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If I understand correctly, linear regression involves fitting a linear function to a dataset and computing the error in that function. There's also a notion of "general linear model" which seems to be more connected to ANOVA than to regression (or, at least that's how it works in Minitab; see here). If I understand correctly, ANOVA does not do any curve-fitting and hence my impression is that the term "general linear model" doesn't actually coincide with the fitting of linear functions to the data. Is this correct? Also, is Minitab terminology standard in this area?

goblin GONE
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  • Seems a little confused. I can't comment on Minitab documentation but "general linear model" covers both analysis of variance and regression in the plain or vanilla sense. Consider height in a linear model predicted by a single predictor, male or female, so that you end up fitting two means, mean height if male and mean height if female. That qualifies as an example of a regression and an example of analysis of variance. Whether you want to call the fit a "curve" is a different question. Informally, I wouldn't. No-one promised that a linear model means fitting a curve! – Nick Cox Jul 15 '18 at 09:50
  • @NickCox, the tag associated with the term "linear model" does. You can mouse-over to check this. – goblin GONE Jul 15 '18 at 10:08
  • General linear model is the umbrella term to both ANOVA (including ANCOVA, MANOVA...) and linear regression. It is _possible_ to do any ANOVA model throught a correct application of a linear regression program (see a dense [answer](https://stats.stackexchange.com/a/221868/3277)). However, a "general linear model" program will typically not use a regression software approach, rather, it will use "indicator variable matrix or overparameterization" approach _computationally_, exploiting generalized inversions. – ttnphns Jul 15 '18 at 10:09
  • Nothing in the tag about curves. But $y = b_0 + b_1 x$, say, defines a line. Statistically only the points $(y, b_0)$ and $(y, b_0 + b_1)$ are of much interest if $x$ is restricted to the set 0 and 1, but the geometry comes for free with the equation. Tell us what you understand by "linear function" here. – Nick Cox Jul 15 '18 at 12:20
  • @NickCox, I'm a student of mathematics. To me, a line is an example of a curve. My understanding of linear function is that it's used inconsistently. Some people would say $f(x,y) = ax+by + c$ defines a linear function. But some would say that unless $c = 0$, it's non-linear. Basically you have to pay attention to context. – goblin GONE Jul 15 '18 at 14:55
  • @NickCox, in more detail, my opinion is that $ax+by+c$ should be referred to as an *affine* function of $x$ and $y$, while the term *linear* should be reserved for $ax+by.$ In the language of polynomials, we could say: a polynomial (possibly involving multiple variables) is *affine* iff it is of degree $1$. It is *linear* iff it is *homogeneous* of degree $1$. – goblin GONE Jul 16 '18 at 05:58
  • Your latest comment seems to need to be edited into the question. Otherwise, the short answer to your question is an overwhelming but puzzled Yes. In statistical science, this is how the terms are used, that a linear function of predictors is fitted to the response. – Nick Cox Jul 16 '18 at 06:57

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