try doing a canonical anaysis. "Patrick Noffke" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > 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
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