What I wrote is correct hehe1223.

More specifically, thesampleregression function can be expressed as:

which estimates thepopulationregression function written as:

.

As such, it is legitimate to write,

.

Now, we know that the estimate of the intercept term is an unbiased estimate i.e.

Therefore,

where the mean of the stochastic disturbance term is (by assumption) zero.