Uncertainty of coefficients after a least square fit

[sth]

Fitting data to a linear function (y=a0+a1*x) with least square gives the coefficients a0 and a1. I am having trouble with calculating the uncertainty of a0. I understand that the diagonal elements of the covariance matrix C is the square of the uncertainty of each coefficient if there are no off-diagonal elements. But what is the uncertainty of a0 if there are off-diagonal elements?

 

[BvU]

Hello sth,

Found your answers and a good reference in this thread

[edit] on second thought: the errors are the diagonal elements. The off-diagonal elements come in when you evaluate expressions where both coefficients appear and you want the uncertainty in the result.

 

[sth]

Hi BvU,
Thank you for welcoming and the reference. Seems like Eq 22 of Kirchner's note is what I was looking for.