Useful Formulae for Nonlinear Regression

Unlike in linear regression where exact results can be obtained under the stated assumptions, in nonlinear regression the results are only approximate. Furthermore, there do not exist nice matrix-based solutions for the various parameters. This section provides a convenient summary of the useful equations for nonlinear regression. In general, to compute the approximate confidence intervals for a nonlinear regression problem, the final grand Jacobian matrix, J, can be used in place of A and J in place of in the linear regression formulae. 

The approximate 100(1—a)% mean response confidence intervals, that is, the region within which the mean value of repeated measurements will lie 100(1—a)% of the time, for the point xa is given by 

Model validation would be performed in the similar manner as that for ordinary, least-squares analysis bearing in mind that the computed confidence intervals are only approximate. cannot be used as a measure of performance in nonlinear regression, since the relationship between the sums of squares is no longer orthogonal. 

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