Constrained regression in chemical engineering practice

Abstract

Absolute equality constraints in multiple regression are shown to introduce only minor modifications in the normal equations by a subset of the regression parameters. It is essential that these are ordered such that the subset is observable through the constraints. The constraints are shown to give greater residuals about the regression, but the precision in the parameter estimation is improved. In general power function curve fitting, a quadratically convergent iterative computation of the optimal exponents uses the normal equations as equality constraints. The correlations between the coefficients and the exponents in a sum of power functions become very high, when the number of terms increases such that their individual observability is being greatly reduced. The effect is shown to be a very poor precision in the parameter estimation and a heavy oscillation in the coefficients. The algorithms suggested are illustrated by curve fitting of some binary equilibrium data, where the relative volatility model gives a superior fit to the data.