Answer Key for Problem Set 2
1. (1)
n
(Yi X i )
2
i =1
n
d
= 2 (Yi X i ) X i = 0 =
d
i =1
X iYi
i
X i2
i
(2)
=
X Y
X
i i
i
2
i
i
X i Yi
) = E i
E (
2
Xi
i
=
X E (Y ) X X
=
X
X
i
i
i
i
i
i
2
2
i
=
i
i
i
.
~
(3) Yi = X i + ei ( X , Y ) X = Y
.
Answers to Selected
Exercises
For
Principles of Econometrics, Fourth Edition
R. CARTER HILL
Louisiana State University
WILLIAM E. GRIFFITHS
University of Melbourne
GUAY C. LIM
University of Melbourne
JOHN WILEY & SONS, INC
New York / Chichester / Weinheim
Econometrics
Homework #4
1. Algebraically show that the fitted least squares line = 1 + 2 passes through the point
( , ).
2. Algebraically show that the average value of equals the sample mean of . That is, show
that = , where = t /.
3. Question 2.1.
4. Q
Problem Set 5
(: 2009/4/16()
1. 6 188 3 .
( Wi ) ( C i ) 200
.
C i = 50 + 0.9Wi ,
R 2 = 0.88
(
) .
(18) (0.3)
(1) ( M i ,
Mi =
Wi
)
12
, C i = 1 + 2 M i + i 2
.
(2) (1) 2 t- .
2. 6 190 5 .
PITCHER -
.
Log ( Money) i = 1 + 2Wini + i
(1)
Problem Set 3
(: 2009/4/2()
1. 119 4 .
.
(1) X Y
.
(2)
(3) Yi = + X i + i ,
(X , Y )
.
X i = + Yi + u i b
d , b d 1 .
2.
. (INFL) (M2G)
.
( yt ) (, ) ( gt )
:
gt =
yt yt 1
100
yt 1
SNA2006(annual)
Problem Set 2
(: 2009/3/26()
1. : Yi = X i + i .
, 75 -79 2- 6
1
: Yi = X i + i
.
(1) .
(2) (1) ? .
(3) Yi = X i + ~i
e
(X , Y ) ? .
2. 119 5 .
( 1 Yi = 1 + 2 X i + i
, 1 = 0 1
Problem Set 1
1. 3 ( 73 ) 4, 5, 6
2. Yi = + i ,
E ( i ) = 0
n
(Y )
i =1
i
2
= Y .
(Note)
Xi
.
Yi = 1 + 2 X i + i
3.
Yi = 1 + 2 X i + i
Yi = X i + i
.
(1) .
n
(2)
e
i =1
i
= 0 ? .
4. Yi X i Yi = b1 + b2 X i
.
n
n
i =1
(1)
i =1
Yi = Yi .
Answer Key for Problem Set 4
1.
n
(X
(1) False.
i =1
V (b2 ) =
2
n
(X
i =1
i
X)
i
X ) 2
. 2
2
.
(2) False. i
BLUE .
BLUE [ 1]~[ 6] .
(3) False. 1 , 2
. V (e f ) = V ( f ) = 2 0
.
(4) False.
Answers for Problem Set 1
1.
(a) < 4 >
Yi * =
Yi Y
Sy
n
X i* =
i =1
(X
X i* =
n
1
Sx
i =1
i
Xi X
Sx
n
Yi* =
i =1
1
Sy
(Y
n
i =1
i
Y ) = 0
X ) = 0 . Y * X * 0 . 1* b1*
b = Y b X * , Y * X * 0 b1*
*
1
*
*
2
0 .
(b) < 5 >
(1)
1 8
1 8
GPAi = 3.212
Answer Key for Problem Set 3
n
ei
1. Note that R 2 = 1
i =1
(Y
n
i
i =1
(Y Y )
n
2
Y )
2
=
2
i
i =1
n
(Y
i
i =1
Y )
.
2
Since Yi Y = b2 ( X i X ) ,
R2 =
b2
2
(X
n
i =1
n
(Y
i =1
i
X)
( X i X )(Yi Y )
= i
2
(X X )
i
i
2
i
Y )
2
2
(X
i
X)
i
Y
Answer Key for Problem Set 5
1. (1) Substitute Wi = 12 M i into original estimation equation, then
C i = 50 + 0.9Wi
= 50 + 0.9 12 M i
= 50 + 10.8M i
Therefore 2 = 10.8.
(2) No change.
2. The estimated result is as follows:
Dependent Variable: LOG(MONEY)