The sum of chi-squared values

For the single residue models of $\mathfrak{F}_i$ and $\mathfrak{T}_i$ the chi-squared value χ²_i which is optimised is simply Equation (15.13) on page in which the relaxation data is that of residue i. However for the global models $\mathfrak{D}$ and $\mathfrak{S}$ in which all selected residues are involved the optimised chi-squared value is the sum of those for each residue,

$$\sum^{l}_{{i=1}}$$ (15.8)

where i is the residue index and l is the total number of residues used in the analysis. This is equivalent to Equation (15.13) when the index i ranges over the relaxation data of all selected residues.