Consider the following population regression model:
$$y_{i} = \beta _{1} + \beta_{2}x_{i} + \epsilon _{i},$$
where $i=1,...,n$. Assume $\epsilon \sim iid$, with the pdf in equation: $f(\epsilon ) = \alpha \epsilon$ for $0\leq \epsilon \leq 1$.
I have the following data: $X = (3,1,2,2)^{'}$, and $Y = (3,0,1,4)^{'}$.
By calculating the estimated intercept and the slope, I have $b_{1} = -1$, and $b_{2}=1.5$.
Two classical assumptions are violated in this model: one is no mean-zero errors $E(\epsilon {_i})\neq 0$, and the other one is the errors not being normal.
From this, can I infer anything about the true intercept of the model? I think we could either be overestimating or underestimating the true intercept.
Also, as long as I have an intercept in the model, then is the OLS still BLUE? I think that our estimate of the intercept is biased, but the OLS is still BLUE because we have an intercept in the model.