The data were calculated using this formula: Y = 10 + X(l) + 0.5 X(r) + € (using the same 120 X 120 grid as before).

X(l) refers to the local value of X while X(r) refers to the regional (neighbourhood) value of X, defined as the average value of X for a defined area surrounding areal unit ij but not including it.

The augmented model incorporates a moving average in addition to the standard variables (of X and Y), when computing the moving average (of window size m) the central cell is excluded in the calculation. Note that the combined coefficients [b(l) + b(r)] provide an unbiased estimate of the true value (this suggests that one should not use the individual coefficient values).