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ANOVA is usually thought as equivalent to linear regression, which is very interesting.

Who first discovered this fact? Did Fisher know about this when he worked on ANOVA?

kjetil b halvorsen
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Alby
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  • Isn't it more that linear regression (ordinary least squares regression) and ANOVA are both cases of the general linear model. See this Q&A for a related discussion. I recalled reading somewhere that the general linear model entered the literature in the 50s or 60s, somewhat before the later generalization to generalized linear models (GLMs) in the 1970s and later, but I can't see to find or recall where I read the bit about the general linear model any longer. – Gavin Simpson Jun 18 '15 at 16:02
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    In terms of treating them as different classes of the same basic regression model, didn't that originate with Jacob Cohen with Psych Bull paper in 1968? Jacob Cohen (1968), "Multiple regression as a general data-analytic system", Psychological Bulletin 70 (6): 426–443 – user78229 Oct 19 '15 at 16:32
  • @MikeHunter I think you are right. I know this is a very old question, but do you want to turn your comment into an answer? If not, I may try. – Peter Flom Dec 07 '23 at 22:56
  • @PeterFlom be my guest... – user78229 Dec 10 '23 at 05:29
  • Oops. The Cohen paper is behind a pay wall. Oh well. – Peter Flom Dec 10 '23 at 10:52
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    @PeterFlom The original paper is paywalled but there are many ungated copies of it on various university websites. Here's one.... https://users.cla.umn.edu/~nwaller/prelim/cohenmultiplereg.pdf – user78229 Dec 13 '23 at 05:02
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    Thanks for that link, @MikeHunter . The article starts off by noting that the fact that ANOVA is the same as linear regression would not be news to a mathematical statistician. But it doesn't give a reference for that. So, I think Cohen introduced the equivalence to a larger audience, particularly psychologists, but he was not the first to notice it. – Peter Flom Dec 13 '23 at 10:17

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