Correlation between source point and raster

[KatieSweeney]

I am trying to find a correlation between a point feature class of sites (source) to high (optimal area) values in a raster (with continuous data).

I was thinking some sort of cost path analysis would be most appropriate however I'm not trying to find a least cost path between two points but rather find the least cost path, or most likely path considering distance from source point (the closer optimal values to the source, the better) to reach the optimal (high) value areas in the raster.

Any spatial statistic or spatial analysis tool ideas? I've created distance cost layers from each source point as well as a cost layer from the original raster with values I'm trying to correlate with but am stuck as I can't use the cost path tool.

Thank you for any help!

[JeffreyEvans]

In this case the term "correlation" is quite vague and your question could use more detailed explanation. If I understand your question, I believe that you are looking for a matrix regression. The most common matrix regression statistic is the Partial Mantel Test. I will however, forewarn you that there are serious issues with type I & II errors and associated statistical significance. It can be quite difficult getting papers using the Partial Mantel Test through review.   

This something that you cannot perform in ArcGIS. I am not aware of any readily available Python libraries that have this statistic. The software R, SAS and SPSS (to name a few) have the Mantel and Partial Mantel statistic available. There is also a spatial statistics software called PASSaGE (http://www.passagesoftware.net/) that has the statistic available.