An alternative to polynomial regression is to use“dummy” predictors that are coded with orthogonal polynomial weights (like those used in orthogonal coding or contrast analyses).
With equallyspaced levels and equal cell sizes, these dummy variables are uncorrelated and hence the hierarchical strategy is unnecessary.
Exploratory: To explore whether a polynomial function of an independent variable is a better predictor of the dependent variable than a linear or lower order polynomial, one can proceed hierarchically and test whether the proportion of the variance explained by each added term is significant.
Despite the fact that the Hamming weight is large, because of the ease of representation and other improvements there are efficient hardware and software implementations for use in areas such as coding theory and cryptography.
See Also: cyclotomic polynomial, proof that the cyclotomic polynomial is irreducible, factoring all-one polynomials using the grouping method
This is version 4 of all one polynomial, born on 2005-02-05, modified 2005-02-09.
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