Download Midterm, Summer/I 2005

KIMEP
Department of Economics
ECON 3184: Econometric Methods
Midterm
20 June 2004
Instructor: Dr. M. Balcilar
Part I: Briefly answer all the questions. (40%)
(a) Suppose you run the following regression:
yˆ t  ˆ1  ˆ2 xt
Where the small character yt and xt are the deviations from their respective mean
values. What will be the value of ˆ 2 ? Will it be the same as that ( ˆ 2' ) obtained
'
'
from the equation with all level terms of X and Y (i.e., Yˆt  ˆ1  ˆ2 X t )? (10%)
(b) What are the definitions of R2 and adjusted R2? What are their basic properties?
(10%)
(c) Briefly describe what are the three important assumptions related to the stochastic
errors of the classical normal linear regression model? (10%)
(d) Suppose you want to run the following regression model:
Yi  1   2 X i  ui
Show what will be the results of ˆ1 and ˆ 2 when you multiply 1000 to Yi and Xi
at the same time? (10%)
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Part II: Answer the following question. (60%)
1. Suppose you regress Y on X2, X3 X4, and X5 as following:
Yi  1   2 X 2i  3 X 3i   4 X 4i  5 X 5i  u1
Y = the number of wildcats drilled (Thousands)
X2 = price at the wellhead in the previous period (in constant dollars, 1972=100)
X3 = domestic output ($millions of barrels per day)
X4 = GNP constant dollars ($billions)
X5 = trend variable
The regression result is obtained from EVIEWS as follow:
(a) Fill in the missing numbers due to the malfunction of printer. (5%)
(b) How would you interpret this result is good or not? How would you interpret the
coefficients ˆ 2 and ̂ 3 ? (7%)
(c) Would you reject the hypothesis that the domestic output (X3) has the effect of
3.00 on wildcat drilled (Y)? (5%) And why you are using the t-test but not using
the normal distribution test? (3%)
(d) Set up the ANOVA table for this example. (10%)
Formulas for the normal two-variable classical linear regression:
2
ˆ 2 
 xy   ( X  X )(Y  Y ) ;
x
(X  X )
2
2
ˆ1  Y  ˆ 2 X
R
2
 yˆ

y
2
2
 ˆ 2
2
x
y
2
2

( xy) 2
x y
2
2
ˆ 2
;
var( ˆ2 ) 
 x2
ˆ 2  X 2
var( ˆ1 ) 
;
n x 2
ˆ
2
 uˆ

2
n2
(X  X )
var( X ) 
n 1
 (Y  Y )
var(Y ) 
2
x

2
n 1
;
2
n 1
c
t0.025,26
 2.056 [‘
3