Etymology of "regression"

Solution 1:

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.

Solution 2:

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.