Calculating error in coefficients determined from fitting a curve to data?

[pergradus]

I have a set of data points (x₀, y₀), (x₁, y₁), ... (x_i, y_i)

With each y_i there is an associated error e_i.

The data is modeled by the function:

y = a\exp(-bln^2(c/x))

I have determined values for the coefficients a, b, c and I know the residuals produced from the values of the coefficients I've calculated and the set of data. What I'm trying to do now is to calculate the error, or uncertainty if you prefer, associated with each coefficient. How do I go about this?

 

[Petr Mugver]

A rough approach could be this one:

if you calculated the coefficients a, b, and c starting from your data, it means you have at your disposal a formula for theese coefficients. For example

a = a (x_1,\dots,x_n,y_1,\dots,y_n)

Then you could write

\Delta a = \sum_{k=1}^n\frac{\partial a}{\partial y_k}\epsilon_k