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I was given 10 data-points of time and the number of decays. I linearized them (by looking at $ln(A(t))$ where $A(t)$ is the number of decays) and wanted to compare linear regression, weightened linear regression and poisson regression.

For the Poisson regression I used the sekant method to find $a$ and $b$ for $y=a+bx$. I'd like to know the uncertainty of the a and b I found. For the linear regression we deduced a formula for the uncertainties by the gaussian error propagation, but this is not possible here as I have found $a$ and $b$ numerically here.

I'd like to know whether there's a better way than calculating the gaussian error for every step of iteration by taking partial derivatives for the used $a,b,x_i,y_i$ from the previous step.

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