Prediction Intervals
Suppose that we have calculated parameter estimates 
for our linear regression problem. Suppose further that we have a vector of values, x, for the predictor variables. We may obtain an α level confidence interval for the value 
, which is the value of the dependent of the observed variable predicted by our model, according to the formula:
for our linear regression problem. Suppose further that we have a vector of values, x, for the predictor variables. We may obtain an α level confidence interval for the value , which is the value of the dependent of the observed variable predicted by our model, according to the formula:where t(n – p;α/2) is the value at α/2 of the cumulative distribution function for a T distribution, S is the estimated variance, and X is the regression matrix.
