error window to a model function after nlinfit

Hi I use nlinfit to fit an equation to a model, and get the value of the parameter with its associated error. Now I want to use this parameter with its error and plot another function, which should show the error region as well! For example: Equation 1: y=Acos(x)+Bsin(x) is fitted using nlinfit to give this. A=5 +- 0.1 B=3+-0.2 Now I want to use these values of A and B (with errors) to plot a function Y+-delY=(A+-delA)cosx +(B+-delB)sinx where del is the error .

Thanks

Answer 1

[John BG]

Hi Debi

clear all

dx=.001;x=[-2*pi:dx:2*pi];

a0=5;
da=.1;
alow=a0-da;
ahigh=a0+da;
a=[alow:0.1*da:ahigh];

b0=3;
db=.2;
blow=b0-db;
bhigh=b0+db;
b=[blow:0.1*db:bhigh];

y2low=0;
y2high=0;

for k=1:1:numel(x)

      y2=a*cos(x(k))+b*sin(x(k));
      y2low = [y2low min(y2)];
      y2high = [y2high max(y2)];

end

y=a0*cos(x)+b0*sin(x);
ny=[1:1:numel(y)];
plot(ny,y,'r');grid on
hold all;
plot(ny,y2low([2:end]),'b');
plot(ny,y2high([2:end]),'b');

.

the error function you want delY is

delY=y2high-y2low

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer

please click on the thumbs-up vote link

thanks in advance

John BG

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[John BG]

Thanks Debi, any more questions? if so feel free to ask

regards

John BG

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[DebiPrasad]

Thanks John, I had some questions related to your answer. I have emailed you . Please let me know

Answer 2

[Star Strider]

You have used the nlparci function to get the parameter confidence intervals.

The correct way to do what you want, that is to express the errors in the fit with respect to your data, is to calculate the confidence intervals on the prediction with the nlpredci function. That will give you the correct statistical result. It is also much more straightforward to implement.

The initially accepted answer is incorrect.

[DebiPrasad]

Hi Star Strider, This question is actually a follow up to a previous question which was answered by you: https://uk.mathworks.com/matlabcentral/answers/324424-nlinfit-to-an-equation . The equation from where I get the paramter is not a simple fitting function, but is solved for minima to get the values of the parameters best fitting to raw data. Now the fit is not great if I keep one of the parameter constant, but fits well when all the paramter are free. However the value obtained do not match to the experiment. But if I keep one value fixed, the not good fit give me a reasonable value of the other value. So I want to see if the raw data is in the error estimate of the model data found from the parameters. Thanks Debi

[Star Strider]

Hi Debi,

The nlinfit function does not allow you to constrain the parameters. The lsqcurvefit function does.

If you have the Optimization Toolbox, see if using the lsqcurvefit function with constraints on the parameter you want to limit will give you an acceptable fit to your data. I believe you can use nlparci and nlpredci with constrained parameter estimation outputs returned by lsqcurvefit, and I see nothing in the documentation for either function that indicates it would not be appropriate. (I know you can use them with lsqcurvefit with unconstrained parameters.)

Answer 3

[Jan]

See also:

• https://www.mathworks.com/matlabcentral/fileexchange/58262-pretty-area-error-bar-plot
• https://www.mathworks.com/matlabcentral/fileexchange/29534-stdshade

[DebiPrasad]

Thanks Jan Simon