Yes, REGRESSION is a Scrabble word!

Letter values in Scrabble US: R 1, E 1, G 2, R 1, E 1, S 1, S 1, I 1, O 1, N 1.

Is it a valid word?

REGRESSION is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

an abnormal state in which development has stopped prematurely
(psychiatry) a defense mechanism in which you flee from reality by assuming a more infantile state
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)
returning to a former state

Also: arrested development, infantile fixation, simple regression, regression toward the mean, statistical regression.