Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Reversion; retrogression.
 n. Relapse to a less perfect or developed state.
 n. Psychology Reversion to an earlier or less mature pattern of feeling or behavior.
 n. Medicine A subsidence of the symptoms or process of a disease.
 n. Biology The return of a population to an earlier or less complex physical type in successive generations.
 n. Statistics The relationship between the mean value of a random variable and the corresponding values of one or more independent variables.
 n. Astronomy Retrograde motion of a celestial body.
 n. Geology A relative fall in sea level resulting in deposition of terrestrial strata over marine strata.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. An action of regressing, a return to a previous state.
 n. A psychotherapeutic method whereby healing is facilitated by inducing the patient to act out behaviour typical of an earlier developmental stage.
 n. An analytic method to measure the association of one or more independent variables with a dependent variable.
 n. An equation using specified and associated data for two or more variables such that one variable can be estimated from the remaining variable(s).
 n. The reappearance of a bug in a piece of software that had previously been fixed.
from the GNU version of the Collaborative International Dictionary of English
 n. The act of passing back or returning; retrogression; retrogradation.
from The Century Dictionary and Cyclopedia
 n. The act of passing back or returning; retrogression.
 n. In astronomy, motion from east toward west.
 n. In geometry, contrary flexure; also, the course of a curve at a cusp.
 n. In mathematics, a discrete series which has a last element but no first.
 n. In statistics, the tendency of one variable phenomenon that is correlated with another to revert to the general type and not to equal the amount of deviation of the particular phenomenon with which it is correlated.
 n. In breeding, the decline toward mediocrity of offspring from the mean of the two parents. Sometimes called filial regression.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. an abnormal state in which development has stopped prematurely
 n. (psychiatry) a defense mechanism in which you flee from reality by assuming a more infantile state
 n. the relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x)
 n. returning to a former state
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

The study of this phenomenon gave rise to the term regression, which has since been documented in many areas.

Cheng said that, among a list of 10 grievances, Chen also described Taiwan's legal system as "dead" and said he mourned what he described as a regression in Taiwan's democracy.

We should be moving forward and devising ways to enhance all of our citizens 'lives rather than instill fear and hatred, and that only rejection of concepts and forward looking ideas leading to regression is our salvation. simp

It reveals the regression from the Christian love of one's neighbour back to the pagan privileging of our tribe versus the barbarian Other.
Liberal multiculturalism masks an old barbarism with a human face

The recent regression is more about class politics than anything else.

These retired citizens have no interests in the well being of the country as a whole, regression is their only agenda and will not allow the Democrats to take this country in the right direction .. too bad America voted for change.

They are called the "omitted variables" or "error term" in regression terminology.
More on the Height of Bravery, Arnold Kling  EconLog  Library of Economics and Liberty

As far as the fairytale characters go, I just regard it as another indication of NASA's regression from a serious view of its mission.
Mars Phoenix Embarks on A New Career as a Guest Blogger  NASA Watch

However, though we talk a lot about the effects of demography and aging populations, etc., there is a curious sense in which we suddenly stop thinking about them when assuming things like long term regression to the mean of economic growth, and many other things.
The Volokh Conspiracy » Comparative Demographic Charts on Aging Populations

The theme of regression is certainly interesting, but this story somehow seemed to lack the import of such a weighty topic.
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