LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.A. DEGREE EXAMINATION – ECONOMICS
FOURTH SEMESTER – APRIL 2011
ST 4207 – ECONOMETRICS
Date : 05-04-2011 Dept. No. Max. : 100 Marks
Time : 1:00 – 4:00
PART – A
Answer ALL questions (10 x 2 = 20)
- Distinguish between mathematical and econometric model.
- Let X be a random variable with the following probability distribution:
-3 | 6 | 9 | |
Find E(X) and E(X2) and using the laws of expectation, evaluate.
- Distinguish between R2 and adjusted R2
- What is meant by linearly dependent?
- Write any two consequence of multicollinearity.
- Define variance inflation factor.
- Write down Durbin-Watson d-statistic in autocorrelation
- Define Heteroscedasticity.
- What are the types of specification error?
- Define Lagged variable.
PART – B
Answer any FIVE questions (5 x 8 = 40)
- Three news papers A, B and C are published in a certain city. It is estimated from a survey that of the adult population: 20% read A, 16% read B, 14% read C, 8% read both A and B, 5% read both A and C, 4% read both B and C, 2% read all three. Find what percentage read at least one of the papers.
- A variable X is distributed at random between the values 0 and 4 and its probability density function is given by . Find the value of k, the mean and standard deviation of the distribution.
- Explain in detail the applications of econometrics.
- Derive least square estimators for simple linear regression models.
- Establish the unbiasedness property of a OLS estimators for simple linear regression model.
- Find the value of R square for the following data. The fitted regression model for the given data is = 5.275-0.321X1+0.664X2
Y | 10 | 7 | 5 | 6 | 4 |
X1 | 3 | 5 | 4 | 5 | 7 |
X2 | 4 | 6 | 8 | 7 | 3 |
- State the assumptions and also prove the linearity property in simple linear regression models.
- From the following data estimate d-statistic and test for autocorrelation.
et : 0.6, 1.9, -1.7, -2.2, 1.3,3.2, 0.2,0.8, 2.1, -1.5, -1.1
(Given dL = 1.45 and du = 1.65)
PART – C
Answer any TWO questions (2 x 20 = 40)
- a) Let X be a continuous random variable with p.d.f.:
- Determine the constant a, and
- Compute P(X ( 5 + 5)
- b) Let Find
- E(XYX =)
- Var(YX = ) ( 3 + 3 + 6)
- Consider the following data on Y and X
X | 50 | 42 | 71 | 35 | 61 | 45 | 53 | 45 | 38 | 41 | 63 |
Y | 145 | 123 | 155 | 120 | 150 | 130 | 155 | 120 | 135 | 160 | 165 |
- Estimate the regression equation of Y on X
- Test the significance of the parameters at 5% level of significance
- a) Explain multicollinearity and also explain the consequences of perfect multicollinearity
- b) Consider the model with the following observations on Y and X
X | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Y | 2 | 2 | 3 | 3 | 1 | 1 | 4 | 4 | 5 | 3 |
The estimated model is =1.533+0.23X ; Examine the existence of heteroscedasticity using spearman’s rank correlation test. (8 +12)
- Construct a linear regression model for the given data by the use of dummy variables
Aptitude score | 3 | 8 | 9 | 6 | 4 | 5 | 7 | 3 | 6 | 7 |
Education qualification | HSC | UG | PG | UG | HSC | UG | PG | HSC | PG | UG |
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