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Managerial Economics (ARE) 106
University of California, Davis, Summer Session II, 2009
Dr. John H. Constantine
Midterm 2, Thursday, August 27, 2009
75 TOTAL POINTS
For all problems, assume
α
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Problem 1 (20 points)
:
See the associated SHAZAM output.
A life insurance company wants to examine the relationship between the amount of life insurance held by a family and
family income.
Data were collected from a random sample of 20 households on family income (
x
) and the amount of
life insurance the family has (
y
); all data are in thousands of dollars.
(a)
State the estimated sample regression function equation as given on the SHAZAM printout.
(3 points.)
The linear relationship between life insurance and income is estimated as:
t
y
ˆ
= 6.8550 + 3.8802
x
t
(b)
Using the estimated numeric values, provide economic interpretations for both b
1
and b
2
.
(7 points.)
The relationship in part (a) indicates that, as income increases, the amount of life insurance increases, as is
expected.
The value of
b
1
= 6.8550 implies that if a family has no income, then they would purchase $6855 worth of
insurance. It is necessary to be careful of this interpretation because there are probably no data for families
with an income close to zero.
The value of
b
2
= 3.8802.
If income increases by $1000, then an estimate of the resulting change in the amount
of life insurance is $3880.20.
(c)
One member of management claims that for every $1,000 increase in income, the amount of life insurance will
increase by $5,000.
State your hypothesis test (both H
0
and H
A
) and whether you reject or do not reject your
stated hypothesis, that is, whether you accept or not accept the manager’s claim.
Use the confidence interval
approach
.
(10 points.)
H
0
:
β
2
= 5
H
A
:
β
2
≠
5
tcritical =
101
.
2
2
/
05
.
0
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 Spring '09
 CONSTANTINE
 Statistics, Normal Distribution, SS df MS, Regression Error Total

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