where \mathbf{\hat \beta}_\mathtt{GLS} is the vector of estimated regression coefficients, \mathbf{C} is the covariance matrix of the residuals, {\mathbf{q}} is a matrix of predictors at the sampling locations and \mathbf{z} is the vector of measured values of the target variable. The GLS estimation of regression coefficients is, in fact, a special case of the geographically weighted regression. In the case, the weights are determined objectively to account for the spatial auto-correlation between the residuals.
