## Predicted Values of the Mean

*Predicted Values*

A predicted value, or fitted value, of the mean corresponding to the vector of covariates **x**_{i} is given by

where *g* is the link function, regardless of whether
**x**_{i} corresponds to an observation or not.
That is, the response variable can be missing and the
predicted value is still computed for valid **x**_{i}.
In the case where **x**_{i} does not correspond to a valid
observation, **x**_{i} is not checked for estimability.
You should check the estimability of **x**_{i}
in this case in order to ensure the
uniqueness of the predicted value of the mean.
If there is an offset, it is included in the predicted value
computation.
Approximate confidence intervals for predicted values of the mean
can be computed as follows.
The variance of the linear predictor
is estimated by

where is the estimated covariance of .

Approximate confidence intervals are computed as

where *z*_{p} is the 100*p* percentile of the standard
normal distribution and *g* is the link function.
If either endpoint in the argument is outside the valid range
of arguments for the inverse link function, the corresponding
confidence interval endpoint is set to missing.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.