How to determine start and end points of fitting curve?

Hi all, I have

x=[0.25 0.50 0.75 1]
   y=[0.0001 0.1 0.6889 10]

and I use power(2) to get the fitting curve. Is there a way to determine some points in the fitting curve? Because, when I get my fitting curve equation and use the above data, I get for x=0.25,y = 0.048 which is quite far from 0.00001. Any idea anyone how can I fix this?

Answer 1

[dpb]

A power model doesn't fit these data worth a hooey at the lower end...try

plot(f,x,y,'*')
set(gca,'yscale','log')
ylim([y(1)/2 y(end)*2])

to see the problem; the curvature is positive for the fitted curve but negative in that region for the actual data. It appears either a 'power1' or linear in both log(x) log(y) would be a better fit of these data than 'power2'.

Addendum

b=polyfit(log(x),log(y),1);             % fit log-log
yh=exp(polyval(b,log([x(1) x(end)])));  % Evaluate at end points
hold on
plot([x(1) x(end)],yh,'c')              % add to the previous plot

You'll see this is quite a lot closer...but looking at residual errors one finds that the power1 model may be best overall...will leave that as "exercise for the student" :)

[dpb]

Oh, which illustrate why one should never curvefit w/o first plotting the data to see what gives...