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Linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

the term "regression" is coined by Francis Galton.

it seems Galton did't use the term "Linear regression" in his paper, so, who and when coined the term "Linear regression"?

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Early regressions used what we would now call "non-linear methods" that were iterative and quite tedious to manually perform before the invention of computers, electronic calculators or even publication of books with logarithm tables. Using derivative calculus, it was found that fitting equations which were linear in their coefficients, such as polynomials, could be directly solved using linear algebra. So the name "linear regression" historically refers both to the linear algebra and the type of equations that can be used with it - and a great cheer rose up throughout the world as well. Linear equations can also be solved by iterative, non-linear methods, but there is seldom reason to do so now.

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  • $\begingroup$ does "Early regressions" mean the approach Francis Galton used? $\endgroup$ – shi95 Apr 30 '19 at 3:22
  • $\begingroup$ There were many people trying to model data at the time of Galton. One of the few ways to model data back then was to plot points on a graph, draw a straight line through them by eyeballing it, and then create a "y = mx + b" model from that straight line - not so accurate, but often workable. Whether Galton used this crude method as a quick first approximation I do not know, but certainly the accuracy would have been too low for his work. The details of his technique for modeling data I do not have. My understanding is that he created the term "regression" as in "regression to the mean". $\endgroup$ – James Phillips Apr 30 '19 at 11:01

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