Next: , Up: Least-Squares Fitting   [Index]  37.1 Overview
Least-squares fits are found by minimizing \chi^2 (chi-squared),
the weighted sum of squared residuals over n experimental
datapoints (x_i, y_i) for the model Y(c,x),  \chi^2 = \sum_i w_i
(y_i - Y(c, x_i))^2  The p parameters of the model are c = {c_0,
c_1, …}. The weight factors w_i are given by w_i = 1/\sigma_i^2,
where \sigma_i is the experimental error on the data-point y_i.
The errors are assumed to be Gaussian and uncorrelated. For
unweighted data the chi-squared sum is computed without any
weight factors.  The fitting routines return the best-fit
parameters c and their p \times p covariance matrix. The
covariance matrix measures the statistical errors on the best-
fit parameters resulting from the errors on the data, \sigma_i,
and is defined as C_{ab} = <\delta c_a \delta c_b> where < >
denotes an average over the Gaussian error distributions of the
underlying datapoints.  The covariance matrix is calculated by
error propagation from the data e