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I have two datasets and I'm trying to determine the extent of their spatial relationship. I suspect they are closely related but I would like to produce a map output to illustrate this relationship.

A points layer and polygon layer, i want to illustrate the relationship between density of points and what is their control from any attribute of polygons. the variables are not numerical fields. i don't know if is better to work only from one layer obtaining the relationship between tow attributes (extracting before the polygon's attributes)

I don't know which technique will provide me with what I want. i have been reading about Geostatistical Analyst tool, but i didn't find what i have to use.

Does anyone have any ideas of how I can investigate and represent this relationship in Arcgis?

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Two options - If you are doing a global correlation (between all points or cells in your study area) then extract values to points and you can use the OLS tools in the Spatial Statistics toolbox. Then you can plot the residuals. You can view this as deviation from the line of fit.

If, on the otherhand, you are interested in performing the correlation locally in a moving window fashion then take a look at my Topography Toolbox - moving window correlation - http://www.arcgis.com/home/item.html?id=b13b3b40fa3c43d4a23a1a09c5fe96b9 . This approach was used in Bill Peterman's dissertation Figure 3c for example. This maps the degree of correlation between two variables across a landscape.

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