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The purpose of a disambiguation page is to refer users to one of several articles that could, in principle, have the same title, in this case "Linear regression." On this page, both of the two entries ultimately directed the reader to the same article, namely Linear regression model. Wikipedia is not a dictionary. Accordingly, it seemed best to revert to the redirect. --R'n'B (call me Russ) 11:24, 9 May 2010 (UTC)[reply]
The page redirects to two different articles: either linear regression model or ordinary least squares. The two concepts are so frequently confused that disambiguation seems appropriate. In particular, more than half of articles linking to linear regression are in fact meant to refer to OLS. Having this page as a disambig will raise flags for “links to the disambiguation page”, and the links will be corrected. // stpasha » 18:35, 9 May 2010 (UTC)[reply]
First of all, it’s not really appropriate to say “For the use of the term in statistics, see Linear regression model” since both uses of this term are in statistics, and therefore such phrase is equivalent to the absence of any definition.
Secondly, linear regression IS a line/hyperplane. The fact that you can nonlinearly transform the data before fitting the regression does not change it. The fact that you might transform the data back and then make a picture in which the regression line does not look like a line anymore still does not change it either. Linear regression IS the line, meaning that it reduces the 2-dimensional joint probability cloud of (y,x) to a geometric line in the 2-dimensional space. // stpasha » 17:12, 20 May 2010 (UTC)[reply]
But if you fit a parabola or a sine wave by least squares in the usual way, it's still linear regression regardless of the fact that what you're fitting is not a line nor a hyperplane. Hence the way you've written this page is incorrect. Michael Hardy (talk) 17:11, 20 May 2010 (UTC)[reply]
Fitting a parabola means that you create a new variable x², go into 3-dimensional space, and fit a plane through the points (x, x²) of that space. So it’s still a linear regression regardless of the fact that what i'm fitting is actually a hyperplane (only in a higher-dimensional space). Fitting sine wave usually requires estimating the amplitude, the phase and the frequency — that's nonlinear regression already. // stpasha »
Michael, if you don't like my definition then provide yours. But you can't leave the term undefined. // stpasha »
It is linear regression if you're projecting onto the space spanned by two columns, the ith entry of one of which is sin ti and of the other is cos ti. And that gets you amplitude and phase shift. You're confused if you think that's nonlinear regression. Michael Hardy (talk) 00:02, 21 May 2010 (UTC)[reply]
But frequency parameter makes it nonlinear: sin(ωti). But then again, it depends on the model, — maybe in some settings the frequency could be assumed to be known exogenously. // stpasha »
I'm not a stats expert, but I do have some background in math and linear algebra. It seems like you guys are over-analyzing this from my perspective. Why not something like:
linear regression (disambiguation) listing the following:
linear regression -> linear regression (univariate)
general linear model -> linear regression (multivariate)
