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February 4th, 2012, 09:11 AM   #1
Joined: Nov 2010
From: Sweden

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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. .

Now my question, should I take a,b,c as my parameter-. That is differentiate f like df/dc, and multily that with the uncertainty , etc like this.

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?

Please point out any flaws in this!!!
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