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# I need help with uncertainty of a curve fit

## I need help with uncertainty of a curve fit

(OP)
I'd like to know how I can find the uncertainty in "m" and "b", the two constants you get when you make a linear curve fit "y=mx+b".

I know there's a similar topic just below here

But it seems to be that the mean and standard deviation obtained through that method has the same units of "y". How would I find uncertainties that have the same units as "m" and "b"?

For example, say I'm curve fitting stress and strain data to get the Young's modulus of a material. How would I determine the uncertainty in the Young's modulus, in units of MPa?

### RE: I need help with uncertainty of a curve fit

Well...

Consider the equation y = mx

You get an uncertainty (via comparison of data) for the modelled vs. actual y.  The resulting "uncertainty" in m would then be simply calculated by U(m) = U(y)/x where U() are the uncertainties (errors).

In a similar manner, one could calculate uncertainties for both m and b, by plugging in the calculated value for m, and calculating what deviation in b is required to give the correct y value, and vice versa for m.

### RE: I need help with uncertainty of a curve fit

Any half-way decent Statistics textbook will derive for you formulas giving the expected values E(m) & E(b), and the variances V(m) & V(b).  These will all preserve the appropriate units.

The textbook should then go further and show you how to use these quantities to estimate the variances associated with using your regression equation for predictions:  V(y) and V(E(y)).  Make sure you understand the subtle difference between these two.

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