Those interested should also look at the contribution to the discussion group
by David Colquhoun (posted April 21st, 1997).

I thank Donald Jenkinson for his very useful information. Indeed, when
disabling the "Use Chi^2-Formula for errors" option, the error estimates for
the parameter of the fitted function are the same as in Origin 3.5.
The curve fitting does seem to work correctly! I must therefore retract my
harsh criticism. Sorry, folks! On the other hand, this option really should
be documented quickly and that should have been done in the first place.
It is strange why one would want to consider the errors of each data point
for the parameter estimation but not for the error of the parameter.

When you select a weighting method (Instrumental, Statistical, Arbitrary
Dataset, or Direct Weighting) from the Weighting Method drop-down list in the
fitter's Control Parameters dialog box (Options:Control), the Use Chi-Squared
Formula for Errors check box becomes active. This check box affects the
(parameter) Error list box values in the Fitting Session dialog box
(Action:Fit) when fitting by clicking the n Iterations button. (The Use
Chi-Squared Formula for Errors check box does not affect the fit curve; it
only
affects the calculation of parameter errors.)
If the Use Chi-Squared Formula for Errors check box is cleared, then the
parameter errors are calculated as follows:
error[i] = SQRT[cov[i][i]]
If the Use Chi-Squared Formula for Errors check box is selected, then the
parameter errors are calculated as follows:
error[i] = SQRT[cov[i][i] *ChiSqr]
Note 1: The error values obtained when the check box is cleared are the same
results obtained in Origin 3.5.
Note 2: When No Weighting is selected from the Weighting Method drop-down
list
in the Control Parameters dialog box, the parameter errors are calculated as
follows:
error[i] = SQRT[cov[i][i] * ChiSqr]