LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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FIFTH SEMESTER – April 2009
ST 5405 – ECONOMETRIC METHODS
Date & Time: 30/04/2009 / 1:00 – 4:00 Dept. No. Max. : 100 Marks
SECTION A
Answer all questions (10 x 2 = 20)
- What is the difference between a ‘Mathematical model’ and an ‘Econometric model’?
- Define Sample Regression Function.
- Mention any two properties of OLS estimators.
- What is meant by ‘Time series’ data? Give an example for the same.
- Interpret the following regression equation.
Y = 2.5 + 0.21X1 + 1.0X2 ,
where Y denotes the weekly sales( in ‘000’s)
X1 denotes the weekly advertisement expenditure
X2 denotes the number of sales persons.
- In a multiple regression model, the value of R2 is found to be 0.657. How is it interpreted?
- For a two variable regression model, the observed and estimated (under OLS) values of Y are given below:
Observed Y: 10 14 13 12 17
Estimated Y: 10 13 11 14 15
Calculate the standard error of the regression.
- What is meant by ‘dummy variable’?
- Mention any two methods of overcoming multicollinearity.
- Define Heteroscedasticity.
SECTION B
Answer any five questions (5 x 8 = 40)
- Explain the various steps involved in an Econometric study.
- Explain the method of least squares and hence obtain the OLS estimators for the intercept and slope parameters based on a two variable linear model.
- The following data relates to the family income(X) and expenditure(Y) (both in dollars per week) of 8 families randomly selected from a small urban population.
Y: 40 55 50 70 80 100 90 78
X: 60 65 70 63 120 75 68 52
Assuming there is a linear relationship between Y and X, perform a regression of Y on X and estimate the regression coefficient. Also find an unbiased estimate for the variance of the disturbance term.
- Consider the following information from a 4 variable regression equation:
Residual sum of squares = 94;
Y = 10,12,14,9,7,8,2,22,4,12.
a.) Find TSS and ESS.
b.) Test the hypothesis that R2 = 0 at 5% level.
- Explain the procedure of obtaining a 100(1-α) % confidence interval for the slope parameter in a two variable linear model.
- What is meant by ‘structural change’? Explain the Chow test for detecting structural change in a ‘k’ variable model.
- What is meant by dummy variable trap? Explain the methods to overcome it.
- Consider the following data set:
Sample no.: 1 2 3 4 5
Y: 15 10 14 8 3
X: 1 2 3 4 5
Calculate the standard errors of the intercept and slope coefficients if their OLS
estimates are 17.8 and -2.6 respectively.
SECTION C
Answer any two questions (2 x 20 = 40)
- a.) For a two variable linear model, show that the least squares estimators are
unbiased.
b.) Mention the various assumptions in a Classical Linear Regression model.
(10 + 10)
- Consider the following data on annual income (Y) (in 000’s $), total
experience (X1) and age (X2).
Y: 12 10 14 15 6 11 17
X1: 8 7 9 10 4 6.5 12
X2: 32 29 35 33 26 28 39
Perform a regression of Y on X1 and X2. Interpret the results. Also test the
hypothesis that all the slope parameters are significantly different from zero at
5% level by constructing the ANOVA table.
- a.) Consider the following ANOVA table based on an OLS regression
| Source of
Variation |
Degrees of
Freedom |
Sum of
Squares |
| Regression | ? | 1000 |
| Error | 35 | ? |
| Total | 39 | 2200 |
- i) How many observations are there in the sample?
- ii) How many independent variables are used in the regression?
iii) Find the missing values in the above table
- iv) What is the standard error of regression?
- v) Calculate the value of R2
- vi) Test the hypothesis Ho : R2 = 0 vs H1 : R2 ≠ 0 at 5% level.
b.) What is meant by multicollinearity? Explain its consequences. (12+8)
- a) Explain the method of generalized least squares to obtain the estimators of
a linear model in the presence of heteroscedasticity.
b.) Write short notes on:
1.) Disturbance term in a linear model.
2.) Differences between correlation and regression.
3.) Differential intercept coefficient.
4.) Adjusted R2. (10+10)
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