M.Sc. (Semester III) (CBCS) Examination Nov/Dec-2018
Statistics
MULTIVARIATE ANALYSIS
Time: 2½ Hours Max. Marks: 70
Instructions: All Questions carry equal marks.
Figures to the right indicate full marks.
Q.1 Choose the most correct alternative: 14
An examination of differences across groups lies at the heart of the basic
concept of
PCA discriminant analysis
factor analysis None of these
Total variation explained by all principal components is that by the
original variables.
less than greater than
equal to none of these M
A is a graphical device for displaying clustering results.
dendrogram scatter plot
scree plot histogram
is a clustering procedure where all objects start out in one giant
cluster.
Non-hierarchical clustering Agglomerative clustering
Divisive clustering Single linkage clustering
are simple correlations between the variables and the factors.
Factor scores Specific variances
Communalities Factor loadings
The sample generalized variance is a measure of of a multivariate
distribution.
variability closeness
centrality none of these
A principal component analysis was run and the following eigen values were
obtained: 2.137, 1.5218, 0.442. How many components would you retain so
that 50% of the variation present in the old variables will be explained?
1 2
3 0
Statistical techniques that focus upon bring out the structure of simultaneous
relation among three or more variables are called analysis.
bivariate parametric
multivariate non-parametric
An unbiased estimator of Σ in based on a sample of size n is

A
n

A
n2

A
n−1
None of these
10) As the distance between two populations increases, misclassification error
increases decreases
remains constant none of these
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SLR-VR-485
11) If and Σ)are independent vectors, then is
distributed as
2 ∗ Σ
− Σ None of these
12) A measure of variability for the vector of principal components is

Both a and b None of these
13) Let and be a × vector which is independently distributed.
Then is distributed


is distributed as






14) Based on a random sample of size n from the distribution of is
Q.2 Answer the following (any four) 08
State definition of multivariate normal distribution.
Define Wishart matrix.
Define multiple correlation coefficient.
State additive property of multivariate normal distribution.
Define Hotelling's T2 statistics.
Write notes on following (any two) 06
Properties of Wishart distribution
Complete linkage algorithm
Mahalanobis distance.
Q.3 Answer the following (any two) 08
Show that a linear combination of components of a multivariate normal
random vector follows univariate normal distribution.
Describe canonical variable and canonical correlations.
Describe Roy's Union-Intersection principle.
Answer the following (any one) 06
Define variance-covariance matrix. State its properties.
Explain singular and non-singular multivariate normal distribution.
Q.4 Answer the following (any two) 10
Define hierarchical clustering. Explain single linkage algorithm for
clustering.
Explain discriminant analysis using ECM rule.
Derive characteristic function of multivariate normal distribution.
Answer the following (any one) 04
Find maximum likelihood estimator for based on a random sample from
multivariate normal distribution Np Σ .
State and prove additive property of Wishart distribution.
Q.5 Answer the following (any two) 14
Discuss principal components analysis. How it can be used as a dimension
reduction technique.
Discuss the procedure developed to classify a multivariate observation to
either of two available populations and Π2.
Derive moment generating function of Wishart distribution.