How to calculate the prediction interval without knowing the functional form

If I have predictions derived empirically without knowing the functional
form, is there a way to calculate the prediction interval?

As Bert said, this isn't really an R question, but I'd say the answer is 
"probably not".  The prediction interval depends on the uncertainty of 
individual observations, and that isn't usually reflected in 
predictions.  For example, if y_i is N(mu, sigma^2), and we fit the 
model to N observations, all of our predictions will be ybar, and there 
will be no indication of sigma.

Duncan Murdoch