# Poisson-Regression for finding the half-time

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.