# Conditional expectation in regressions

• Mar 23rd 2013, 02:43 PM
ButterflyM
Conditional expectation in regressions
Hello!

Does anyone know what is the difference in a regression between $\displaystyle E[\hat{\beta}]$ and $\displaystyle E[\hat{\beta}|X]$? One is called the unconditional one the other conditional. So far I can get it. But conditional on what exactly? Does it mean that $\displaystyle E[\hat{\beta}]$ refers to the expected value of $\displaystyle \hat{\beta}$ in the (total) population, while $\displaystyle E[\hat{\beta}|X]$ to a chosen sample and we treat X as fixed? But if we had no X, how would be obtain $\displaystyle E[\hat{\beta}]$ otherwise? And why would we fix X? I am not exactly sure where their difference lies.. Please help.. I know it's a basic question but it confuses me. (Crying)

Thanks!
Mxo
• Mar 23rd 2013, 04:49 PM
chiro
Re: Conditional expectation in regressions
Hey ButterflyM.

Is X a sample or is it a design matrix (I'm guessing its a sample set of observations)?
• Mar 23rd 2013, 04:54 PM
ButterflyM
Re: Conditional expectation in regressions
X is a NxK non-singular matrix of random variables. N observations and K independent variables.
• Mar 24th 2013, 01:48 AM
chiro
Re: Conditional expectation in regressions
Hint: The thing you have to focus on is whether X is a random variable or not. If it isn't then the expectation won't be affected by the value of X.