A Standardization Technique to Reduce the Problem of Multicollinearity in Polynomial Regression Analysis

This paper attempts to explain how the problem of multicollinearity can be reduced in polynomial regression analysis. A simple standardizat ion technique is il lustrated to deal wi th curvi 1 ineari ty and mul ticoll ineari ty problems, Suppose we have a cubic relationship to solve, and that the independent variable.1 ’ has large values. (1) Y = co + clx + @X2 + QX3 Then, it is very likely that the problem of multicell variables X, A’: and X3 in equation (1) are collinear inearity arises s inte the independent wi th each other. In case of severe multicollinearity, this regression equation cannot be solved sinte the rank of the matrix is less than its order, If the tolerante is very small, but still larger than the specified tolerante level, unstable beta weights(standardized regression coefficents) and calculations can be expected. In this case, multicollinearity can also be detected by size of the standard errors o f beta, The problem of multicollinearity can be removed or reduced substantially by standardizing the linear, quadratic, and cubic terms in the polynomial regression equation. First, it is suggested that the independent variable is transformed in such a way that the resul ting mean is zero and the resul ting standard deviation is one. For example, the independent variable J’can be standardized by using the following linear transformation: (2) Standard i zed Vari ab 1 e (Z) = ~%,T’)/Sx Then, new quadratic and cubic terms are created by taking squared and tubed values of this standardized variable, (3) Squared Variable(ZZ) = (ciu_.~~/S~)~ (4) Cube