Assignment # 1
Due Monday Feb 14
th
at 2:30pm
Instructions: While cooperating on the assignment is encouraged, plagiarism is
not. I will only accept
hand written
assignment submitted in person. Do NOT
submit your assignment electronically. No late assignment will be accepted; late
assignments (during or after the correction in class) will receive a mark of zero.
Question 1 (20 pts)
Let Y
1
, …, Y
4
be a random sample such that the four random variables Y
j
for j=1,
…,
4 are independent and identically distributed from a population with mean
and variance σ
2
.
Define the sample mean estimator Y = 1/4
Σ Y
j
, the average of these four random
variables and define the following estimator:
Ϋ
= 1/4 (1/2Y
1
+ 3/2Y
2
+ 1/2Y
3
+ 3/2Y
4
), a weighted average of the four random
variables such that the observations are alternately weighted by 1/2 and 3/2.
(a) Calculate the mean of
Y and Ϋ
.
(b) Calculate the variance
of
Y and Ϋ
.
(c) Based on your answers in part (a) and (b), which estimator do you prefer
between the two?
Question 2 (10) pts)
(a) Assume the regression model Y
i
= 10
+ βX
i
+ ε
i
What is the ordinary least square estimator of
β
in this case? Calculate E(
β
)
showing that it is unbiased.
(b) Assume the regression model Y
i
= βX
i
+ ε
i
What is the ordinary least square estimator of
β
in this case? Calculate E(
β
)
showing that it is unbiased.
Question 3 (20 pts)
Suppose you are interested in testing the rationality of assessments of used cars.
A simple model is:
Price = β
0
+ β
1
assessment + u
The assessment is rational if β
0
=0 and β
1
=1.
The estimated equation is:
Price = 12.23 + 0.981 assess
(15.13)
(0.048)
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Where the standard errors of the coefficient are given in parenthesis.
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 Fall '09
 Adam
 Regression Analysis, regression model Yi, associated description file

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