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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.

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  • $\begingroup$ 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". $\endgroup$
    – Adrian
    Oct 22, 2016 at 20:38
  • $\begingroup$ 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. $\endgroup$
    – z8080
    Oct 22, 2016 at 20:45
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    $\begingroup$ The use of the term "regression" is far from coincidental $\endgroup$
    – Glen_b
    Oct 22, 2016 at 23:17

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