# Regarding the assumption of Classical Linear Regression Model

For the given model $y = x\beta + \varepsilon$, the four assumptions would be

1. The model is linear in $x$ and $\beta$, also additive in $\varepsilon$
2. The conditional mean of the error terms are zero (i.e. $E[\varepsilon|x] = 0)$
3. $Var[\varepsilon|x] = \sigma^2I_n$
4. Exogeneity of $x$ (i.e. either $x$ is fixed or independent of $\varepsilon$)

My questions is that in the case of the following situations which assumptions have been violated.

Case 1. $E[x'\varepsilon] \neq 0$ [I am not sure whether this implies the second or fourth assumption has been violated]

Case 2. $Cov(x_i,\varepsilon_i) \neq 0$ [I suppose the third one has been violated but could it imply the violation of other assumptions?]

Any help will be greatly appreciated.

• Just a quick point. These are some assumptions that are appropriate for certain things. There are not the assumptions, as there is no one unique set of assumptions that covers all uses of the model. – Matthew Drury Jun 5 '18 at 23:58