Great question. I certainly agree with Fezter that using a programming language is a great tool in performing these types of spatial analysis. Python is fitted to work smoothly within ArcGIS assuming the IDE you are using has been synced to your ESRI account. My submissions (seen below) uses the RStudio IDE to create a multivariate Poisson regression analysis for broadband internet acquisition in Kentucky counties with x variables as percentiles of college graduates, age, and unemployment rates.
As it pertains to running a regression analysis in R, the 'GIS Tools' package can create the linear models which produce the descriptive statistics often cited in a Poisson analysis.
#connect the broadband info from the excel sheet into an sf object spatial #dataframe 'KY_df'
KY_df <- inner_join(Ky_counties, KY_bb, by=c("NAMELSAD10"="ck_name"))
#fit a linear model, where the first argument is your dependent variables #followed by your explanatory variables
mod1 <- lm(adopt05~college + unemp, data = KY_df)
#view your results!
Again, using R or any programming language can be difficult at first but with every new exercise you get more experience and better results. I hope this is helpful!