We must first decide how to model the data to find the regression that minimizes the error vector in Eq. 4. The error vector after regression will have a residual variance of 𝜎 2 . For an unweighted graph, we could solve Eq. 4 with linear regression provided that the values in 𝚫𝐆 𝐨𝐛𝐬 meet a few conditions, including linear correlation, normal errors, and low expected covariance magnitudes for our predictions of the changes in free energy. In our case, the covariance criterion does not hold because the final changes in free energy depend on a series of pairwise differences, so the final Δ𝐺 values that we will solve for depend on one another. Linear regression also requires homoscedasticity, meaning that the variances for our predictions are constant . Recall that some alchemical transformations perform better than others . As a consequence, our data does not satisfy the homoscedasticity condition for unweighted linear regression. Accordingly, we assign edge weights with the matrix 𝐖 based on a transformation's anticipated complexity and chemical similarity (Software Methods). This choice of a weighted graph to model the experimental design means we use weighted linear regression to minimize 𝐞 𝚫𝐆 .