In geostatistical analysis the mean function of the spatial process is specified by a parametric model, $$\mu(s; \beta)$$. The most commonly used parametric mean model is a linear function, given by

$\mu(\mathbf{s}; \mathbf{\beta}) = \mathbf X(s)^T\mathbf{\beta}$

where $$X(s)$$ is a vector of covariates (explanatory variables) observed at $$s$$, and $$\mathbf{\beta}$$ is a parameter vector. The covariates may also include the geographic coordinates (e.g., latitude and longitude) of $$s$$, mathematical functions (such as polynomials) of those coordinates, and attribute variables.

The standard method for fitting a provisional linear mean function to geostatistical data is ordinary least squares (OLS). This method yields the OLS estimator $$\hat{\beta}_{OLS}$$ of $$\beta$$, given by

$\hat{\beta}_{OLS} = \text{argmin} \sum_{i=1}^n[Z(\mathbf s_i) -\mathbf X(\mathbf s_i)^T\mathbf{\beta}]^2$

Fitted values and fitted residuals at data locations are given by $$\hat z = \mathbf{X^T}\mathbf{\hat{\beta}}_{OLS}$$ and $$\hat e= z-\hat z$$, respectively. The latter are passed to the second stage of the geostatistical analysis, to be described in the next section.