I'm trying to figure out some simple regression
theory and would
appreciate help/comments from the talented folks
reading this.

In Simple Linear Regression (SLR),

Yi=beta0 + beta1 Xi + epsilon i

we assume that the parameters beta0 and beta1 are
constants along with
Xi

Now, the estimated SLR eqn is :

Y^i = bo + b1 Xi , where "^" denotes hat which is an
estimate of the
parameter

Now, when we make inferences for bo and b1, we talk
about their
expectations, variances and sampling distributions
which means that we
are saying at the outset that they are random
variables (RVs).

So, then would it be correct to say that bo, b1 are
RVs, but the
paramaters beta0, beta1 are NOT (they are constants)
?

Thanks,
Dave

P.S: I havesome follow up questions and will be
putting them up here
shortly

The good news is that the estimates have the property
that the mean of their sampling distribution is equal to
the population parameter they estimate. We get the
sampling distribution by the assumption of IID N(0,1)
errors.