# Is the assumption of indepence only for the sampled values informing the regression, or should it also apply to the cells of a prediction grid?

I have 200 discrete, well-spaced plots with reasonably independent sampled values from which I've derived a regression equation. If I use it to predict values on a similarly sized fishnet grid, how much does it matter that neighboring grid cells are correlated in the predictor and response variables and is there anything to be done about it?

• Non independence will primarily affect tests of significance of the parameters in the model that you are trying to estimate (and/or tests of significance of the regression model). – coreydevinanderson Nov 11 '18 at 17:02

The observations $$y_i$$ should be independent, given the linear predictor. Of course - this assumption should be checked. Often you can do this with a plot of residuals (depending on the model) - these should show no discernable spatial pattern. If there is a pattern consider adding a spatially structured random effect (see GAMs or Gaussian Random Fields)
• Global Moran's I for the $y_i$ 0.14. But, the predicted $\hat{y}_i$ have a Moran's I of 0.54. – J Kelly Nov 7 '18 at 23:29
• In other words, the $y_i$ are nearly spatially independent. The concern is predicting beyond those i locations, into areas where all of the various x's are locally correlated. There are no residuals in those places. – J Kelly Dec 13 '18 at 16:46