**LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034**

B.A. DEGREE EXAMINATION – ECONOMICS

FOURTH SEMESTER – APRIL 2006

# ST 4204 – ECONOMETRICS

Date & Time : 22-04-2006/9.00-12.00 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’?
- Give any two properties of variance.
- Mention any two properties of OLS estimates.
- Let the sample space for a random experiment be S = {1, 2,…, 50}.Let A and B be two events defined on S with the event space A={all odd numbers between 1 to 50} and B={prime numbers between 1 to 50}.Are A and B independent?
- Give one example each for discrete and continuous random variable.
- What is meant by ‘Time series’ data? Give an example for the same.
- Interpret the following regression equation.

Y = 1.7 + 0.251X_{1} + 1.32X_{2}

where Y denotes the weekly sales( in ‘000’s)

X_{1} denotes the weekly advertisement expenditure

X_{2} denotes the number of sales persons.

- In a multiple regression model, the value of R
^{2} is found to be 0.894.How would you interpret it?
- 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 estimate.

- What is meant by ‘dummy variable’?

**Section B**

**Answer any five questions ( 5 x 8 = 40 )**

- Define the following:

- Sample space
- Independent events
- Conditional probability
- Random variable

- If X is a random variable distributed as normal with mean 10 and variance 3 Find a.) P(X<8) b.) P(-1<X<5) c.) P(X>15)
- The following data relates to the family size(X) and family food spending(Y)

of 8 persons randomly selected from a small urban population.

Y: 40 50 50 70 80 100 110 105

X: 1 1 2 1 4 2 4 6

Assuming there is a linear relationship between Y and X, perform a regression of Y on X and estimate the regression coefficients. Also find the standard error of the estimate.

- 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 R^{2} = 0 at 5% level.

- Explain the concept of point and interval estimation with an example.
- Give the procedure for Chow’s test.
- Explain the ANOVA and ANCOVA models in regression analysis using

example.

- 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.

**Section C**

** **

**Answer any two questions ( 2 x 20 = 40 )**

- a.) Explain the different steps involved in an Econometric study.

b.) Mention the various assumptions in a Classical Linear Regression model.

(10 + 10 )

- A bag contains three balls numbered 1, 2, 3 . Two balls are drawn at random , with replacement , from the bag. Let X denote the number of the first ball drawn and Y the number of the second ball drawn.

- Find the joint distribution of X and Y
- Find the marginal distributions of X and Y
- Find variance of X and variance of Y
- Are X and Y independent ?
- Calculate the correlation between X and Y

- a.) Explain the procedure for testing structural change using dummy

variables.

b.) Consider the following data on annual income (in 000’s $) categorized by

gender and age.

Income: 12 10 14 15 6 11 17

Gender: 0 1 1 0 0 1 1

Age: 1 1 0 1 0 0 1

where Gender = 1 if male; 0 if female

Age = 1 if less than or equal to 35; 0 if greater than 35.

Perform a regression of Income on Gender and age. Interpret the results.

What is the benchmark category for the above model? ( 8 + 12 )

- a) Explain the construction of 95% confidence interval for the slope

coefficient in a two variable regression model.

b.) Define the following:

1.) Standard error of the estimate

2.) Correlation coefficient

3.) Differential intercept

4.) Mutually exclusive events.

Go To Main Page