We develop regression methodology to identify subsets of single nucleotide polymorphisms (SNPs) within candidate genes related to quantitative traits and apply our methods to the simulated Genetic Analysis Workshop (GAW) 12 data set. In the data set we find 694 SNP loci with minimum allele frequencies of at least 0.01. We assume an additive casual model between these SNPs and all five quantitative traits. After initial screening using one-way analysis of variance, we employ a computationally efficient, simulated annealing algorithm to select among all possible subsets of SNP loci, using a generalization of Mallows' Cp as our optimality criterion. The simple transition kernel we develop evaluates new subsets in O(1), by requiring just three arithmetic operations to calculate the proposed RSS based on the Gauss-Jordan pivot. We identify an SNP loci located at 6-5782 related to traits 2 and 3 and several sites on gene 2 related to trait 5 using a subsample of 1,000 individuals and the full data set (n = 8,250) for comparison.