Study the following output for Principal component analysis on "heptathlon" data and answer the following questions.

Output:

Importance of components:

PC1PC2PC3PC4PC5PC6

Standard deviation2.11191.09280.721810.676140.495240.27010

Proportion of Variance0.63720.17060.074430.065310.035040.01042

Cumulative Proportion0.63720.80780.882230.947540.982580.99300

PC7

Standard deviation0.2214

Proportion of Variance0.0070

Cumulative Proportion1.0000

1) If you want to take into account almost 95% variability in the data then how many principal components will you choose?

a) 1 b) 2 c) 3 d) 4

2) Now if you use Kaiser's criterion of selecting optimal number of Principal components then how many principal components will you choose?

a)1 b) 2 c) 3 d) 4

3) In principal component analysis what is the angle between principal components'?

a)00 b) 450 c) 900 d) >450

4) In order to perform factor analysis on a dataset having dispersion matrix ?, we must have,

a) ? = I, b) ? ? I c) ? can be anything d) None.

5) What can you say about Promax and Varimax rotations in Factor Analysis?

a) Factors obtained in both rotation methods are orthogonal (perpendicular).

b) Factors obtained in both rotation methods are not orthogonal.

c) Factors obtained in Promax rotation are orthogonal whereas factors obtained in Varimax rotation are not.

d) Factors obtained in Varimax rotation are orthogonal whereas factors obtained in Promax rotation are not.

2 3-i For matrix given by H = 3+i -1 answer questions 7 - 10 7 - Is H Hermitian? 8 - Find the Eigen-values of H. 9 - Find the Eigen-vectors of H. 10 - Find the transformation matrix U and show that it is unitary. Evaluate the following matrix product U-1HU.QUESTION 2 Find the best match for each. There may be repeats or responses that match to nothing. A symmetric continuous distribution with a mean equal to its mean and to its mode where the standard deviation is less than 1/2. A. Normal distribution X is continuous and defined for X>0, the density of X decreases monotonically, and E[X] = Var(X). B. Exponential Distribution X is a continuous random variable on (5,25) and Prob(X>x X>15) = (x-15)/10 for 15