Which interval should I use to bound actual values around a predicted value?

[kcros]

I have a 'black box' model that outputs model predictions, but I don't know what actually goes on inside the model. I also have a bunch of data that I can pass through the model so that I can compare the predictions with actual results. Which interval would I use to bound most of the actual values around the predicted value? I don't think that I would use the prediction interval because that would give me a range that the next prediction is likely to be in, correct? I would like to say that for a single prediction, I am 95% confident that the actual value falls into this interval.

[Rick_SAS]

The confidence limits for the mean predicted values account for the variation due to estimating the parameters. The confidence interval for individuals adds in the variability of the error term, so it is wider.

Are you saying that you can bootstrap your data and create new predictions? If so, then check out the example of constructing bootstrap confidence intervals for the TPSPLINE procedure. Maybe you can modify that example for your situation.