# Error on Measurement

I did an experiment on the Hall Effect, and found the voltage for the Hall "probe" (it was a strip of bismuth) as a function of a current magnetizing the B-field. Anyway, I did a least squares fit to find the regression line with A^T A = A^T b, and found four lines for each of my four data sets. I also found the uncertainties on the each of the four with $$\sigma = \sqrt{\frac{1}{N-2} \sum_{i=1}^N (y_i - A -Bx_i)^2}$$.

My question is that if I find the average regression line, using $$\sum_{i=1}^N \frac{y_i}{N}$$, would I simply take the mean of errors since they will all be dependent on the same factors? Should I add the errors in quadrature since they were all errors would be random, and dependent on different random factors?

marcusl