How to obtain the uncertainties in the obtained fitting parameters from the confidence bounds in the curve fitting toolbox?

Hi,

I have fitted an equation to the data and I have gotten the value of the fitting parameters using curve fitting toolbox. Therefore, I have also gotten the 95% confidence bounds for each fitting parameter. I am wondering how can I obtain the uncertainties in the fitting parameters from the confidence bounds I have for each parameter?

Thanks in advance!

Answer 1

[Nayan]

Hi

The uncertainty of a fitted parameter can be estimated from the confidence bounds obtained from the Curve Fitting Toolbox in MATLAB.

1. The uncertainty of the parameter can be estimated from the half-width of the confidence interval, which is given by:Uncertainty = (Upper Bound - Lower Bound) / 2 where Upper Bound and Lower Bound are the upper and lower limits of the confidence interval, respectively.

Note that the uncertainty of a parameter depends on the quality and representativeness of the data, the validity of the model assumptions, and the appropriateness of the chosen model. Therefore, it is important to use good judgment and statistical expertise when interpreting the results.

I would suggest you to refer to the following Matlab link to evaluate your fit better :-

https://www.mathworks.com/help/curvefit/evaluate-a-curve-fit.html

Fit Postprocessing - MATLAB & Simulink (mathworks.com)

Hope this helps!

[Shaily_T]

Thanks for your response @Nayan.

Are the uncertainties obtained this way reliable?

And to make sure I got it correctly, let's say I have obtained a fit parameter "A" as 2.567 (2.520, 2.620) then the uncertainty would be (2.620-2.520)/2 = 0.05 and we can write the parameter "A" as 2.567+- 0.05. Is this correct?

Thank you!