Principal Component Analysis

Tan 2θ: slope term, varies between -1/2 and 1/2:

• The strength of the covariance, divided by the difference in variance.

• θ<45: term is positive because the variance in x is larger than in y (or if equal, x-error greater than y-error)
  θ=45: term is infinite (variance in x same as in y),
  θ>45: term is negative because variance in y greater than in x (or if equal, y-error greater than x-error).

• Note: since tan^-1 is a degenerate function, theta is ambigous - just a reference frame in which the variances are orthogonal to the coordinate axes.

σ_a and σ_b: variance terms

• σ_a: Variance of "size"...hybrid coordinate of height and weight

• σ_b: Variance of "overtall/undertall"...hybrid coordinate of difference of height and weight