Genetic networks for gene expression data are often built by graphical models, which in turn are built from pair-wise correlations of gene expression levels. A key feature of building graphical models is the evaluation of conditional independence of two traits, given other traits. When conditional independence can be assumed, the traits that are conditioned on are considered to 'explain' the correlation of a pair of traits, allowing efficient building and interpretation of a network. Overlaying genetic polymorphisms, such as single nucleotide polymorphisms (SNPs), on quantitative measures of gene expression provides a much richer set of data to build a genetic network, because it is possible to evaluate whether sets of SNPs 'explain' the correlation of gene expression levels. However, there is strong evidence that gene expression levels are controlled by multiple interacting genes, suggesting that it will be difficult to reduce the partial correlation completely to zero. Ignoring the fact that some sets of SNPs can explain at least part of the correlation between gene expression levels, if not all, might result in missing important clues on the genetic control of gene expression. To enrich the assessment of the causes of correlation between gene expression levels, we develop methods to evaluate whether a set of covariates (e.g. SNPs, or even a set of quantitative expression transcripts) explains at least some of the correlation of gene expression levels. These methods can be used to assist the interpretation of regulation of gene expression and the construction of gene regulatory networks.