At the minimum in  the system can be approximated to a linear one, the residuals in the case of unit weights are related to the observations by
The symmetric, idempotent matrix  is known in the statistics literature as the hat matrix, . Thus,
and
where  is an identity matrix and  and  are the variance-covariance matrices of the residuals and observations, respectively. This shows that even though the observations may be uncorrelated, the residuals are always correlated.
The diagram at the right shows the result of a refinement of the stability constants of Ni(Gly), Ni(Gly) and  (where GlyH = glycine). The observed values are shown a blue diamonds and the species concentrations, as a percentage of the total nickel, are superimposed. The residuals are shown in the lower box. The residuals are not distributed as randomly as would be expected. This is due to the variation of liquid junction potentials and other effects at the glass/liquid interfaces. Those effects are very slow compared to the rate at which equilibrium is established.