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(gnuplot.info)statistical overview

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 The theory of non-linear least-squares (NLLS) is generally described in terms
 of a normal distribution of errors, that is, the input data is assumed to be
 a sample from a population having a given mean and a Gaussian (normal)
 distribution about the mean with a given standard deviation.  For a sample of
 sufficiently large size, and knowing the population standard deviation, one
 can use the statistics of the chisquare distribution to describe a "goodness
 of fit" by looking at the variable often called "chisquare".  Here, it is
 sufficient to say that a reduced chisquare (chisquare/degrees of freedom,
 where degrees of freedom is the number of datapoints less the number of
 parameters being fitted) of 1.0 is an indication that the weighted sum of
 squared deviations between the fitted function and the data points is the
 same as that expected for a random sample from a population characterized by
 the function with the current value of the parameters and the given standard
 deviations.

 If the standard deviation for the population is not constant, as in counting
 statistics where variance = counts, then each point should be individually
 weighted when comparing the observed sum of deviations and the expected sum
 of deviations.

 At the conclusion `fit` (Note: fit ) reports 'stdfit', the standard
 deviation of the fit, which is the rms of the residuals, and the variance of
 the residuals, also called 'reduced chisquare' when the data points are
 weighted.  The number of degrees of freedom (the number of data points minus
 the number of fitted parameters) is used in these estimates because the
 parameters used in calculating the residuals of the datapoints were obtained
 from the same data.

 To estimate confidence levels for the parameters, one can use the minimum
 chisquare obtained from the fit and chisquare statistics to determine the
 value of chisquare corresponding to the desired confidence level, but
 considerably more calculation is required to determine the combinations of
 parameters which produce such values.

 Rather than determine confidence intervals, `fit` reports parameter error
 estimates which are readily obtained from the variance-covariance matrix
 after the final iteration.  By convention, these estimates are called
 "standard errors" or "asymptotic standard errors", since they are calculated
 in the same way as the standard errors (standard deviation of each parameter)
 of a linear least-squares problem, even though the statistical conditions for
 designating the quantity calculated to be a standard deviation are not
 generally valid for the NLLS problem.  The asymptotic standard errors are
 generally over-optimistic and should not be used for determining confidence
 levels, but are useful for qualitative purposes.

 The final solution also produces a correlation matrix, which gives an
 indication of the correlation of parameters in the region of the solution;
 if one parameter is changed, increasing chisquare, does changing another
 compensate?  The main diagonal elements, autocorrelation, are all 1; if
 all parameters were independent, all other elements would be nearly 0.  Two
 variables which completely compensate each other would have an off-diagonal
 element of unit magnitude, with a sign depending on whether the relation is
 proportional or inversely proportional.  The smaller the magnitudes of the
 off-diagonal elements, the closer the estimates of the standard deviation
 of each parameter would be to the asymptotic standard error.