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
parameters
. Then we must
minimize

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