LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.A., DEGREE EXAMINATION – ECONOMICS

## FOURTH SEMESTER – APRIL 2004

**ST 4204/STA 204 – ECONOMETRICS**

07.04.2004 Max:100 marks

9.00 – 12.00

**SECTION -A**

Answer **ALL** questions. (10 ´ 2 = 20 marks)

- Define the term ‘econometrics’.
- Give any two properties of expectation.
- List down the axioms of probability.
- Mention the difference between statistic and parameter.
- Give any two properties of least square estimates.
- Consider the regression of y on x given by y = . How will you interpret the regression coefficients?
- What is analysis of variance?
- Give an example for structural change.
- Mention the consequences of multicollinearity.
- What is meant by heteroscedasticity?

**SECTION – B**

Answer any **FIVE** questions. (5 ´ 8 = 40 marks)

- a) A, B and C are mutually exclusive and exhaustive events associated with a random experiment. find P(A) given that P (B) = P(A); P(C) = P(B).
- b) If 2 dice are thrown, what is the probability of getting a sum greater than 8?
- c) If find P(A) and P(B). Hence show that A and B are independent. (2+2+4)

- a) Explain the term ‘linear’ with reference to a regression model.
- b) Write down the assumptions in a simple linear regression model. (4+4)

- Suppose that a researcher is studying the relationship between gallons of milk consumed by a family per month (y) and the price of milk each month (x in dollars / gallon). The sample consists of observations in 12 consecutive months. Analysis of the data assuming a linear model of y on x reveals the following:

. For this sample, find (i) (ii) (iii) Least squares slope (iv) Least squares intercept (v) Standard error of regression (vi) standard error of slope (vii) Test the hypothesis that the slope coefficient is zero at 5% level.

- Consider the following data set:

Sample No: 1 2 3 4 5

y : 15 10 14 8 3

x: 1 2 3 4 5

- i) Calculate the least square estimates for and assuming the model

y = for the above data.

- ii) Calculate for each sample.

iii) Calculate TSS and RSS.

- iv) Calculate the coefficient of determination.

- Justify / interpret the following statements:
- P { – 0.725 < b
_{1} < 2.35} = 0.90
- R
^{2} = 0.6735

- the estimates obtained by the least squares method are the best when compared with the estimates obtained by some other method.

- .

- Explain the concept of interval estimation.

- What are dummy variables? Explain how the data matrix is specified in the presence of dummy variables.

- Explain the method of Generalized least squares.

**SECTION – C**

Answer any **TWO** questions. (2 ´ 20 = 40 marks)

- a) The joint probability distribution of two random variables X and Y in given by

X

-1 0 1

-1 0 0 1/3

Y 0 0 0 0

1 0 1/3 1/3

find i) the marginal distribution of X and Y.

- ii) Var(X), Var(Y)

iii) Cov(X,Y)

- iv) Conditional probability of X given Y = 1.
- v) Var(X + Y)

- b) Define: Independent events, mutually exclusive events and sample space. (15+5)

- a) Explain the test of overall significance of a multiple regression.

- b) Consider the following ANOVA table:

SOURCE |
df |
Sum of Squares |

All Variables
(X_{1}, X_{2}, X_{3}, X_{4}) |
? |
800 |

First two Variables (X_{1,} X_{2}) |
? |
300 |

Difference |
? |
? |

Residual |
? |
? |

Total |
25 |
1500 |

- Complete the table by filling the missing values.
- Test H
_{0}: b_{1} = b_{2} = b_{3} = b_{4} = 0

Vs

H_{1} : atleast one b_{k }0, k = 1,2,3,4 at 5% level

iii) Test H_{0}: b_{1} = b_{2 }= 0

Vs

H_{1}: b_{1} 0 (or) b_{2} 0 at 5% level.

- iv) Test H
_{0} : b_{3} = b_{4} = 0 Vs H_{1}: b_{3} 0 (or) b_{4} 0 at 1% level (8+12)

- a) Consider the following data

y X_{1} X_{2}

1 1 2

3 2 1

8 3 -3

Based on this data, estimate the following regressions:

y_{i} = a_{0}+ a_{1} X_{1 i} + u_{1i}

_{ }y_{i} = b_{0} + b_{1}X_{1i}+ b_{2}X_{2i} +u_{2i}

Is a_{1} = b_{1}? Why or why not?

- b) i) Explain the concept of structural change.
- ii) Give the steps involved in ‘Chow test’ to test for structural change. (10+10)

- a) Explain the remedial measures for multicollinearity.

- b) Write short notes on:
- Coefficient of determination
- Statistical inference

Random variables. (10+10)

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