Results from regression analysis are only trustworthy when the model and data meet the assumptions/limitations of that method. Statistically significant spatial autocorrelation in the regression residuals indicates misspecification (a missing key explanatory variable). Results are invalid when a model is misspecified.
Run the Spatial Autocorrelation (Moran's I) tool on the regression residuals in the output feature class. If the z-score indicates spatial autocorrelation is statistically significant, map the residuals and perhaps run a hot spot analysis on the residuals to see whether the spatial pattern of over and under predictions provides clues about missing key variables from the model. If you cannot identify the missing key variables, results of the regression are invalid and you should consider using a spatial regression method designed to deal with spatial autocorrelation in the error term. When spatial autocorrelation in OLS residuals is due to nonstationary spatial processes, use Geographically Weighted Regression instead of OLS.