MINIMIZING THE EFFECTS OF COLLINEARITY IN POLYNOMIAL REGRESSION

Data transformation for obtaining the most accurate and statistically valid correlation is discussed. It is shown that the degree of a polyn omial used in regression is limited by collinearity among the monomial s. The significance of collinearity can best be measured by the trunca tion to natural error ratio. The truncation error is the error in repr esenting the highest power term by a lower degree polynomial, and the natural error is due to the limited precision of the experimental data . Several transformations for reducing collinearity are introduced. Th e use of orthogonal polynomials provides an estimation of the truncati on to natural error ratio on the basis of range and precision of the i ndependent variable data. Consequently, the highest degree of polynomi al adequate for a particular set of data can be predicted. It is shown that the transformation which yields values of the independent variab le in the range of [-1,1] is the most effective in reducing collineari ty and allows fitting the highest degree polynomial to data. In an exa mple presented, the use of this transformation enables an increase in the degree of the statistically valid polynomial, thus yielding a much more accurate and well-behaved correlation.