How to find implementation details for a SAS procedure? I was was wondering about where to track down implementation details for SAS: I have certain outputs (depending on small amounts of data) which I would like to understand better by trying to check against a theoretical solution. I'm looking at something pretty specific (how standard errors on predicted probabilities from a regression are found), so I have no idea how to track this sort of thing down.
 A: This information is not documented because SAS is a proprietary statistical software suite. Sharing such info (from their perspective) would compromise the integrity of their license. Because statistics lack any kind of IEEE-like standard for numerical routines, nothing can be inferred about the methods used without inspecting the source code. I get the sense from your question that you are doing this for your own enrichment. If that's the case, I recommend doing this in R (it will benefit you in the long run as well).
To answer your specific question, predicted values from (linear) regression models are based on the covariance matrix of the parameter estimates. By predicted probabilities, I'm not sure if you have some regression routine like logistic or probit GLMs, which estimate probabilities. By writing the fitted values as a linear combination of the model parameters, $x^t\hat{\beta}$, you compute its variance directly:
$
\mbox{var}(x^t\hat{\beta}) = x^t \mbox{var}(\hat{\beta}) x
$
This gives the confidence band. One can use the estimated residual variance to account for resampling variability for predictions. I recommend taking a look at Seber and Lee's ancient text on Linear Regression Analysis if you want more info on this. This is slightly more complicated in the GLM case.
