Curve fitting toolbox can return bogus results for 2 term exponenti... (2024)

Yes, I was going to try setting bounds on these and see if I could fix it. I am in an early exploratory phase just trying out different fits to a larger data set and just sort of stumbled into this issue. However, my real concern here (which I guess I didn't make very clear based on the other comment) was that the toolbox returns coefficients which cause f(x) to work out to zero but then plots and displays stats for a different non-zero curve.

Scroll all the way to the right in my screenshot and you will see what I mean. a=-c and b=d so that f(x)=a*exp(b*x)+c*exp(d*x) is actually a*exp(b*x)- a*exp(b*x)=0.

Well, what you know is that they came out the same to four decimal places . You would have to use coefficients() of the fit object to see more decimal places.

I think you nailed it on that comment. I was only working in the toolbox and hadn't exported any fitobjects to check coefficients. I figured I would go check and when I re-ran the fit, I got a slightly different result. The a and c coefficients on the second attempt are 2 orders of magnitude less and do show some disagreement in the last decimal. I assume the same is true of b and d.

I wonder, is there a way to change the number format of the results window in cftool? It's a little annoying to not have any (obvious) control over that inside the toolbox.

Thanks for your help!

Sorry, there is not much control over the provided apps. Sometimes if you dig into the source code for long enough you can come up with a usable code change, but most of the time it is a change in code that is needed, not a change in some setting. (Occasionally if you dig harder still, it is possible to figure out how to dig into the internals far enough to change some settings without changing the source code.)

mdl1 =

General model Exp1: mdl1(x) = a*exp(b*x) Coefficients (with 95% confidence bounds): a = 0.5475 (0.441, 0.654) b = 0.01853 (0.0175, 0.01957)

G1 = struct with fields:

sse: 1.8182 rsquare: 0.9973 dfe: 10 adjrsquare: 0.9970 rmse: 0.4264

mdl1 =

General model Exp1: mdl1(x) = a*exp(b*x) Coefficients (with 95% confidence bounds): a = 0.5475 (0.441, 0.654) b = 0.01853 (0.0175, 0.01957)

G1 = struct with fields:

sse: 1.8182 rsquare: 0.9973 dfe: 10 adjrsquare: 0.9970 rmse: 0.4264

mdl2 =

General model Exp2: mdl2(x) = a*exp(b*x) + c*exp(d*x) Coefficients (with 95% confidence bounds): a = 0.5936 (0.4233, 0.7638) b = 0.01812 (0.01667, 0.01956) c = -0.6606 (-1.324, 0.002361) d = -0.01838 (-0.07988, 0.04312)

G2 = struct with fields:

sse: 1.0043 rsquare: 0.9985 dfe: 8 adjrsquare: 0.9979 rmse: 0.3543

Sigh? With all due respect, you don't have the context nor did you speak to my question. The issue I noted was that the curve that was plotted and for which statistics (R-square) were reported was not the curve defined by the coefficients that were returned by the toolbox. There is a discrepancy when you say f(x) works out to zero then show a curve that is not zero. This is what I thought was a bug. How would poor starting values result in this mathematically? I don't follow. If I missed this in your reply, I apologize. It was so long, and frankly rude, that I just gave up on it. You spent a lot of energy telling me why my understanding is wrong without the perspective necessary to offer that advice.

The fit you show looks fine, but the one I show in my screenshot has a=-c and b=d so that f(x)=a*exp(b*x)+c*exp(d*x) is actually a*exp(b*x)- a*exp(b*x)=0.

As it turns out I have a decent understanding of curve fitting and the limitations of fitting small data sets to functions with multiple coefficients. Unfortunately, I have hundreds of similar curves of data (most of which have 2x to 3x the points) to which I have to find fits which share the same form. I am in an exploratory phase, trying out different things to see what works and what doesn't and was seemingly faced with a contradiction when f(x)=0 was not zero in the plot. I just happened to be on the 2-term exponential when this issue arose. I have tried many different forms, both built into the toolbox and custom forms, including 1-term exponentials, and my personal favorite at this stage f(x)=exp(a*x)+b*x-1. It isn't perfect and it presented its own buggy issues which is why I was trying the built in 2-term exponential. (That’s a story for a different thread).

After re-reading my original question, I see that I could have made the issue more clear. I apologize for any confusion that sprang from that.