For analysis of spatial data, geographers and statisticians have introduced various approaches to removing spatial autocorrelation in regression residuals by augmenting the design matrix with vectors that represent spatial patterns. We propose a fully Bayesian method that balances model fit and reduction of residual correlation. It is computationally fast and performs competitively with established methods. We illustrate with data on the 2018 Iowa gubernatorial election. This is largely joint work with my former PhD student Juan Cervantes.