Uncertainty in values from Matlab Curve Fitting

[tommyball]

Hi-

I apologize if this has been covered elsewhere, but after much searching with no luck...

I am taking a lab class, the first in a while, and am using Matlab's Curve Fitting tool to fit data to exponential curves.

My question is how to translate (if possible) the "goodness of fit" data it returns into uncertainties in the returned coefficients.

For example, this is an exponential decay of the form:

a*(1-2*exp(-x/b))

I need to report the returned value for b with an uncertainty.

I have not had much schooling in statistics or error analysis, just a couple lectures 2 years ago covering sig figs and least squares. I'm just thinking that with all Matlab's Curve Fitting Toolbox can do, there has to be a way to produce an uncertainty for the coefficients.

Thank you,
T.

 

[mmwave]

Hi T,

Thank you for your question. It is important to consider uncertainties when reporting your results, especially in scientific research. Fortunately, Matlab's Curve Fitting tool does have the capability to calculate uncertainties for your fitted coefficients. Here are the steps to do so:

1. After fitting your data to the exponential curve, select the "Curve Fit" tab at the top of the Curve Fitting window.

2. Under the "Fit Options" section, click on the "More Options" button.

3. In the new window that appears, select the "Coefficient Covariance" option under the "Output Options" section.

4. Click on the "Apply" button and then close the window.

5. Now, when you view the fit results, you will see a table that includes the values for your fitted coefficients as well as their corresponding uncertainties.

The uncertainties are calculated based on the covariance matrix, which takes into account the errors in your data points and the correlation between your fitted coefficients. I suggest looking into some resources on error analysis and uncertainty calculation for a better understanding of these concepts.

I hope this helps and best of luck with your lab class!
Scientist and Matlab User