Regression point

where W([s.sub.0]) is an m x m weighting diagonal matrix, with m being the number of sample points around the regression point at location [s.sub.0]; X is an m x (p + 1) explanatory variable matrix, with p being the number of environmental variables; [X.sup.T] is a transpose of X matrix; and T is an m x 1 vector formed by values of soil properties at m sampling points.

Influence of each sampling point on the regression point is controlled by the weighting matrix.

where [w.sub.ij] denotes the weight for the sampling point at location j used for estimating the soil properties at location i, [d.sub.ij] represents the distance between sampling point and regression point, and h is the bandwidth.