M.Sc. (Semester II) (CBCS) Examination Nov/Dec-2018
Statistics
LINEAR MODELS
Time: 2½ Hours Max. Marks: 70
Instructions: Q. No. 1 and Q. No. 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 Gauss-Markoff setup σ2 the least square estimator β
is unique if and only if X is
Full rank matrix Non-full rank matrix
Rank 1 matrix None of these
In linear model errors are
uncorrelated have constant variance
with zero mean all the above
Gauss Markov theorem states that in σ2) the lease square
estimate is itself
a unique BLUE not BLUE
not unique BLUE None of these
In ANOVA table the F-statistic will be large if error degrees of freedom
will
small large
n-p zero
The parametric function is contrast if
1 0
−1 None of these
Fill in the blanks: 05
One way ANOVA model is given by
In random effect model, the treatments are
If the linear function belongs to error space, then E ′
In linear model σ2 rank of estimation space
In a BIBD λ r k − 1
State whether the following statement are True or False 04
BIBD is always connected.
In the linear model Y Xβ ε, where σ2 the parametric λ′β is
estimable, if and only if λ′H λ′ . Where H S−S, S X′X.
A connected block design is said to be orthogonal if and only if v b.
A Randomized Block Design is always connected and balanced.
Q.2 Explain the following terms:- 06
Analysis of variance
Connected design
Page 2 of 2
SLR-VR-483
Define the terms with an diagram:- 08
Incomplete block design
Estimability of a parametric function
Q.3 State one-way ANOVA model and obtain least square estimates of the
parameters.
07
State and prove the Gauss Markov theorem. 07
Q.4 Write down two-way ANOVA model without interaction. Obtain estimates of
parameters in it.
07
Define BIBD. Write down parametric relationship in it. 07
Q.5 State and prove necessary and sufficient condition for orthogonality of a
block design.
07
Prove following properties of a BIBD(v, with appropriate
assumptions.
07
N′N r − λ Iv λ Evv
r k − 1 λ −
Q.6 In the linear model Y Xβ ε, where σ2). Prove that a linear
parametric function λ′β estimable if and only if λ €
07
Describe Tuckey's multiple comparison test. 07
Q.7 State and prove general linear hypothesis in a general linear model. 07
Write one-way ANOCOVA model and obtain LSE of the parameters. 07