Yes .. it is possible. I may be getting the name wrong but I saw a demo from Ben Shneiderman's research group a few years ago where they did every possible statistical analysis on pairs of variables to look for high correlation. To their credit, they weren't selling the idea as automatic stats analysis. Their domain was health data and they were merely stating that their tool could give scientists an insight as to what factors to look at. Still ... it made me wonder where this could go.