# Prediction Intervals

#### r007k

##### New Member
Can someone help me with prediction intervals ? I dont get understand how you get the t-distrbution of (Y0 - U~) / (sigma * sqrt(1 +1/n))

where does the sigma * sqrt(1 +1/n) come from ?!?!?!??!

thanks

r007k

#### JohnM

##### TS Contributor
It's just an adjustment factor to the standard error or standard deviation "s" based on the sample size.

It comes from [ (n + 1) / n ] = (n/n) + (1/n) = 1 + 1/n

and uses the fact that as n approaches infinity, the quantity [ (n + 1) / n ] approaches 1