For each of the four brain regions, a regression analysis was performed on the residuals described in the preceding section for (a) mRNA expression and (b) the methylation values generated for CpG sites. The trait residuals were then used as the quantitative phenotype for that probe in genome-wide association analysis looking for quantitative trait loci. These analyses were performed using the assoc function within Plink, which correlates allele dosage with change in the trait. Each of the four tissue regions was analyzed separately, and independent genome-wide association analyses were performed looking for (a) expression quantitative trait loci (eQTLs) for mRNA and (b) methylation quantitative trait loci (methQTLs) for CpG sites. The Plink toolset quantitative trait association analysis fits data to the following model:Where Y is the quantitative trait and ADD represent genotypes encoded as allele dosage. See Plink Quantitative trait association and Linear and Logistic models documentation for more information.