Saturday, August 31, 2013

Karl Pearson - Lines & Planes of Closest Fit

  I took another look at Cramer's Numerical Methods of Statistics and the section on Orthogonal Mean Square Regression (p. 309) seems more familiar now with the derivations of the last few blogs filling in a lot of the gaps. The section also cites Karl Pearson's 1901 paper On Lines and Planes of Closest Fit to Systems of Points in Space. This paper provides a lot of the missing details on the history of using normal errors but appears a little antiquated now. There are a lot of advantages to the approach using the Calculus of Variations. Pearson's analysis is a little different from the reduction of the variational equations to an eigenvector equation that was used here. It has come to be known as Principal Component Analysis.

Edits (Aug 31):  Pearson link & Principal Component Analysis

Supplemental (Sep 17): Pearson's paper was published in the Nov 1901 issue of Philosophical Magazine. The use of perpendicular deviations from a line was mentioned in a letter to the editor in the March 1901 issue of Nature by Ravenshear.

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