Can we see the beta coefficients in OLS as mean values?

Question

Can we see the beta coefficients in OLS as mean values?

I mean the estimator β alone.

y=Xβ+ε

Answer 1

No, since the coefficient is the slope of line which minimizes the sum of squared residuals. In that sense it cannot be interpreted as the as the mean, you should rather interpret it as the marginal impact of X on Y.