The Simple Linear Regression Least Squared Estimators, b0 and b1, are unbiased. In this video I show the proof.
What does it mean for X to not be random? I discuss this more in this video:
https://youtu.be/5Ezg9UXIyZs
Near minute 4, I mention that Sum(xi - xbar) = 0, here is a video showing this:
https://youtu.be/oyjkFmNMMKA
Near minute 8, I mention that Sum (xi - xbar)xi = Sum (xi - xbar) * (xi - xbar) = Sxx, here is a video showing this:
https://youtu.be/b0FCezzWqIg