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.
With one variable, the answer is to use orthogonal polynomials. Then the lower order coefficients don't change by adding higher order terms. Does this concept extend to multivariate regression? Are there multivariate orthogonal polynomials? My first guess would be there are (maybe with terms like cos^2(u), cos(u)cos(v), and cos^2(v)?). Does the idea that addition of higher order terms won't affect your lower order coefficients also extend to the multivariate case? Could someone please enlighten me or point me to a reference (preferrably one with practical & useful examples in addition to the theory)? Thank you kindly in advance for your help, Pat . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
