There are a variety of tools in the Spatial Statistics toolset Spatial Statistics toolbox sample applications—Help | ArcGIS for Desktop
If you are looking to do this in a spatial context but your data are interpolated values, so I would advise against it..
Since you are extracting values from surfaces not using observation points, but from a grid, correlation and regression wouldn't be advisable. You might want to look at looking for 'associations' beween the two variables. I would suggest reclassifying the two layers to and using the combine tool Combine—Help | ArcGIS for Desktop to denote the associations that may arise between elevation and erosivity.
However... it is not elevation per se that will contribute to erosivity directly, but through its terrain derivatives such as slope (steep slopes--> high erosive potential) and even aspect (dominant direction to prevaling weather perhaps).
There is also the cavaet, that elevation or its derivatives (slope etc) can't be used in determining a correlation with a variable that may be derived from it. So if the determination of erosivity index/value requires elevation, then you shouldn't be correlating the two since a tenant of correlation is independence of the variables