LEAST-SQUARES ANALYSIS - PROPAGATION OF RANDOM ERRORS AND NEWTON-RAPHSON ITERATIVE FORMULA

The standard deviation and/or variances of least squares residuals in parameter evaluation in nonlinear models are often calculated approximately using Taylor's series, i.e. using the equation of propagation of random errors. A new iterative method is described to evaluate the standard deviations of least squares residuals without any approximation. It is suitable for nonlinear models with several independent variables, for implicit models and for experimental data with nonzero covariances as well.