This section describes how predicted probabilities and confidence limits are calculated by using the pseudoestimates (MLEs) obtained from PROC SURVEYLOGISTIC. For a specific example, see the section Getting Started: SURVEYLOGISTIC Procedure. Predicted probabilities and confidence limits can be output to a data set with the OUTPUT statement.
For a row vector of explanatory variables , the linear predictor
is estimated by
where and are the MLEs of and . The estimated standard error of is , which can be computed as the square root of the quadratic form , where is the estimated covariance matrix of the parameter estimates. The asymptotic confidence interval for is given by
where is the percentile point of a standard normal distribution.
The predicted value and the confidence limits for Pr are obtained by backtransforming the corresponding measures for the linear predictor.
Link 
Predicted Probability 
Confidence Limits 

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