1. A computer-implemented method for approximating resource consumption of a computer system, comprising: creating load measurements for a set of computer resource metrics of the computer system to analyze dependencies between different computer resource metrics; creating a correlation matrix between the set of computer resource metrics; clustering the set of computer resource metrics in the correlation matrix into a set of clusters; building a reduced computer work gradient matrix based on the set of clusters; constructing a set of task work paths that characterize consumption levels of a set of resources in response to a computing task applied to the computer system at a particular background loading level; and approximating consumption levels of the set of resources for the computing task at any background loading level using the reduced computer work gradient matrix and the set of task work paths.