I can't understand how this works:
$e$ is the error term and $x$ is the explanatory variable.
$$Var(e|x) = E(e^2|x) – [E(e|x)]^2$$
I know that $[E(e|x)]^2$ = 0 because $E(e|x) = 0$, and squaring 0 is still 0.
So that leaves $Var(e|x) = E(e^2|x)$
I am confused on this part.
This may be a clearer idea of what I am after:
I am interested in understanding how $E(e^2|x) – [E(e|x)]^2$ = $Var(e|x)$ How do I get $E(e^2|x) – [E(e|x)]^2$? It is just given as a fact in the text, without an after thought.
Best Answer
I assume you are refering to linear regression. Thus we have $$y=x^Tbeta+e$$ Now the homoscedasticity assumption means that the variance does not depend on $x$. so we have $$var[e|x]=var[e]$$ This means each observation is equally important for estimating the mean square error.