Economics 140A
Winter 2014
Sketched Out Answers for Quiz 1
Note that not all the details are shown here. The sketches here are just to point you in the right
direction. A good exam answer would have more details.
Question:
Let:
X ~ N(0,4)
Y = 2 – 5X
(a)
Find
𝐸𝐸
(
𝑌𝑌
)
.
𝐸𝐸
(
𝑌𝑌
) =
𝐸𝐸
(2
−
5
𝑋𝑋
) =
𝐸𝐸
(2) +
𝐸𝐸
(
−
5
𝑋𝑋
) = 2
−
5
𝐸𝐸
(
𝑋𝑋
) = 2
−
(5
∗
0) = 2
(b)
Find
𝑉𝑉𝑉𝑉𝑉𝑉
(
𝑌𝑌
)
.
𝑉𝑉𝑉𝑉𝑉𝑉
(
𝑌𝑌
) =
𝑉𝑉𝑉𝑉𝑉𝑉
(2
−
5
𝑋𝑋
) =
𝑉𝑉𝑉𝑉𝑉𝑉
(
−
5
𝑋𝑋
) = (
−
5)
2
∗ 𝑉𝑉𝑉𝑉𝑉𝑉
(
𝑋𝑋
) = 25
∗
4 = 100
(c)
Find
𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉
(
𝑋𝑋
,
𝑌𝑌
)
.
𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉
(
𝑋𝑋
,
𝑌𝑌
) =
cov(
𝑋𝑋
,
𝑌𝑌
)
�
var(
𝑋𝑋
)
∙
var(
𝑌𝑌
)
What is
𝑐𝑐𝐶𝐶𝑐𝑐
(
𝑋𝑋
,
𝑌𝑌
)?
𝑐𝑐𝐶𝐶𝑐𝑐
(
𝑋𝑋
,
𝑌𝑌
) =
𝑐𝑐𝐶𝐶𝑐𝑐
(
𝑋𝑋
, 2
−
5
𝑋𝑋
) =
𝑐𝑐𝐶𝐶𝑐𝑐
(
𝑋𝑋
,
−
5
𝑋𝑋
) = (1)(
−
5)
𝑐𝑐𝐶𝐶𝑐𝑐
(
𝑋𝑋
,
𝑋𝑋
) =
−
5
∗ 𝑐𝑐𝑉𝑉𝑉𝑉
(
𝑋𝑋
)
=
−
5
∗
4 =
−
20
So
𝐶𝐶𝐶𝐶𝑉𝑉𝑉𝑉
(
𝑋𝑋
,
𝑌𝑌
) =
−
20
√
4
∙
100
=
−
20
20
=
−
1
Question:
You work for a health insurance company, and have been asked to model the
number of doctor visits elderly (65+) clients make in a year. The dataset you have is large, with
4406 elderly clients in it. Your coworker has already started using the dataset you’ve been
given and shows you the following (incomplete) table of regression results:
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page 2
a.
Having one more chronic condition increases the number of doctor visits a client makes
each year by 1.32, holding everything else constant.
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 Spring '08
 Staff
 Economics, Econometrics, Normal Distribution, Standard Deviation, 90%, Bias of an estimator, Health Insurance Company

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