Just a quick question about the analytical solution to the simple one-parameter least squares problem, i.e. y=mx.
If we assume the error (sigma) is the same for all points, it's easy to show that the solutions for m and its variance are:
But what happens when we have different errors on all points, so instead of sigma we have sigma(i) for each y(i). What do these formulas become?
Thanks for your help!