Spain
6.5
86
Denmark
2.9
220
Sweden
1.6
207
Finland
0.8
297
Switzerland
5.8
115
France
9.1
71
United Kingdom
1.3
285
Iceland
0.8
211
United States
1.2
199
Ireland
0.7
300
West Germany
2.7
172
Italy
7.9
107
Σ
x
= 57.5,
Σ
y
= 3,630,
Σ
x
2
= 287.39,
Σ
y
2
= 777,726,
Σ
x
y
= 8,381.4,
Σ
(
x
–
x
)
2
= 113.3768421,
Σ
(
y
–
y
)
2
= 84,204.94737,
Σ
(
x
–
x
) (
y
–
y
) = –
2,604.126316.
a)
Find the equation of the leastsquares regression line.
b)
Compute the correlation coefficient.
c)
Describe the form of the relationship. Is there a linear pattern? How strong is the
relationship? Is the direction of the association positive or negative? Explain in
simple language what this says about wine and heart disease.
d)
Test
H
0
:
ρ
= 0 vs.
H
a
:
< 0 at a
1%
level of significance.
e)
Do you think these data give good evidence that drinking wine
causes
a reduction
in heart disease deaths? Why?
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Test
H
0
:
ρ
= 0.60 vs.
H
a
:
< –
0.60 at a
1%
level of significance. What is
the pvalue of this test?
2.
A researcher investigates the relationship between a teacher’s experience and
students’ performance on the standard test, Michigan Educational Assessment
Plan (MEAP). The results are shown by the scatter plot below. The researcher
concludes:
“Since the correlation coefficient
r
is close to zero, there seems to be
no relationship between
Experience
and
Student Performance
.”
Can you offer a reasonable criticism of his argument and his conclusion?
Teacher’s Experience vs. Student’s Performance on the MEAP
3.
In a college health fitness program, let
X
denote the weight in kilograms of a male
freshman at the beginning of the program and let
Y
denote his weight change during
a semester. Assume that
X
and
Y
have a bivariate normal distribution with
μ
X
= 75,
σ
X
= 9,
μ
Y
= 2.5,
σ
Y
= 1.5,
ρ
= – 0.6. (The lighter students tend to gain weight,
while the heavier students tend to lose weight.)
a)
What proportion of the students that weigh 85 end up losing weight during the
semester? That is, find P
(
Y < 0

X = 85
).
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 Spring '07
 STEPANOV
 Linear Regression, Normal Distribution, Regression Analysis, rejection region, heart disease deaths

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