1.  regression(n = noun.state) arrested development, fixation, infantile fixation - an abnormal state in which development has stopped prematurely;
is a kind of abnormalcy, abnormality

2.  regression(n = noun.process) - (psychiatry) a defense mechanism in which you flee from reality by assuming a more infantile state;
is a kind of defence, defence mechanism, defence reaction, defense, defense mechanism, defense reaction

3.  regression(n = noun.cognition) regression toward the mean, simple regression, statistical regression - 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);
is a kind of statistical method, statistical procedure
is a part of regression analysis
has particulars: linear regression, rectilinear regression, curvilinear regression

4.  regression(n = noun.act) regress, retrogression, retroversion, reversion - returning to a former state;
is a kind of reversal
Derived form verb regress₂

   The act of passing back or returning; retrogression; retrogradation. Sir T. Browne. [1913 Webster]

regression, n.
1 a backward movement, esp. a return to a former state.
2 a relapse or reversion.
3 Psychol. a return to an earlier stage of development, esp. through hypnosis or mental illness.
4 Statistics a measure of the relation between the mean value of one variable (e.g. output) and corresponding values of other variables (e.g. time and cost).

Etymology:
L regressio (as REGRESS)

N  reversion, return, revulsion, turning point, turn of the tide, status quo ante bellum, calm before a storm, alternation, inversion, recoil, retreat, regression, retrogression, restoration, relapse, recidivism, atavism, vicinism, reverting, regressive, revulsive, reactionary, retrorse, a rebours.

N  regress, regression, retrocession, retrogression, retrograduation, retroaction, reculade, retreat, withdrawal, retirement, remigration, recession, recess, crab-like motion, refluence, reflux, backwater, regurgitation, ebb, return, resilience reflection, reflexion (recoil), flip-flop, volte-face, counter motion, retrograde motion, backward movement, motion in reverse, counter movement, counter march, veering, tergiversation, recidivation, backsliding, fall, deterioration, recidivism, recidivity, reversal, relapse, turning point, receding, retrograde, retrogressive, regressive, refluent, reflex, recidivous, resilient, crab-like, balky, reactionary, back, backwards, reflexively, to the right about, a reculons, a rebours, revenons a nos moutons, as you were.

curvilinear regression, infinite regression, linear regression, multiple regression, rectilinear regression, regression analysis, regression coefficient, regression curve, regression equation, regression line, regression of y on x, regression toward the mean, simple regression, statistical regression