fitting data with equation

Hi guys, so I have alot of experimental data in column matrix y. And I want to use the equation below to find the best fit for my data y. This means have constant b adjusted with x varying, I know that x typically ranges from 1 to 5 with y and b ranges from 0 to 2.

I'm thinking of using a double loop. Would anyone give me tips on how to solve for it effectively? Thanks in advance. The equation is:

y= (1-0.05*x^(b))/(1-0.05*x^b)^2

Answer 1

[Star Strider]

I would use a nonlinear curve fitting function such as nlinfit, lsqcurvefit (or fminsearch indirectly).

However if your (x,y)>0, are not noisy, y>1, and you want an estimate of ‘b’, this might work:

b = log(20*(1-1./y))./log(x);

Otherwise, use a nonlinear parameter estimation routine.

[sarah]

Thanks.

What if I want to put in all the values of y into the equation, and i know the range for b and want it to estimate for x. However how can matlab tell me the error for each value?

[Star Strider]

I got the impression that ‘x’ is your independent variable, ‘y’ is your dependent variable, and you wanted to estimate the parameter ‘b’.

If you know ‘y’ and ‘b’ and you want to estimate ‘x’ I would still prefer a nonlinear parameter estimation routine. However, with the appropriate assumptions and reservations as I mentioned earlier, a bit of algebra produces this simplified expression:

x = (20-(1./y)).^(1./b);

The error for estimates of ‘x’ would be easiest to calculate using your original equation with the Statistics Toolbox nlinfit function, then nlparci, since x appears to be a parameter.

[sarah]

And may I ask how did you derive this expression? Thanks

[Star Strider]

Sure!

y = (1-0.05*x^b)/((1-0.05*x^b)^2

(1/y) = 1-0.05*x^b

(1-(1/y))*20 = x^b

x = ((1-(1/y))*20)^(1/b)

Then vectorise it to do the calculation:

x = ((1-(1./y))*20).^(1./b);