Principal components can be used as multivariate indices, for example, when evaluating toxicity in phase III clinical trials for cancer treatment. The following table of n = 6 observations for p = 3 random variables is given by Herson (1980).
(a) Compute the PC correlation loadings, given that all three variables are standardized to unit length. (b) Compute the percentage of variance which all three PCs explain of the observed variables.
(c) Compute the percentage of covariance which all three PCs explain of the observed variables.