Thank you for your reply Jim.
Yes, the paper is
Karl Pearson, 'On Lines and Planes of Closest Fit to Systems of Points in Space'
[Philosophical Magazine 2:559-572, 1901]
I don't have access to the paper but the situation is this: I'm helping John Browne with his Grassmann Algebra application. He already has an axiom based implementation of the Pearson method. However, whenever I can, I like to make connection to the Mathematica array routines because they provide increased efficiency, especially on numerical problems. But I'm not familiar with all the statistical routines.
The method returns an exterior product in which the first factor is the centroid point (which is the best fit to a point) and then a series of normalized vectors which extend the fit to a line, then a plane, then a 3D multiplane etc., until the full dimension of the space is reached when the fit is trivially perfect. The lesser dimension fits are all subsets of the higher dimension fits.
