M.Sc. (Semester II) (CBCS) Examination Oct/Nov-2017
Statistics
LINEAR MODELS
Day Date: Monday, 20-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Q.1 Choose the correct alternative: 05
In two way ANOVA with levels of factor levels of factor B and r
observations per cell, the d. f. for errors are
abr-1
ab None of these
If X1 and X2 are iid Then
Chi square with 2 d.f. Chi square with 1 d.f.
Normal ½) Normal
In the model with usual assumption, which of the
following parametric functions are estimable?
0 0
None of these
The C-matrix of a block design is
Never of full rank Always of full rank
May be of full rank None of these
If is an estimable linear parametric function in Gauss-Markoff
model, then its BLUE is
Not unique Unique
does not exists not unbiased
Q.1 Fill in the blanks: 05
If is the vector of adjusted treatment totals, then
In the model where ∈ iid is estimable.
The linear function for which E 0 for all is called
ANOCOVA is extension of
In the BIBD
Q.1 State whether following statements are True or False 04
In the one-way ANOCOVA with covariates error has − 1 d. f.
Balanced design is never connected.
The necessary and sufficient condition for connectedness of orthogonal
bloc design is
A system of normal equations is always consistent.
Q.2 Write short notes on the following. 08
One-way ANOCOVA model.
Multiple comparison tests.
Page 2 of 2
SLR-MS-650
Illustrate with example:- 06
Balancedness of a block design.
Estimation space.
Q.3 Explain Scheffe's multiple comparison procedure. 07
Obtain unbiased estimates of the parameters in the model
i …, j …ni where iid
07
Q.4 State ANOCOVA model. Obtain an expression for the residual sum of
squares in the ANOCOVA model.
07
Explain the following terms:-
Error space ii) Estimable parametric function.
07
Q.5 State and prove necessary and sufficient condition of orthogonality of a
connected block design.
07
Obtain the expression for reduced normal equations for treatments in a
GBD.
07
Q.6 Define BIBD. State and prove their parametric relationship. 07
In the two-way ANOVA model, with usual
assumptions, obtain least square estimates of the parameters.
07
Q.7 Explain three types of errors in the comparison procedures. 07
Prove that any solution to normal equation reduces residual sum of square. 07