To approximate the unknown but true changes in free energy, we need a tool to map 𝚫𝐆 𝐓𝐫𝐮𝐞 onto our observations. The mapping is similar to how a slope, 𝑚, relates 𝑥 and 𝑦 in the equation for a line, 𝑦 = 𝑚𝑥 + 𝑒, where 𝑒 is the error. Our multidimensional analogy to 𝑚 that maps 𝚫𝐆 𝐓𝐫𝐮𝐞 onto our collection of observations and relative changes in free energy is a design matrix, 𝐀.