The explained variance ($R^2$) of each eQTL for gene expression was estimated based on the following formula:

$$ R^2 = \frac{U_1}{\rm{SST}} = \frac{b_{1}^2/c_{11}}{\rm{SST}} $$

where $U_1$ represents the partial sum of regression squares for the specific eQTL, $b_1$ is the partial regression coefficient indicating the estimated marker effect size, $c_{11}$ corresponds to the relevant element in the inverse matrix of the coefficient matrix within the normal equation group, and $\rm{SST}$ denotes the total sum of squares, reflecting the sum of squared differences between the actual gene expression level and its mean.

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