ALWAYS plot everything. Do that before you do anything else.
plot(xavg_40s1,havg_40s1,'.')
grid on
So your data looks like a simple sigmoid function. One option might be to just use a scaled cumulative normal CDF.
ft = fittype('a + b*normcdf(x,mu,sig)','indep','x')
ft =
General model:
ft(a,b,mu,sig,x) = a + b*normcdf(x,mu,sig)
Fopts = fitoptions(ft);
Fopts.Lower = [-1 0 15 .1];
Fopts.Upper = [1 2 16 3];
Fopts.StartPoint = [0 1 15.2 1];
mdl = fit(xavg_40s1',havg_40s1',ft,Fopts)
mdl =
General model:
mdl(x) = a + b*normcdf(x,mu,sig)
Coefficients (with 95% confidence bounds):
a = -0.03595 (-0.03972, -0.03218)
b = 1.037 (1.031, 1.042)
mu = 15.21 (15.2, 15.21)
sig = 0.1 (fixed at bound)
plot(mdl)
hold on
plot(xavg_40s1,havg_40s1,'.')
It fits reasonably well. The toe and shoulder regions have some lack of fit, but I would not expect any nonlinear function to fit that terribly well in those areas, because it almost looks like a strange quasi-linear segment in there at the top.
Could I do a better job? Well, yes. I'd use a spline model. With little effort, my SLM toolbox, for example, gives this:
slm = slmengine(xavg_40s1,havg_40s1,'increasing','on','leftslope',0,'rightslope',0,'plot','on','knots',[12, 13 14:.1:16 17 18]);
