Data transformation for obtaining the most accurate and statistically valid correlation is discussed. It is shown that the degree of a polynomial used in regression is limited by collinearity among the monomials. The significance of collinearity can best be measured by the truncation to natural error ratio. The truncation error is the error in representing 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. The use of orthogonal polynomials provides an estimation of the truncation to natural error ratio on the basis of range and precision of the independent variable data. Consequently, the highest degree of polynomial adequate for a particular set of data can be predicted. It is shown that the transformation which yields values of the independent variable in the range of [-1,1] is the most effective in reducing collinearity and allows fitting the highest degree polynomial to data. In an example 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.
ASJC Scopus subject areas
- Chemistry (all)
- Chemical Engineering (all)
- Industrial and Manufacturing Engineering