A new scheme for calculating weights and describing correlations in nonlinear least‐squares fits Free

The equations for nonlinear least‐squares analysis are reformulated in terms of dimensionless vectors and matrices. The diagonal elements of a dimensionless curvature matrix give the relative weights of the fit variables. Eigenvectors and eigenvalues of this matrix are used to describe the correlations between all of the parameters, and bivariant correlation coefficients may be calculated directly from its matrix elements. With the dimensionless formulation it is easy to compare confidence limits, correlations, and predictions based on the curvature matrix with results of Monte Carlo simulations. This provides a direct test of the parabolic approximation. Examples from a linear and biexponential model are presented to demonstrate these ideas. © 1996 American Institute of Physics.