Variable Resolution Modeling is a collection of techniques designed to make higher fidelity models operate dynamically with lower fidelity level simulations. Previously, we have illustrated an example of these techniques with DeLoRes, a set of software tools developed to perform the state variable analysis, data base management, functional abstraction, and algorithmic implementation. We previously showed two classes of functional abstraction, multivariate, multidimensional linear and nonlinear interpolation and neural network representations. Now we extend the functional abstraction techniques to include stochastic information in some of the state variables. We illustrate this process by using the mean value at each interpolation node and fit the data with various linear multivariate interpolation techniques and then illustrate hypothesis testing of the stochastic data for consistency with a Gaussian (normal) distribution and discuss how this can be used in variable resolution modeling.