LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.A. DEGREE EXAMINATION – ECONOMICS

YB 16

FOURTH SEMESTER – April 2009

ST 4207/ ST 4204 – ECONOMETRICS

 

 

 

Date & Time: 27/04/2009 / 9:00 – 12:00       Dept. No.                                                        Max. : 100 Marks

 

 

SECTION  A                                

                               Answer all the questions                        10 x 2 = 20 marks

1    If  A and B are two events such that P(AU B) = 0.57 , P( A^c ) = 0.50 and

P( B^c ) = 0.60  , find P( A ∩ B ).

• Mention any two properties of variance.
• If X is a continuous random variable having the probability density function

f (x) = (1/9) x²   , 0 ≤ x ≤ 3  ;  0  , elsewhere

find  P(0 < X < 1).

• Define maximum likelihood estimation.
• Write a note on interval estimation.
• Define sample regression function.
• Distinguish between R² and adjusted R².
• Write the importance of dummy variables in regression models.
• Define variance inflating factor.
• Write any two consequences of multicollinearity.

 

                                         SECTION  B

                              Answer any five questions                         5 x 8 = 40 marks  

11. If 10 fair coins are tossed simultaneously , find the probability of getting

(i) exactly 4 heads   (ii) at least 8 heads  (iii) at most 9 heads (iv) between 7 and 9 heads inclusive.

12. Given the following probability distribution:

X=x    :   -3          -2          -1         0         1          2          3

p(x)     :   0.05       0.10      0.30      0        0.30     0.15     0.10

Compute E(X) and V(X).

13. Let X be normally distributed with mean 8 and standard deviation 4.

Find    (i) P(5≤X≤10)       (ii) P(10≤X≤15)    (iii) P(X≥15)   (iv) P(X≤5).

14. A random sample of 10 boys had the following I.Q.’s: 70 120  110  101

88  83  95  98  107  100 .Construct 95% confidence limits for the population mean.

15. Two random samples drawn from two normal populations are:

Sample I   : 20  16  26  27  23  22  18  24  25  19

Sample II :  27  33  42  35  32  34  38  28  41  43  30  37

Test whether the populations have the same variances. Use 1% significance level.         16. Fit a regression model of the form

Y = β₁ + β₂X + u     for the following data:

Y  : 55    88    90    80   118  120   145   135   145   175

X  : 80   100  120  140  160  180   200    220  240   260

Also find residual sum of squares.

17. Explain the log-linear and semi log models.
18. Explain the ANOVA for testing the equality of parameters for a k-

variable linear regression model.

 

   SECTION  C

                              Answer any two questions                          2×20 = 40 marks  

19. Let X₁ and X₂ have the joint p.d.f.

f(x₁,x₂) = 2  ,  0<x₁<x₂<1   : 0   , elsewhere.

• Find the marginal distributions of X₁ and X₂
• Find the conditional mean and variance of (i) X1 given X₂ = x₂ and

(ii) X₂ given X₁= x₁.

• Find the correlation between X₁ and X₂.

20. (a) Obtain the maximum likelihood estimators of μ and s², if X₁,X₂,…X_n is

a random sample from normal distribution with mean μ and variance s². .

(b) Fit a linear regression model of the form

Y_i = β₂ X_i + u_i  for the following data:

Y  : 10     20    25    22    27    15   12

X  :  8      12    15    13    16    10    9

Also find

• Standard error of slope parameter
• Residual sum of squares
• 95% confidence interval for β₂.

21. (a) Mention the assumptions underlying the method of least squares in the

classical regression model.

(b) Write a note on:

(i) t-distribution         (ii) F-distribution    (iii) Chi-square distribution

(iv) Normal distribution

22. Fit a regression model of the form

Y_i  = β₁ + β₂ X_2i + β₃ X_3i + u_i   for the following data:

Y :  1     3    8     11   15   14

X₂ : 1     2    3      5     7     6

X₃ : 2     1    4      3     5     4

Also find :

(i) Standard errors of estimators of β₂ and β₃.

(ii) Covariance between the estimators of β₂ and β₃.

 

 

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