Model-parameter estimation using least squares

The use of the least-squares techniques for parameter estimation is critically evaluated by analyzing linear and non-linear models for situations in which the absolute or relative errors had a constant variance. Special emphasis is given to the estimation of the Monod-model parameters using biodegradation batch-test data. The error structure determines the optimum least-squares technique to be used for parameter estimation. The traditional absolute least-squares criterion, which minimizes the sum of the absolute residuals, should be used only when the absolute error has variance homogeneity. On the other hand, the non-traditional relative least-squares criterion, which minimizes the sum of the relative residuals, is the proper choice for cases in which the relative error has an approximately constant variance, a common characteristic for many analytical assays. The superiority of the relative residuals criterion is accentuated when the magnitude of the dependent variable varies widely.