For the minimisation of the model-free models a chain of calculations, each based on a different theory, is required. At the highest level the equation which is actually minimised is the chi-squared function

where the index *i* is the summation index ranging over all the experimentally collected relaxation data of all spins used in the analysis;
R_{i} belongs to the relaxation data set R for an individual spin, a collection of spins, or the entire macromolecule and includes the
R_{1},
R_{2}, and NOE data at all field strengths;
R_{i}(*θ*) is the back-calculated relaxation value belonging to the set R(*θ*); *θ* is the model parameter vector which when minimised is denoted by
; and *σ*_{i} is the experimental error.

The significance of the chi-squared equation (7.1) is that the function returns a single value which is then minimised by the optimisation algorithm to find the model-free parameter values of the given model.

The relax user manual (PDF), created 2020-08-26.