# variance of theoretical mean of y at given value of x in regression [duplicate]

Could someone tell me where I might find information on deriving the standard error used in confidence and prediction intervals of y at a given value of x on a regression line. I can't find anything on the internet. Thanks for any help.

• If it's Simple Linear Regression, then the expression can be derived easily by expanding the variance term into variance of both the parameters and the covariance between them.Also in S.E for Prediction Intervals,sigma square term is added. You may refer to this problem [link] (cheenta.com/isi-mstat-psb-2013-problem-4-linear-regression) Jun 27, 2020 at 4:31
• Thanks a ton, Napoleon. I was able to derive it like you said. Jun 27, 2020 at 22:34