There seems to be a problem with the upper and lower confidence limits
in the NLSF.

I have some measurements which according to theory should follow an
exponentially decaying trend.

When I fit the Origin function ExpDecay1, the curve fit works fine but
the confidence limits becomes just the same as the curve fit, even though
the fitted data is scattered around the fitted curve.

One solution is to define a new function y=A*exp(-B*x), this gives a
curve fit which is equal to ExpDecay1(with y0=0) and confidece limits
outside the curve fit.

Martin,

In order to test your problem I opened up the project called Fitexmp1.OPJ.
This is a file located in the Samples folder inside your Origin directory
that exhibits an exponentially decaying behavior. I then opened up the
Non-Linear Curve Fitter (Analysis: Non-linear curve fit...) and selected
the ExpDecay1 function from the list of functions. This is the function
that has the formula y = y0 + A1*exp[-(x-x0)/t1]. I then assigned my
datasets (Action: Dataset) and fitted (Action: Fit) using the default
parameter initializations. The fit progressed normally. When I was happy
with my fit I plotted the Confidence Limits (Action: Results) and found
that the 95% CFs were plotted quite a ways away from the actual fit line.
I then looked at the parameters and saw that two of them were in a one-to-
one dependency which suggested to me that one of them was unecessary to
the fit. I therefore set x0 to 0 and fixed it. Once I did this I clicked
the iteration button again and then went back to Action: Results to re-
plot my Confidence Limits. At this point the CF lines plotted nicely.
The only time I found that they plotted right over the fit line was
when I reduced the percentage for the Confidence Limits from 95% to
something much lower. Is this what you did?

If this is not the way it happens for you, then how? Perhaps it would
be a good idea to explain the procedure that you went through. It
might also be helpful if this explanation were accompanied by your
data and sent to Technical Support at Microcal where we would be able
to assist you further. The necessary information is provided below.

Sincerely,
Ryan Toomey
Technical Services
Microcal Software, Inc.