 Since the data in this context is defined to be ("x", "y") pairs for every observation, the "mean response" at a given value of "x", say "xd", is an estimate of the mean of the "y" values in the population at the "x" value of "xd", that is formula_10.The variance of the mean response is given by

This expression can be simplified to

where "m" is the number of data points.To demonstrate this simplification, one can make use of the identity

The "predicted response" distribution is the predicted distribution of the residuals at the given point "xd".