Calculating Standard Errors of Predicted Values Based on Nonlinear Functional Forms

Whenever we report predicted values, we should also report some measure of the uncertainty of these estimates. In the linear case, this is relatively simple, and the answer well-known, but with nonlinear models the answer may not be apparent. This short article shows how to make these calculations. I first present this for the familiar linear case, also reviewing the two forms of uncertainty in these estimates, and then show how to calculate these for any arbitrary function. An example appears last.