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Suppose I have a quadratic (weighted) least-square fit result obtained from a given set of data:

$$ f(x) = \underbrace{-0.243(\pm0.3324)}_{quad\_a}x^2\underbrace{-0.921(\pm0.061)}_{quad\_b}x\underbrace{-2.12(\pm0.0223)}_{quad\_c} $$ If I'm taking the derivative of $f(x)$ to have $f'(x) = Ax+B$, I wonder how can I figure out the uncertainties on $A$ and $B$? I also have the correlations

C(quad_a, quad_c) = -0.422
C(quad_a, quad_b) = -0.278

Thanks for the help!

ZR-
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  • Because $(A,B)$ is a known linear combination of the three fitted coefficients, all you need do is apply the (standard) formula for the variance of a linear combination. – whuber Aug 25 '21 at 18:05
  • @whuber Thanks for the comment! Is that $Var(aX+bY) = a^2Var(X) +b^2Var(Y) + 2abCov(X,Y)$ I'm still confused how to find the uncertainties of $A$ and $B$ from that. – ZR- Aug 25 '21 at 18:20
  • The duplicate asks exactly the same question and gives explicit formulas for the answer. All you have to do is plug in your particular values. – whuber Aug 25 '21 at 18:25

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