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.
I think it inherits it merely from being part of the larger concept of regression analysis. From that, as per Wikipedia: