For a quantitative trait, we assume the following linear model y=Xλ+ϵ, where y is a mean-centered vector of values of a quantitative trait for n individuals, X a column-standardized SNP genotype matrix of dimension n × m and p(ϵ)=N(ϵ|0,σ2In). The Maximum Likelihood Estimate (MLE) of the causal SNP effects λ depends on X and y only through the SNP correlation matrix R=n−1XTX and single-SNP z-scores zˆ=(nσ2)−1/2XTy λˆ=(XTX)−1XTy=n−1/2σR−1zˆ V[λˆ]=σ2(XTX)−1=n−1σ2R−1.
