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Study Questions for Midterm 1
ECG 561, Spring 2008
1.
Consider two discrete random variables, X and Y.
Their joint probability distribution is given in the table
below:
X
012
Y
01
/
30
0
10
1
/
3
1
/
3
a.
Are X and Y independent?
Support your answer.
b.
Calculate E(Y) and Var(Y).
c.
Plot E(YX) as a function of X.
Label your diagram clearly.
d.
Calculate Cov(X,Y).
2.
You have just calculated a simple linear regression with n observations.
After you perform your analysis,
you discover that there is one (x,y) pair that you overlooked; i.e., you really had n+1 observations available to you,
but you only used n.
It turns out that x
n+1
=
and y
n+1
=
: the overlooked data pair has x
and
y values equal to
the sample means of the first n x's and y's.
If you recalculate your regression results using all n+1 observations:
(a)
Will
change?
If so, how?
(b)
Will
change?
If so, how?
(c)
Will Var(
) change?
If so, how?
(d)
Will the estimate of Var(
) change?
If so, how?
3.
Suppose that a researcher estimates a linear regression and is concerned about the validity of the
assumption that E(u) = 0.
To investigate, she calculates the sample mean of the residuals of the regression to see if
it is likely that the population mean of the disturbances is nonzero.
Comment on the advisability of the
researcher’s procedure.
4.
Consider a multiple regression with two independent variables:
y
i
=
β
o
+
β
1
x
1i
+
β
2
x
2i
+ u
i
.
(a)
State the two conditions that imply that the least squares multiple regression coefficient on x
1
,
, will equal the simple coefficient from a least squares regression of y on x
1
,
.
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 Fall '08
 ERYURUK

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