Finding the 95% fit on an exponential graph
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Taylor Thomson on 1 Jun 2021
Commented: Jakob B. Nielsen on 3 Jun 2021
I'm trying to find the 95% fit from an exponential curve I'm running. The exponential curve is fit, but I would like to find the coefficient for the dotted line (95% prediction bound). Is there a way to do this from the cftool I am using? Or am I better going another way entirely?
Jakob B. Nielsen on 1 Jun 2021
There really should be a clever way to extract that info! I've looked at the cftool and I can't find an easy way. There is a rather involved way, though... Hit file -> generate code. Then run said code, you will get a figure and a handle named h. (Dont close the figure!)
In the command window, you can then inspect h. It will come up as a line array probably 3x1 in your case. This means h(3) is your prediction bound handle. You can then go and get h(3).XData and h(3).YData and you can put this back into the cftool and fit them, and this is your prediction bound expression.
If anybody has a more smooth way of doing this - up with it! :p
Jakob B. Nielsen on 3 Jun 2021
Yeah you are correct, it is fitting a curve to a curve. But I couldn't see any other clever way of extracting the 95% prediction bound, and since you fit a curve to a curve, the expression you get out should be your 95% prediction bound expression.
One issue: your xd,yd fit looks like a straight line fit, even though the shape of the data is very obviously exponential in nature. An exponential decay tapers off approaching 0 as x goes to inf, and since this is data representing an upper bound you have data hitting what looks like 5,4 ish at x -> inf. You should try to subtract 5,4 (or whatever the correct value is, you can tell much more easily from the data than I can :) from the yd array and fit again - then add 5,4 to the finished full function.
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