(adsbygoogle = window.adsbygoogle || []).push({}); 1) Linear fit

I am running an experiment to find the linear relation between displacement (X) and voltage reading (V) of the measurement, when fitting a linear line to my measured data, such that:

V= m*X + b;

Based on the following links http://en.wikipedia.org/wiki/Regression_analysis (under Linear regression)

and

http://en.wikipedia.org/wiki/R-squared ( under Definitions)

I can find the The standard errors of 'm' and 'b' parameters, Sm and Sb, respectively. and R-squared

So the Uncertainty of my measurement is :

m -/+ Sm

and

b -/+ Sb

But I would like to use the fit in the following way :

x=(V-b)/m

How can I relate the fit error to this form of the equation ?

2) Non-Linear fit

In the second experiment I have the following cubic fit:

X= a3 * (V ^3) + a2 * (V ^2) + a1 * (V) + a0

How can I find the uncertainty of a3, a2, a1, and a0 ? because I could not find any reference for doing so.

Can I use the same formula I used in the linear case to find the R-squared here for the non-linear fit?

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# Uncertainty of linear and non linear least-squares fit

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