Econ 104  Problem Set 3 Solutions
Lorenzo Braccini
*
October 4, 2011
Problem 1
a) First note that:
E
[
Y
i

X
i
] =
β
0
+
β
1
X
i
Therefore we have that:
E
[
Y
i

X
i
= 1]

E
[
Y
i

X
i
= 0] =
β
1
where
Y
i
is the probability of causing an accident and
X
i
is the color
of the car (1 if red).
Last equality tells us that
β
1
represents the diﬀerence in the ex
pected probability of causing an accident between a red car owner
and the rest of the world.
The estimate
ˆ
β
1
= 0
.
15 suggests that a red car owner has, on aver
age, a probability of causing an accident 0
.
15 greater than the owner
of a diﬀerently colored car.
b) For Susan to judge that her estimate is signiﬁcantly diﬀerent from
0 at a 5% level we need that:
±
±
±
±
±
ˆ
β
1
SE
(
ˆ
β
1
)
±
±
±
±
±
> z
0
.
975
= 1
.
96
(1)
where
(
ˆ
β
1
) is the estimate for the asymptotic standard error of
the OLS estimator for
β
1
.
*
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1
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View Full DocumentThis result comes from the fact that, asymptotically:
ˆ
β
1

β
1
SE
(
ˆ
β
1
)
∼ N
(0
,
1)
Hence, testing the null hypothesis
H
0
:
β
1
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 Spring '12
 gg
 Statistics, Normal Distribution, Null hypothesis, Statistical hypothesis testing, red car owner

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