I was asked to expand SSxy
which can be written as
by expanding that as well.
You can drop either sample mean in SSxy, but not both.
Once again thanks for the help guys, its made this whole concept a lot easier to understand. I think I have definitely improved especially dealing with sigmas.
I had to study the same question in my university and as a homework question we had to derive the least square estimator in matrix notation. The full step by step derivation for the estimator for beta is provided here.