My Math Forum Least square fit - uncertainty

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 February 4th, 2012, 09:11 AM #1 Newbie   Joined: Nov 2010 From: Sweden Posts: 18 Thanks: 0 Least square fit - uncertainty I used the least square method to fit a function, a second order polynomial function, to some data. Further I calculated the uncertainty in each coefficient. f(x) = a + b*log(x) + c*x Now I'd like to calculate some values using the function and determine the uncertainty in each derived value. For starters I'd like to find any maximum/minimum and calculate the uncertainty to any I find. My data is in this form, not actual data just a similar example: x 1, 2, 3, 4, 5, 6, 7 y 2, 1, 1, 0, 1, 2, 3 I've found a formula for calculating propagation of measurement uncertainties. $\displaystyle u_f= \sqrt{\sum\limits_{i=0}^n{ \left(u_i * \frac{\delta f}{\delta a_i}\right)^2} }$. Now my question, should I take a,b,c as my parameter-$a_i$. That is differentiate f like df/dc, $f'_c = x$ and multily that with the uncertainty $u_c$, etc like this. $\displaystyle u_f= \sqrt{ \left(u_b * \log(x)\right)^2 + \left(u_c *x\right)^2 }$ If this is right what x-value should I use to calculate the uncertainty to a calculated value? The value where there happens to be a maximum..? Like this? $\displaystyle u_f= \sqrt{ \left(u_b * \log(x_{max})\right)^2 + \left(u_c *x_{max}\right)^2 }$ Please point out any flaws in this!!!

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