The scaled prediction variance at a particular design point is the variance of the predicted value, multiplied by the sample size N, and divided by the error variance. (See, for example, Montgomery et al., Section 8.2.1). It depends on the design point, but for a symmetric design, it depends only on the distance from the origin and the direction. This function provides a simple way to examine the variance function directly. (There are other more sophisticated methods available that integrate-out the direction, for example Vdgraph in the Vdgraph package.)
If vectors is not specified and contour==FALSE, the function generates default directions along one axis, and on a diagonal through a corner in each dimension. For example, with four design variables, the default directions are (1,0,0,0), (1,1,0,0), (1,1,1,0), and (1,1,1,1). The graph produced shows how the scaled variance changes along each of these vectors, for the distances provided. In a rotatable design, these curves will all be the same.
When countour==TRUE, only the ordering of columns in vectors matters. A grid is constructed over the distance range for the first two variables in vectors. The design points are also plotted for reference, with different symbol sizes depending on replications. When there are more than two response-surface predictors, the contour plot may be misleading, as it does not display what happens as one simultaneously varies three or more variables.