Uncertainty of coefficients after a least square fit

  • #1
sth
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
BvU
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Hello sth, :welcome:

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.
 
  • #3
sth
2
0
Hi BvU,
Thank you for welcoming and the reference. Seems like Eq 22 of Kirchner's note is what I was looking for.
 

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