A least squares regression formulation is developed to study the expected errors in the coefficients of a modal expansion of observational data. Given an empirical or theoretical vertical mode number energy spectrum and assuming that certain modes (signal) are to be resolved and that the remaining modes (noise) are a contamination, then there exists an optimum set of weights which will minimize the expected errors of the signal modal amplitudes. These expected errors, as well as those associated with any other set of weights, can be evaluated and the adequacy of a given array determined. Examples from the equatorial Pacific Ocean are used to show the utility of this technique and to explore several existing or possible measurement arrays.