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Regression to the Mean is a concept in sampling not regression. Why is it not called Sampling to the Mean?

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    Probably because it suits an alternative meaning of "regression": "a return to a former or less developed state." – Sycorax Jul 28 '16 at 13:39
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    What is the basis for your preliminary assertion? Could you elaborate a little on what you think "regression to the mean" is? (I believe both the original and conventional concepts of this phrase are not about sampling at all.) – whuber Jul 28 '16 at 13:39
  • Regression is when we predict a quantitative variable. Regression to the mean is when we sample, if we get an extreme observation then we can expect the next to be closer to the mean: this is statistical sampling concept. –  Jul 28 '16 at 13:41
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    Although that is a fair account of the *application* of "regression to the mean," the phenomenon itself is simply a mathematical theorem about certain kinds of bivariate distributions and related statistical models. This is what caused Hotelling, in a review of Secrist's book of business data, to complain that what Secrist did was akin to "proving the multiplication table by arranging elephants in rows and columns, and then doing the same for numerous other kinds of animals." – whuber Jul 28 '16 at 14:09
  • Neat, that's cool to know. –  Jul 28 '16 at 14:11
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    The interesting question is surely why do we call it linear regression when it does not fall backwards. – mdewey Jul 28 '16 at 14:45
  • hm, don't get it –  Jul 28 '16 at 15:00
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    You sort of have it backwards - 1. the "regression" in "linear regression" is kind of named after "regression to the mean" (since linear regression can be used to measure how much of it there is). 2. as just hinted regression to the mean *does* have something to do with linear regression. See the discussion [here](http://stats.stackexchange.com/questions/225882/what-does-this-plot-tell-me-about-my-linear-model/226054#226054) which illustrates this connection in some detail. Or [this](http://onlinelibrary.wiley.com/doi/10.1111/j.1740-9713.2011.00509.x/pdf) which takes us back to the origins – Glen_b Jul 28 '16 at 17:40

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Coming at this from the software world (rather than mathematics) a regression is usually defined as a step back in behaviour - i.e. regressing to an earlier state. Often this relates to something that used to work in an earlier release now being broken.

I (as a maths layman) therefore read "Regression to the Mean" to mean* as being to return (regress) back to a normal (mean) state. I.e. it's using "regression" in terms of its English language meaning, rather than something specifically mathematics related.

*no pun intended

Gordon
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    Although this is approximately the sense in which Galton first used the term "regression," it is also at the root of many misunderstandings and errors. The technical meaning being requested differs substantially from this one. See http://stats.stackexchange.com/a/17395/919 for a brief account of a famous example and http://stats.stackexchange.com/a/24649/919 for a little more information about the distinction. Conflating your colloquial understanding with the technical meaning is known as the "Regression Fallacy." – whuber Jul 28 '16 at 15:37
  • Interesting links - thanks (and I understand your point about the dangers of colloquialisms). Changing topic slightly - it's amusing the "metric mishap" is referenced in one; at the time I was working in the space industry, and it was understandably a, errr, how shall I put it politely... "talking point" – Gordon Jul 28 '16 at 16:32