Interpretations of Estimation

We have a sample,

Xbar is the best estimate we have for mu.

Frequentist: Xbar is a random variable that its pdf is concentrate around mu. xbar is most probably mu.

Expected value of xbar is mu therefore it is an unbiased estimator.

 

MLE: xbar is most likely to happen if mu is xbar.

Bayesian: Mu is an unknown variable for me, conditional to this data, if I bet that it is Xbar, I will right most of the time. I will be probably be right.

 

Both Baysians and frequentists agree that least square method provide an unbiased estimator for regression line?