Spatial Autocorrelation

A value of 0.6 indicates moderate to strong positive spatial autocorrelation: locations with high values tend to be surrounded by neighbours that also have high values, and vice versa. Whether this is statistically significant depends on the sample size and the spatial weights used; always report the associated z-score and p-value.

For polygon data, queen contiguity (shared edges or corners) is the most common default; rook contiguity (shared edges only) is appropriate for regular grids. For point data, a fixed-distance band or k-nearest-neighbours weights are standard. Always test sensitivity to the choice, because different specifications can materially change the Moran's I value.

Yes — this is one of its most important uses. Applying Moran's I to OLS residuals tests whether the independence assumption is violated. A significant result means the model is spatially mis-specified and that a spatial lag, spatial error, or other spatial model should be fitted instead.

The global Moran's I summarises the overall tendency to cluster across the entire study area in a single number. Local Moran's I (LISA) decomposes this into location-specific scores, revealing where significant clusters or spatial outliers occur — information that the global measure averages away.

Both. As a feature it reveals genuine geographic processes and structures worth mapping and explaining. As a problem, autocorrelated residuals in a regression model invalidate OLS standard errors and inflate the apparent precision of estimates; the remedy is to use a spatial econometric model or spatial filtering.