# Solved – Understanding the homoscedasticity assumption

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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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.

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# Solved – Understanding the homoscedasticity assumption

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.

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.

Rate this post