# Math Help - Conditional expectation in regressions

1. ## Conditional expectation in regressions

Hello!

Does anyone know what is the difference in a regression between $E[\hat{\beta}]$ and $E[\hat{\beta}|X]$? One is called the unconditional one the other conditional. So far I can get it. But conditional on what exactly? Does it mean that $E[\hat{\beta}]$ refers to the expected value of $\hat{\beta}$ in the (total) population, while $E[\hat{\beta}|X]$ to a chosen sample and we treat X as fixed? But if we had no X, how would be obtain $E[\hat{\beta}]$ 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.

Thanks!
Mxo

2. ## 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)?

3. ## Re: Conditional expectation in regressions

X is a NxK non-singular matrix of random variables. N observations and K independent variables.

4. ## 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.