CLASS: B.STAT.
13N/262
St. JOSEPH’S COLLEGE (AUTONOMOUS) TIRUCHIRAPPALLI – 620 002
SEMESTER EXAMINATIONS – NOVEMBER 2013
TIME: 3 Hrs.
MAXIMUM MARKS: 100
SEM
SET
PAPER CODE
TITLE OF THE PAPER
V
2011
11UST530212
LINEAR MODELS AND ECONOMETRICS
SECTION – A
Answer all the questions:
20 x 1 = 20
Choose the correct answer:
1. The density function of multivariate of normal distribution is
a) N(, )
b) N(, 2)
c) N(, )
d) N(, 2)
2. Experimental design model takes the values between
a) 0 and 1
b) -1 to 1
c) 0 to 1
d) None of these
3. The point estimates of the parameter in the general linear hypothesis of
a) 2S-1
b) 2S
c) N(, 2)
d) None of these
4. Who made national income in India, for the first time.
a) C.R. Rao
b) D.R. Gadgil
c) V.K.R.V Rao
d) Dadabhai Naroji
5. Autocorrelation is a special case of
a) Multiple correlation
b) Rank correlation
c) Serial correlation
d) Partial correlation
Fill in the blanks:
6.
The shape of Multivariate normal distribution is ______.
7.
The model is yij…k =  + βi + j +…….+ eij….k called _______.
8.
Y = Xβ + e is a general linear hypothesis model of full rank and e is distributed as _______.
9.
Who was the chairman of national income in India, in 1949_______.
10.
Multicollinearity problem arises when the linear relationship between some or all _______
variables.
State True or False:
11. Multivariate normal distribution is more than one variable.
12.
13.
14.
Estimate an average value of y close to the true Y value.
The matrix equations
X Xˆ  X Y are called the normal equations.
Econometrics is a branch of statistics.
15. Constant variance may always be valid.
Answer in one or two sentences:
16. Define multivariate normal distribution.
17.
Define equation error.
18.
State any four properties of general linear hypothesis of full rank.
19.
Define Econometrics.
20.
Why is heteroscdasticity?
SECTION – B
Answer all the questions:
5 x 4 = 20
21. a. Show that any linear combination of n independent multivariate normal variate, is also
multivariate normal variate.
OR
22.
b.
If X is distributed according to N(, , then the marginal distribution of any set of
components of X is multivariate normal with means obtained by taking the corresponding
components  and  respectively.
a.
Define the following terms with example:
i) Component of variance models.
ii) Experimental design model.
OR
23.
b.
Define the following terms:
i) Linear model
ii) Measurement error
a.
Discuss the general linear hypothesis model of full rank.
OR
24.
b.
Explain of interval estimation in general liner hypothesis model of full rank.
a.
Explain the scope of econometrics.
OR
25.
b.
What are the difficulties in estimation of National income?
a.
Explain the Durbin Watson test.
OR
b.
Explain any two types of specification problems.
SECTION – C
Answer any FOUR questions:
4 x 15 = 60
26.
Derive the density function of Multivariate Normal distribution.
27.
What are the types of linear model and explain it?
28.
State and prove Gauss Markov theorem.
29.
Describe national income in India.
30.
Consider the model Yt = β0 + β1X1 + e with the following observation on Y on X.
Y 2 2 2 1 3 5 6 6 10 10 10 12 15 10 11
X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The model Ŷ  0.28  0.91X.
Spearman’s rank correlation test.
Examine the existence of heteroscedasticity using
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