Introduction to Econometrics (Econ 107)
Drake University, Fall 2003
William M. Boal
MIDTERM EXAMINATION #1
“Summarizing Data”
Answer Key
I. TRUE/FALSE: [3 pts each—30 pts total]
(1) False (2) True (3) False (4) False (5) False
(6) True (7) True (8) True (9) False (10) True
II. PROBLEMS
(1) [Summation notation: 8 pts] a. 6; b. zero.
(2) [Differentiating sums: 8 pts]
a.
n
i
i
x
d
df
1
2
11
2
b.
x
x
n
n
i
i
11
*
1
1
(3) [Moving average: 10 pts] 3.15, 2.90, 2.925, 2.025, 2.475.
(4) [Moving average and seasonal adjustment: 12 pts]
a. Series (iii) is the raw data. It shows many short-run fluctuations, including seasonal peaks in
spring and fall and troughs in July and January.
b. Series (i) is the 12-month moving average. It shows no short-run fluctuations of any kind.
c. Series (ii) is the seasonally-adjusted series. Is shows small short-run fluctuations, but no
seasonal peaks or troughs.
(5) [Least squares computation: 12 pts] See also chart below.
a.
ˆ
2
= 1/2. b.
ˆ
1
= 5. c.
y
ˆ
= 7, 8, 9. d.
ˆ
= +1, -2, +1.
(6) [Reverse least squares: 15 pts] See also chart below.
a.
2
ˆ
= 1/2. b.
1
ˆ
= 2. c.
RLS
2
ˆ
= 2. d.
RLS
1
ˆ
= -4.
e. The answers are different because the RLS estimates minimize the squared horizontal (x-
direction) deviations of the data from the line, whereas the OLS estimates minimize the
squared vertical (y-direction) deviations of the data from the line.
