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.

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#### 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.