The terms “linear” and “nonlinear” refer to the dependence of the fitting function on the parameters and not the dependent variable . Thus if we are fitting to , and we do not adjust , but vary only and , then it is a linear fit, because of the linear dependence in and . But if we are also varying , it becomes a nonlinear fit. To be a linear fit, the second and higher derivatives of the fitting function with respect to all fitting parameters must all be zero.
If the parameter dependence is nonlinear we must use a more general
approach. Suppose our fitting function depends nonlinearly on the
. Then we must