M.Sc.(Statistics) (Semester II) (CBCS) Examination, 2017
LINEAR MODELS
Day Date: Friday, 21-04-2017 Max. Marks: 70
Time: 10:30 AM to 01.00 PM
N.B. Q. No. and Q. No are compulsory.
Attempt any three from Q. No. to Q. No.
Figures to the right indicate full marks.
Q.1 Choose correct alternative: 05
In linear model, X variance of should be
Non- Constant Interrelated Constant Unit
2 Which of the following is not necessary and sufficient
condition for estimability of parametric function
R
R PX=1
3 The degrees of freedom associated with error in two- way
classification with levels of variable levels of variable
B and r observations per cell are
pqr pqr-1 None of these
4 The C-matrix of block design is
Never of full rank Always of full rank
May be of full rank None of the above
5 If X and Y are independent random variables then
X2+XY is distributed as



None of these
Fill in the blanks: 05
Gauss-Mark off theorem states that, LSE of linear parametric
function in is its.
The quadratic forms in normal variables A X and BX are
independently distributed
For a BIBD
For a symmetric BIBD pair of treatments appears
exactly in blocks.
If then system has solutions.
Page 2 of 2
State the following sentence are True or False: 04
Regression analysis is used for data description, parameter
estimation, prediction, estimation and control the data.
In one-way ANOVA, if …. is rejected, then we
stop the analysis.
ANOCOVA is extension of ANOVA.
Balanced design is always connected.
Q.2 Consider the models Y1=
show that is estimable iff
P1= .
3+3
Show that any solution of normal equation actually minimizes
the residual sum of square.
Write short notes on the following: 4+4
Write Tukey's test for non- additivity.
Gauss- Mark off set up.
Q.3 Write one way ANOVA model in standard Gauss- Mark off form.
Obtain BLUE of difference between two treatment effects and
obtain its variance.
7+7
In the normal linear model describe procedure for
testing general linear hypothesis.
Q.4 Explain the following terms: 7+7
Error space
Estimation Space
Write two-way ANOVA model with one observation per cell.
Obtain test for testing H0: …..
Q.5 Define intra block design in BIBD. 7+7
State general block design model. Obtain reduced normal
equation for estimating treatment effects.
Q.6 State and prove Gauss-Morkoff theorem. 7+7
Write one way ANOCOVA model. Obtain test for significance of
Concomitant variable.
Q.7 Describe Tukey's multiple comparison test.
Explain the concepts: 7+7
Connectedness
Balancedness
Orthogenality