# How exactly did Auguste Bravais come up with the regression line?

I am new to statistics and linear regression and I came across the face that auguste bravais discovered regression line but didn't realize it.

Auguste Bravais (1811-1863), professor of astronomy and physics, is probably best known for his work in crystallography (Nelson, 1998). With respect to error theory, he is best known for a paper he wrote in 1846 titled "Analyse mathématique sur les probabilités des erreurs de situation d'un point" [translated: "Mathematical analysis on the probability of errors of a point"]. This work is renowned for being the very first mathematical exposition of the theory of correlation. Pearson (1896), later to recall these remarks, said that it was Bravais who first discussed the fundamental theorems of the correlational calculus. In his famous paper of 1846, Bravais, mathematically, not empirically, found the equation of the normal surface for the frequency of error. Using both analytic and geometric methods, Bravais also essentially found what would eventually be coined "regression line." He did so through investigating how the various elliptical areas of the frequency surface vary given various directly observed quantities. Through this, he found the line of regression, but, in essence, did not realize it, and thus could not "make the leap" (Walker, 1929) necessary to claim the discovery of correlation or regression

My question is how did he use "various elliptical areas of the frequency surface" to come across the regression line? I don't understand it at all. Please use diagrams if you can. Not too much complex maths too cause I am a newbie. Just explain simply how that works.

• The work is available online books.google.com/… On a quick look it seemed to be about the first principal component rather than what we now know as one of the two regression lines but I could very well be wrong about that. Feb 7 at 13:49