Trivia: A little insight to the history & origin of "Least Squares"

[Carl_William]

TRIVIA:

A little insight to the origin and evolution of "Least Squares" and the normal equations:
The normal least square equations are linear.

This is just a little tidbit of info that many or some of you out there may appreciate to know – if you were not aware of it in the past.

I’ll try to keep it very simple. It its simplest form as most of you know; least squares curve fitting involves fitting “selected” data to a curve or straight line (if a linear fit is sufficient). Like the earth’s equator (an imaginary line); the resulting least squares fit is determined by minimizing the sum of the squares of each data point to the resulting line (fit) “excuse double talk.” Now what are the reasons this technique become so popular and useful….

The two most important reasons are:

(1) It is probably one of the most logical ways to create a curve fit (or course there are many other ways not discussed here).

(2) But the more important reason is that the classical least squares technique results in a set of linear equations "defined as the normal equations" which could be solved by hand or by using a simple arithmetic calculator. Reitterating to get my cardinal point across: Many years ago; especially prior to computers in the last 50 or so years and also especially before PCs became so powerful; it was extremely difficult to solve non-linear equations – especially sets of equations with two or more independent variables (and one or more dependent variables).

I hope I have not bored most of you with this blurb….