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What is the etymology of "regression" as in finding the coefficients of polynomials?

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Latin "re-" ("back") plus "-gredior, -gredi, -gressus sum" ("go"); the "-ion" suffix is common for forming nouns.

Thus "regression" literally means "going back". It is more commonly used in a figurative sense (as the opposite of "development"). The mathematical sense you mention comes from the idea that one would normally use a formula to calculate coordinates of a curve, but in "regression" one is starting with the coordinates and "going back" to the formula.

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    I accept your answer and would add that in this case it would seem that "regression" appears to be a misnomer because it assumes that the formula is far more than the artifact of a technique.
    – H2ONaCl
    Commented Apr 25, 2011 at 0:30
  • "progress backwards" feels like regression
    – Martin
    Commented Jun 1, 2019 at 10:16
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I think it inherits it merely from being part of the larger concept of regression analysis. From that, as per Wikipedia:

The term "regression" was coined by Francis Galton in the nineteenth century to describe a biological phenomenon. The phenomenon was that the heights of descendants of tall ancestors tend to regress down towards a normal average (a phenomenon also known as regression toward the mean).[6][7] For Galton, regression had only this biological meaning,[8][9] but his work was later extended by Udny Yule and Karl Pearson to a more general statistical context.

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    Galton later found the reverse, namely that the parents of tall children also tended on average to be taller than the mean of the population but shorter than the mean of their children's heights. So the eugenicist's concern that the population would regress to all being average was wrong in dynamically stable populations, and regression turned out to be the wrong word. Too late by then.
    – Henry
    Commented Feb 6, 2011 at 9:23
  • Etymology is fun stuff.
    – Chris B. Behrens
    Commented Feb 6, 2011 at 20:00
  • "Regression analysis" is not a larger concept than "regression" because second word is unfortunately and often assumed and dropped. Contrary to the appearance the original question is an inquiry about "regression analysis" - both words included.
    – H2ONaCl
    Commented Jul 20, 2011 at 2:09

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