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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034 B.A. DEGREE EXAMINATION – ECONOMICS SUPPLEMENTARY EXAMINATION – JUNE 2009 ST 4207 - ECONOMETRICS Date & Time: 26/06/2009 / 10:00 - 1:00 Dept. No. SECTION A Answer all the questions 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 heads. 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 Answer any five questions (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<x<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? 1 SECTION C Answer any two questions ( 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. ---------------------------- 2