Nonlinear Regression and the Principle of Least Squares

This report gives the principles of the method used by the Helium Research Center of the Bureau of Mines when solving nonlinear-regression problems and contains the mathematical equations necessary to accomplish the following objectives: the evaluation of the parameters in such a way that the sum of the weighted squares of the residuals of an experimental observable is a true minimum, regardless of the functional relationship between the variables and these parameters; and the evaluation of all variances and covariances of the parameters by means of the usual approximation of the law for the propagation of errors.