Decreasing Multicollinearity

When the multicollinearity among the independent variables in a regression model is due to the high correlations of a multiplicative function with its constituent variables, the multicollinearity can be greatly reduced by centering these variables around minimizing constants before forming the multiplicative function. The values of these constants that minimize the multicollinearity are derived, and the conditions are identified under which centering the variables about their means will reduce the multicollinearity. Among the advantages of this procedure are that the mean square error remains at its minimum, that the coefficients for other variables in the model are unaffected by it, and that the OLS estimates for the original model can be calculated from those for the modified model. Thus, even when estimates of the original model are desired, the procedure can be used to reduce numerical error.