On 28 Feb 2003 14:59:52 -0800, [EMAIL PROTECTED] (Patrick Noffke) wrote: > I have a regression application where I fit data to polynomials of up > to 3 inputs (call them x1, x2, and x3). The problem I'm having is > selecting terms for the regression since there is a lot of > inter-dependence (e.g. x1^4 looks a lot like x1^6). If I add one more > term, the coefficients of other terms change greatly, and it becomes > difficult to evaluate the significance of each term and the overall > quality of the fit.
WHY do you want to evaluate the "significance of each term"? The main excuse for doing anything stepwise, IMHO, is that you are only concerned with precision of the achieved fit, because you know you aren't using it for extrapolation beyond the numbers at hand. If you are willing to *try* an equation with x-to-the-third, what is your reason not to *use* it, if it is useful in the slightest? By the way, what you see at any step about one variable is the test on dropping that single term, at that stage, since it is the 'partial' contribution. So you do not need to construct orthogonal polynomials for testing; it mainly simplifies and speeds up the consideration of alternatives. DO you have a purpose that you are trying to reach? Is there any reason you have to reach it in one step? If you are trying to do model-building that is supposed to be meaningful in the coefficients, then you are all messed up, to start with the regression -- For that, you want to *think about* how the values are generated, and where the error (or non-fit) arises, and so on. By the way, engineers tend to say that an equation is nonlinear with any term like X-squared, whereas we statisticians -- and our 'multiple-regression' computer programs -- are satisfied to include as MR any equation that is linear and additive in the coefficients (including what you wanted to call multivariate regression). In statistician's terminology, you are surely describing multiple regression. I once thought that "multivariate regression" was a clear reference to the MANOVA-extension of multiple regression, where there would be multiple Y's, multiple X's. When I searched (pre-Google), it seemed that the phrase had been used now and then in the way that I expected, but it really wasn't consistent. So I won't use that phrase unless I can define it at the time. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
