Find X intercept with error estimates

Hi,

So i have a set of energy values x and corresponding spectral information y.

I fit a straight line to my data with the polyfit function (which uses least square fitting)

I end up with coefficients p and the struct S containing the error estimates.

I want to find the x intercept with the associated uncertainity. How do I do this?

My attempt :

If I can find the errors on the coefficients p, then I can easily find the uncertainity in the x intercept through propagation of errors. But somehow I cant find the bounds of p in S?

PS : I know finding the intercept is just -p(2)/p(1), its the uncertainity I need help with.

Answer 1

[Matt J]

If I can find the errors on the coefficients p, then I can easily find the uncertainity in the x intercept through propagation of errors. But somehow I cant find the bounds of p in S?

The approximate covariance matrix is,

Rinv=inv(S.R);
cov=(Rinv*Rinv')*S.normr^2/S.df