Regression and Propagation of Error Question

Oct 2016
Boston, MA

I am new to this forum and had a question about propagation of error.

I have n independent data sets consisting of mn points on which linear regression was performed for each data set. From these analyses, a slope and corresponding error for the slope were calculated. I want to determine the overall error when I average the slopes. Normally, I know that when averaging n values, each with their own error, the errors are added in quadrature and divided by Sqrt(n) to give an overall error. How do I determine the overall error in the case stated above? Also, are there any references that discuss the above situation? Thank you!