# OLS assumptions

• July 4th 2012, 12:05 PM
usagi_killer
OLS assumptions
http://img201.imageshack.us/img201/8...mptionsols.jpg

I don't get why the part boxed in red.

Note that X, Y and U are all random variables, how is $E(\beta_1 X|X) = \beta_1 X$ ?

Shouldn't it be $E(\beta_1 X|X) = \beta_1E(X|X)$ since $\beta_1$ is just a constant, then $E(X|X) = \sum_{i=1}^n x_i P(X=x_i|X=x_i) = \sum_{i=1}^n x_i since P(X=x_i|X=x_i) = 1$

Thus $E(\beta_1 X|X) = \beta_1 \left(\sum_{i=1}^n x_i\right) \neq \beta_1 X$