Talk:Linear regression
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In reference to recent edits which change stuff like <math>x_i</math> to ''x''<sub>''i''</sub> -- the math-tag processor is smart enough to use html markup in simple cases (instead of generating an image via latex). It seems that some of those changes weren't all that helpful, as the displayed text is unchanged and the html markup is harder to edit. I agree the in-line <math>x_1,\ldots,x_n</math> wasn't pretty; however, it does seem necessary to clarify "variables" for the benefit of readers who won't immediately see x as a vector. Wile E. Heresiarch 16:41, 2 Feb 2004 (UTC)
In reference to my recent edit on the paragraph containing the eqn y = a + b x + c^2 + e, I moved the discussion of that eqn up into the section titled "Statement of the linear regression model" since it has to do with the characterizing the class of models which are called "linear regression" models. I don't think it could be readily found in the middle of the discussion about parameter estimation. Wile E. Heresiarch 00:43, 10 Feb 2004 (UTC)
I have a question about the stronger set of assumptions (independent, normally distributed, equal variance, mean zero). What can be proven from these that can't be proven from assuming uncorrelated, equal variance, mean zero? Presumably there is some result stronger than the Gauss-Markov theorem. Wile E. Heresiarch 02:42, 10 Feb 2004 (UTC)
- At least a partial answer is that the validity of such things as the confidence interval for the slope of the regression line, unsing a t-distribution, relies on the normality assumptions. More later, maybe ... Michael Hardy 19:51, 10 Feb 2004 (UTC)
- It occurs to me that if independent, Gaussian, equal variance errors are assumed, a stronger result is that the least-squares estimates are the maximum likelihood estimates -- right? Happy editing, Wile E. Heresiarch 14:57, 29 Mar 2004 (UTC)
Hello. In taking a closer look at Galton's 1885 paper, I see that he used a variety of terms -- "mean filial regression towards mediocrity", "regression", "regression towards mediocrity" (p 1207), "law of regression", "filial regression" (p 1209), "average regression of the offspring", "filial regression" (p 1210), "ratio of regression", "tend to regress" and "tendency to regress", "mean regression", "regression" (p 1212) -- although not exactly "regression to the mean". So it seems that the claim that Galton specifically used the term "regression to the mean" should be substantiated. -- Also this same paper shows that Galton was aware that regression works the other way too (parents are less exceptional than their children). I'll probably tinker with the history section in a day or two. Happy editing, Wile E. Heresiarch 06:00, 27 Mar 2004 (UTC)
I am confused -- i don't like the notation of d being the solution vector -- how about using Beta1 and Beta0?