I lack your data. But it is simple enough to make some up.
x = rand(50,1);
y = 1 + 2*exp(0.75*x) + randn(size(x))/10;
plot(x,y,'o')
So some arbitrary crap data. The model is exponential.
mdl = fittype('a + b*exp(c*x)','indep','x');
fittedmdl = fit(x,y,mdl,'start',[1 1 1])
Pretty noisy data, so the parameters are not that close to the underlying model. fittedmdl is an object from the curve fitting TB.
whos fittedmdl
If you don't know what methods apply there, then use methods!!!!!!!
methods(fittedmdl)
Scan through the list. There, we see confint is one of the methods. Any bets what confint does? How about predint? Be careful, because you have both confint and predint available. You NEED to know the difference. confint just gives you intervals on the parameters.
xint = linspace(min(x),max(x),100);
CIF = predint(fittedmdl,xint,0.95,'Functional');
CIO = predint(fittedmdl,xint,0.95,'obs');
plot(fittedmdl)
hold on
plot(x,y,'o')
plot(xint,CIF,':b')
plot(xint,CIO,':g')
The wider set of bands allow you to predict where a new observation would fall. The narrow bands are around the estimated function itself. So the observational bands essentially have the estimated process noise added back in.
