I have been looking around online and whenever I see reference to OLS or GWR, few to no one using point (x,y) data in their tutorials. Why is this and is there a way to do a "what is the relationship between these variables" analysis without attaching the x,y point data to polygons. I am comfortable making grids or associating individual points with polygons, but I would rather not lose any granularity if there's another option to be able to work with the point data without aggregating. Thanks.
I would suggest using R to do the analysis of your points and then plotting the result in ArcMap to make the Map. If you are more fluent in using the ESRI's R-bridge than I am, you may be able to figure out a way to do this from within ESRI. Below is a link to a paper which may help. The paper I think is by Prof. C. Brunsdon at University of Leicester. The paper focuses on trying to find out how car ownership varies across the country (England) and uses the centroid (x,y) coordinates of zones where people live as data points. The paper is based on Fotheringham et al. (2002) Geographically Weighted Regression: The Analysis of Spatially Varying Relationship, published by Wiley. Now that said, your ability to do this will depend on your familiarity with R. The attached paper was written some time ago and refers to an earlier version of R which may not be quite the same as the current version of R. So, you may encounter some difficulty lining up the script in the paper with the current version of R. This can cause frustration, but I encourage you to try as you will learn a great deal in the process and improve you Spatial Statistics skills dramatically. R is an excellent tool to know well if your work has you doing a great deal of statistics, spatial or otherwise.
Best Wishes, Bill Meyer, US Army Corps of Engineers - ERDC Champaign
Are you using ArcGIS Pro or ArcMap? Do your point records have any abundance data associated with them. The data points need to contain numeric values that vary in abundance and across space for the ArcGIS regression methods.
If you are using ArcGIS Pro, do take a look at Forest-based Classification and Regression—ArcGIS Pro | ArcGIS Desktop and How Forest-based Classification and Regression works—ArcGIS Pro | ArcGIS Desktop for an alternative regression approach.
For visualizing relationships between two variables, correlation and not regression, I frequently use scatter plots Scatter plot—Charts | ArcGIS Desktop