standard deviation of parameters in lsqcurvefit?

1-Is there a way to get the standard deviation or any measure of error for the optimized parameters when using lsqcurvefit?

2-can someone tell me how to get the error surface( it could one multi-dimensional depending on the number of parameters you're optimizing) in lsqcurvefit? saying it differently the amount of error in each step it is going through along with the value of parameters at that step.

I've attached a simple example of lsqcurvefit. can you show me the standard deviation on that if possible.

Thanks

Answer 1

[Star Strider]

1. If you have the Statistics Toolbox, you can use nlparci to get the confidence intervals on the parameter estimates.
2. I am not certain what you want, but there are output Options you can set that will give you iteration updates with varying degrees of detail.

[Morteza]

All i'm looking for is for a measure of accuracy of these estimated parameters for example if it calculates the parameters to be 5, 15 ,2 . I wanna know whether they are for example 5±0.2, 15±2, 2±0.1 or 5±5, 15±20 and 2±3!!

[Star Strider]

The nlparci function will provide those for you, although instead of presenting them as, for instance, 5±0.2, it will present them as [4.8 5.2]. But it will give you the information you want about them.

For lsqcurvefit, you have to request all the outputs, in this syntax:

[beta,resnorm,resid,exitflag,output,lambda,J] = lsqcurvefit(...)

and then to get the confidence intervals from nlinfit, use this syntax for it:

ci = nlparci(beta,resid,'jacobian',J)

The output ‘ci’ are the confidence intervals for each parameter in the sequence you have presented them to nlparci in the ‘beta’ vector.

[Benjamin]

Correct. So in other words,

Standard deviation = SD = (ci(2) - beta)/2

Because nlparci gives the 95% confidence interval which is (+/-)2*SD.

Answer 2

[Matt J]

1. You could compute parameter covariance estimates from the output Jacobian and residuals,

   [x,resnorm,residual,exitflag,output,lambda,J]= lsqcurvefit(...)

   xCovariance = inv(J.'*J)*var(residual)

2. Wasn't entirely clear to me what you're asking for, but it sounds like you want to use the PlotFcns input option with @optimplotresnorm.