# LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 ```LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.A. DEGREE EXAMINATION – ECONOMICS
SUPPLEMENTARY EXAMINATION – JUNE 2009
ST 4207 - ECONOMETRICS
Date &amp; Time: 26/06/2009 / 10:00 - 1:00 Dept. No.
SECTION A
Max. : 100 Marks
( 10 x 2 = 20 )
1. A letter of the English alphabet is chosen at random. Find the probability that the letter so
chosen is a consonant.
2. Define the independence of three events A, B and C.
3. Mention any two properties of expectation of a random variable.
4. Let X be a random variable with the following probability distribution:
X = x : -2
-1
0
1
2
P(X= x) : 0.05
0.15
0.20
0.25 0.35
Determine E ( X2 ) .
5. If 5 fair coins are tossed simultaneously, find the probability of getting at least 3
6. Define probability of Type I and Type II errors in hypothesis testing.
7. Define population regression function.
8. What is measured by the coefficient of determination r2 and R2 ?
9. What do you mean by structural change in regression models ?
10. When do we say that there is dummy variable trap ?
SECTION B
(5 x 8 = 40)
11 Let A and B be two events with the probabilities P(A) = 1/5 , P(B) = 2/5 and
P(A∩B) = 1/10. Find ( i ) P(A│B) ( ii ) P(A │Bc ) ( iii ) P(Ac │B)
and P(Ac │Bc).
12. If X has the p d f
f(x) = 2(1-x) , 0&lt;x&lt;1 ; 0 , elsewhere ,
find E(X) and V(X).
13. Fit a Poisson distribution to the following data:
Number of mistakes per page: 0
1
2
3
4
Number of pages
:109
65
22
3
1
14. A sample of 900 members has a mean 3.4 cms. and standard deviation 2.61 cms. Find 95%
and 99% confidence limits for true mean.
15. A random sample of 400 observations has mean 95 and standard deviation 12.Could it be a
random sample from a population with mean 98? Test at 5% level of significance.
16. Write the significance of the stochastic disturbance term involved in regression models .
17. For a two variable linear regression , derive the standard error of the estimator of regression
coefficient .
18. How do you detect multicollinearity in regression models involving more than two explanatory
variables?
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SECTION C
( 2x 20 = 40)
19. Consider the following joint probability distribution:
0
1
2
X
0
Y
0
1/27
2/27
1
2/27
3/27
4/27
2
4/27
5/27
6/27
(a)
(b)
(c)
(d)
(e)
Find the marginal distributions of X and Y.
Find E(X) and V(X).
Find the correlation coefficient between X and Y.
Find E(Y│X = 2)
Check whether X and Y are independent.
20 (a)Explain :
(i) Ordinary least squares method
(ii) Unbiased ness and consistency
(iii) Dummy variables
(b) Mention the assumptions underlying the method of least squares in the
classical regression model.
21
Fit a linear regression model for the following data:
Expenditure ‘000 (Y) : 8 11 10 5 6 7 12
Income
‘ 000 (X) : 15 18 16 14 13 17 20
Also find :
(i)
Residual Sum of squares
(ii)
Standard error of slope and intercept.
(iii) 99% confidence interval for slope and intercept
(iv)
Test H 0 : β2 = 0 against H1 : β2 ≠ 0 at 5% level of significance.
22
Write a note on :
(i)
OLS estimation in the presence of heterocedasticity
(ii)
Generalized least square estimation
(iii) Spearman’s rank correlation test.
(iv)
Variance inflating factor
(v)
Properties of OLS estimators.
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