5 - Curve Fitting and Evaluation

Abstract

This chapter draws attention to the fact that the most important parameters in the system evaluation process are the constant coefficients of the equations representing hypotheses. Thus, this chapter presents appropriate procedures for determining and evaluating the state and the output functions of the system. The nonlinear regression process starts with the initial guesses of the model parameters. If these initial values are not appropriate, the process may not converge to the least sum of squares of the error terms. In addition, there is always some uncertainty whether the process converged to the least sum of squared errors, or to a trap. No single rule is valid for all cases for determining the initial guesses of the model parameters. The main criteria for accepting or rejecting the experimental hypothesis are the “t” tests for the constant coefficients of the mathematical model of the system. However, the predictive value and accuracy of the model are estimated from the coefficient of determination and the standard deviation from regression. Sometimes, the correlation matrix of the parameter estimates may also be included in the evaluation of the mathematical model.