I am studying the Classical Regression Model for random samples.
Hence consider the random sample $(y_i,\mathbf{x_i})$
Where:
$$\mathbf{x_i}=\begin{pmatrix}{x_{i1}}\\{x_{i2}}\\.\\.\\{x_{ik}}\end{pmatrix}$$
Define:
1. Linearity: $y_i=x_i'\mathbf{\beta} + e_i$, where $\mathbf{\beta}=\begin{pmatrix}{{\beta}_{1}}\\{{\beta}_{2}}\\.\\.\\{\beta}{k}\end{pmatrix}$
2. Strict Exogeneity: $E(e_i|x_i')=0$
I already proved, without lots of trouble, that 1 and 2 imply that:
3. $E(y_i|x_i')=x_i'\beta$
However know I need to prove that 3 'implies that there exist error terms that satisfy 1 and 2' (where the 'error terms' are the $e_i$). I am not really sure how to do this. Do you have any suggestions?