LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION – STATISTICS
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FOURTH SEMESTER – APRIL 2008
ST 4207/ ST 4204 – ECONOMETRICS
Date : 25-04-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION- A
Answer all the questions. Each carries TWO marks. (10 x 2 = 20 marks)
- Define sample space and event of a random experiment.
- If P(A) = ¼ , P(B) = ½ and P(AB) = 1/6 , find (i) P(AB) and (ii) P(AcB).
- Given:
X= x : 0 1 2 3 4
P(X=x): 1/6 1/8 ¼ 1/12 3/8
Find E(2X + 11).
- If f ( x, y) is the joint p.d.f. of X and Y, write the marginals and conditional
distributions.
- Write any two properties of expected values.
- Define BLUE.
- Define the population regression coefficient .
- Write variance inflating factor of an estimator in the presence of multicollinearity.
- Define autocorrelation.
- Define point and interval estimation.
SECTION –B
Answer any FIVE questions. Each carries EIGHT marks. (5 x 8 = 40 marks)
- Consider 3 urns. Urn I contains 3 white and 4 red , Urn II contains 5 white and 4 red and Urn III contains 4 white and 4 red balls. One ball was drawn from each urn. Find the probability that the sample will contain 2 white and 1 red balls.
- If a fair coin is tossed 10 times, find the chance of getting (i) exactly 4 heads
(ii) atleast 6 heads (iii) atmost 8 heads (iv) not more than 4 heads.
- Derive the least square estimators of the linear model Y = 1 + 2 X + u .
- State any six assumptions of the linear regression model.
- How to fit a non-linear regression model of the form Y = 1 + 2 X + 3 X 2 ?.
- Consider the model Y = 1 + 2 X + u where X and Y denote respectively
consumer income (hundreds of dollars per person) and consumption of purple
oongs (pounds per person) . The sample size is 20 , sum of X is 300, sum of Y
is 120 , sum of squares of deviations of X from its mean is 500 , sum of product
of deviations of X and Y from their respective means is 66. 5 and sum of squares
of is 3.6.
- Compute the slope and intercept.
- Compute the standard error of regression.
- Compute the standard error of slope.
- In a book of 520 pages , 390 typo- graphical errors occured. Assuming Poisson
law for the number of errors per page, find the probability that a random sample
of 5 pages contain (i) no error (ii) atleast 3 errors.
- The mean yield for one-acre plot is 662 kg with a standard deviation of 32 kg.
Assuming normal distribution find how many one-acre plots in a batch of 1000
plots will have yield (i) over 700 kg (ii) below 65 kg .
SECTION – C
Answer any TWO questions. Each carries TWENTY marks. (2 x 20 = 40 marks)
- Consider the following joint distribution of (X,Y):
X 0 1 2 3
0 1/27 3/27 3/27 1/27
Y 1 3/27 6/27 3/27 0
2 3/27 3/27 0 0
3 1/27 0 0 0
(a) Find the marginal distributions of X and Y.
(b) Find E( X ) and V ( X )
(c) Find the correlation between X and Y.
(d) Find E ( Y | X = 2 )
(e) Verify whether or not X and Y are independent.
- (a) Explain the following methods of estimation used in the analysis of regression
models:
(i) Maximum likelihood (ii) Moments
(b) The heights of 10 males of a given locality are found to be 70 , 67, 62 , 68 , 61
68 ,70 , 64 , 64 , 66 inches. Is it reasonable to believe that the average height is
greater than 64 inches ? Test at 5% significance level.
- For the following data on consumption expenditure (Y ) , income ( X2 ) and wealth
( X3 ):
Y($) : 70 65 90 95 110 115 120 140 155 150
X2 ($) : 80 100 120 140 160 180 200 220 240 260
X3 ($) : 810 1009 1273 1425 1633 1876 2052 2201 2435 2686
- Fit a regression model Y = 2 X2 + 3 X3 + u .
- Find the correlation coefficients between Y and X2 , Y and X3 , X2 and X3.
- Find unadjusted and adjusted R2 .
- Test H0 : 2 = 3 = 0 at 5% significance level .
- (a) For the k-variate regression model Y = 1 + 2 X2 +…+k Xk + u
carry out the procedure for testing H0 : 2 = 3 = … = k = 0 against
H1: atleast one k 0.
(b) Write the properties of ordinary least square(OLS) estimators under the
normality assumption.
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