Minimizing the Effects of Collinearity in Polynomial Regression

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• 作者：Modechai Shacham and Neima Brauner
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：1997
• 出版时间：October 1997
• 年：1997
• 卷：36
• 期：10
• 页码：4405 - 4412
• 全文大小：197K
• 年卷期：v.36,no.10(October 1997)
• ISSN：1520-5045

文摘

Data transformation for obtaining the most accurate andstatistically valid correlation isdiscussed. It is shown that the degree of a polynomial used inregression is limited by collinearityamong the monomials. The significance of collinearity can best bemeasured by the truncationto natural error ratio. The truncation error is the error inrepresenting the highest power termby a lower degree polynomial, and the natural error is due to thelimited precision of theexperimental data. Several transformations for reducingcollinearity are introduced. The useof orthogonal polynomials provides an estimation of the truncation tonatural error ratio on thebasis of range and precision of the independent variable data.Consequently, the highest degreeof polynomial adequate for a particular set of data can be predicted.It is shown that thetransformation which yields values of the independent variable in therange of [-1,1] is themost effective in reducing collinearity and allows fitting the highestdegree polynomial to data.In an example presented, the use of this transformation enables anincrease in the degree ofthe statistically valid polynomial, thus yielding a much more accurateand well-behavedcorrelation.