The formula for a prediction interval at a given point $x$ in a linear regression model is ^ y ^ / 2 , 2 t /2,n2 SE in general, where SE is the standard error of the prediction. Define = 1 2 = 1 ( ^ ) 2 s= n2 1 i=1 n (y y ^ ) 2 . What does SE include If you want to make inference for a single observation y when x takes the value x