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(gnuplot.info)beginner's guide

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 `fit` (Note: fit ) is used to find a set of parameters that 'best' fits your
 data to your user-defined function.  The fit is judged on the basis of the the
 sum of the squared differences or 'residuals' (SSR) between the input data
 points and the function values, evaluated at the same places.  This quantity
 is often called 'chisquare' (i.e., the Greek letter chi, to the power of
 2).  The algorithm attempts to minimize SSR, or more precisely, WSSR, as the
 residuals are 'weighted' by the input data errors (or 1.0) before being
 squared; see `fit error_estimates` for details.

 That's why it is called 'least-squares fitting'.  Let's look at an example
 to see what is meant by 'non-linear', but first we had better go over some
 terms.  Here it is convenient to use z as the dependent variable for
 user-defined functions of either one independent variable, z=f(x), or two
 independent variables, z=f(x,y).  A parameter is a user-defined variable
 that `fit` will adjust, i.e., an unknown quantity in the function
 declaration.  Linearity/non-linearity refers to the relationship of the
 dependent variable, z, to the parameters which `fit` is adjusting, not of
 z to the independent variables, x and/or y.  (To be technical, the
 second {and higher} derivatives of the fitting function with respect to
 the parameters are zero for a linear least-squares problem).

 For linear least-squares (LLS), the user-defined function will be a sum of
 simple functions, not involving any parameters, each multiplied by one
 parameter.  NLLS handles more complicated functions in which parameters can
 be used in a large number of ways.  An example that illustrates the
 difference between linear and nonlinear least-squares is the Fourier series.
 One member may be written as
      z=a*sin(c*x) + b*cos(c*x).
 If a and b are the unknown parameters and c is constant, then estimating
 values of the parameters is a linear least-squares problem.  However, if
 c is an unknown parameter, the problem is nonlinear.

 In the linear case, parameter values can be determined by comparatively
 simple linear algebra, in one direct step.  However LLS is a special case
 which is also solved along with more general NLLS problems by the iterative
 procedure that `gnuplot` (Note: gnuplot ) uses.  fit attempts to find the
 minimum by doing a search.  Each step (iteration) calculates WSSR with a new
 set of parameter values.  The Marquardt-Levenberg algorithm selects the
 parameter values for the next iteration.  The process continues until a preset
 criterium is met, either (1) the fit has "converged" (the relative change in
 WSSR is less than FIT_LIMIT), or (2) it reaches a preset iteration count
 limit, FIT_MAXITER (see `fit control variables`
 (Note: control variables )).  The fit may also be interrupted and
 subsequently halted from the keyboard (see `fit`).

 Often the function to be fitted will be based on a model (or theory) that
 attempts to describe or predict the behaviour of the data.  Then `fit` can
 be used to find values for the free parameters of the model, to determine
 how well the data fits the model, and to estimate an error range for each
 parameter.  See `fit error_estimates`.

 Alternatively, in curve-fitting, functions are selected independent of
 a model (on the basis of experience as to which are likely to describe
 the trend of the data with the desired resolution and a minimum number
 of parameters*functions.)  The `fit` solution then provides an analytic
 representation of the curve.

 However, if all you really want is a smooth curve through your data points,
 the `smooth` (Note: smooth ) option to  `plot` (Note: plot ) may be what
 you've been looking for rather than `fit`.