Construct the 5 × 5 covariance matrix for the 5 data sets in Exercise 8.8.1 and find its principal variances and principal directions. What do you think is the dimension of the subspace the data lies in?

Data From Exercise 8.8.1

Find the mean, the variance, and the standard deviation of the following data sets:

(a) 1.1, 1.3, 1.5, 1.55, 1.6, 1.9, 2, 2.1; 

(b) 2., .9, .7, 1.5, 2.6, .3, .8, 1.4; 

(c) −2.9,−.5, .1,−1.5, −3.6, 1.3, .4,−.7; 

(d) 1.1, .2, .1, .6, 1.3,−.4,−.1, .4; 

(e) .9,−.4,−.8, ., 1.,−1.6,−1.2,−.7.