Prof. G. Jakubson
Economics 321
March 2004
Spring 2004
PRELIMINARY EXAM #1
Correct Answers
1.a.
median for AfricanAmericans is in the range $1525K
(5 points). Median
for Caucasian's is higher (in the range $2535K ) (5 points).
b. (10 points) – see calculations below
Afr.Amer.
Class intervals
thousands of families
rel
cum
for family income
Caucasian
AfricanAmerican
freq
freq
< $5,000
2,000
900
.13
.13
$ 5,000 to < $10,000
3,000
1,100
.16
.29
$10,000 to < $15,000
5,000
900
.13
.42
$15,000 to < $25,000
10,000
1,600
.23
.65
$25,000 to < $35,000
10,000
900
.13
.78
$35,000 to < $50,000
12,000
900
.13
.91
$50,000 or more
14,000
600
.09
1.00
Total number of families
56,000
6,900
2.a.
Z
= (1/N)
∑
i
Z
i
= [ (1/N)
∑
i
X
i
 N
X
] / s
x
= 0
(5 points)
b. s
z
= (1/s
x
) s
x
= 1.
(5 points)
c. Since T
i
is just a standardized version of Y
i
, its mean and variance are
also 0 and 1, respectively.
(5 points)
d. CV(Y)/CV(X) = { d
2
s
x
/ d
2
X
} / {s
x
/
X
} = 1
(10 points)
3.a. Let e
i
= Y
i

±
β
0

β
±
1
X
i .
The least squares estimators solve
min
∑
i
(e
i
)
2
(5 points)
b.
FOC
(each worth 3 points)
wrt
β
±
0
:
∑
i
e
i
= 0
wrt
β
±
1
:
∑
i
e
i
X
i
= 0
implications:
(each worth 3 points)
[Note (i) <=> (iii)]
(i)
mean residual = 0
(ii) e and X are uncorrelated
(iii)
regression line goes through the point of means
Economics 321, Spring 2004
Page 1 of 4
Prelim 1 Answers
c:\…\s04pre1a.doc