The confidence limits are computed using Fieller’s theorem (Fieller, 1954), which is based on the following logic. The goal is predicting the value of a single regressor and its confidence limits given the values of the other regressors and the response.
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Let y be the response value.

We desire a confidence region on the value of x[i] such that β’x = y with all other values of x given.
where the parenthesized subscript (i) indicates that the ith component is omitted. A confidence interval can be formed from the relation
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Note: The Fit Y by X logistic platform and the Fit Model Nominal Logistic personalities use t values when computing confidence intervals for inverse prediction. The Fit Model Generalized Linear Model personality, as well as PROC PROBIT in SAS/STAT, use z values, which give different results.