Propagating uncertainty through a regression equation

I want to propagage uncertainties through a regression equation (for now a linear one):

y= ax +b

Using the curve fitting tool I can get the values of a and b alog with their 95% conficence limits. Now my question is:

1. * how can I propagage these confidence limits to y?
2. * if my variable x has also uncertainty, how can it be propagated to y along with the confidence intervals of a and b?

[dpb]

Star's given more general answer; for polynomials a) is available from polyfit and polyval with the optional return arguments. See doc for each for the details.

Answer 1

[Star Strider]

Using the Statistics Toolbox functions nlinfit and nlparci you can get the confidence limits on the parameters. With nlpredci you can get the confidence limits on the estimated values, that are your ‘confidence limits on y’.

If x also has uncertainty, you have to use Total least squares. There are a few File Exchange Total least squares contributions, but no MATLAB toolbox functions implement it. You’ll need to explore them to see if they provide confidence limits on the the parameters and the predictions.