"Regression" versus "regression to the mean" [duplicate]

Are The two concepts really two sides of the same coin ? The latter is often referred to simply as a regression, but surely this is just an unfortunate coincidence?

The former is about predicting values of a dependent variable from a weighted combination of values of independent variables , whereas the second is Simply the observation that, with time, the average of all so far observed values of a random variable will tend to approach its true mean.

• What are you asking exactly? "Are the two concepts really two sides of the same coin" is very vague. A nice connection between "regression" and "regression to the mean" is a stationary AR(1) where $x_t = \rho \, x_{t-1} + \epsilon_t$, $\{\epsilon_t\}$ is white noise and $\rho \in [0, 1[$. This is a linear regression involving a variable that exhibits "regression to the mean". Commented Oct 22, 2016 at 20:38
• By "Are the two concepts really two sides of the same coin" I simply meant to ask whether the two concepts are related, e.g. whether "regression to the mean" is a special case of "regression" (or perhaps vice-versa). Your answer seems to imply that this is indeed the case, i.e. that it is not just a misnomer or an unfortunate coincidence of terminology, although the example you provided does seem to me to forcefully marry the two concepts, i.e. force their usage in the same sentence. Commented Oct 22, 2016 at 20:45
• The use of the term "regression" is far from coincidental Commented Oct 22, 2016 at 23:17