First, R^2 does not validate your experiment. It is one estimate to help you evaluate your model. The better use of R^2 is to compare the R^2 to the Adjusted R^2 to see if you have over-specified the model. The only time I have seen predicted R^2 is with Minitab. Minitab takes a random sample from the data set and uses the model you have entered to calculate how much of the variation in that data is explained by the model.
"Predicted R 2 is calculated with a formula that is equivalent to systematically removing each observation from the data set, estimating the regression equation, and determining how well the model predicts the removed observation."
Whether this is actually useful ...?
There are many ways to "hold out" some data from a data set (e.g., boot strapping, nearest neighbor). Use the rest of the data to estimate the model and then test the model with the data that was held out. Is this what you are asking?
"All models are wrong, some are useful" G.E.P. Box