# sample distribution of residuals

#### azalea

##### New Member
Find the sample distribution of the residual r = y - XBhat under
normal regression model assumptions.*

* I think this means to assume errors are indepedent, have mean 0 and variance sigma squared, are are normally distributed.

Please help! Are residuals not just realizations of the errors and have no variance as they are constants?

#### Masteras

##### TS Contributor
he wants you to prove that.
mean=E(r)=E(y)-x*E(B)=...
variance=Var(r)=V(y)+x^2 * V(B)-cov(y,xB)=...

#### BGM

##### TS Contributor
Are residuals not just realizations of the errors and have no variance as they are constants?
One of the key concept is that you are doing the statistical inference as if you have not observe the random sample yet and you only believe that the random sample satisfy certain distribution properties. So you will want to derived the sampling distribution for the estimator - a function of the random sample. Once you observed the realization of the sample, you will plug in the data into your estimator and get a point estimate, in which of course is not random. Make sure you can differentiate the terminologies here so that you will not get confused.