  We address two questions pertaining to the uniqueness and usefulness of a new
observable: (i) Considering the current theoretical knowledge, what novel
information does new measurement bring in? (ii) How can new data reduce
uncertainties of current theoretical models? We illustrate these points by
studying the radius of the neutron distribution of a heavy nucleus, a quantity
related to the equation of state for neutron matter that determines properties
of nuclei and neutron stars. By systematically varying parameters of two
theoretical models and studying the resulting confidence ellipsoid, we quantify
the relationships between the neutron skin and various properties of finite
nuclei and infinite nuclear matter. Using the covariance analysis, we identify
observables and pseudo-observables that correlate, and do not correlate, with
the neutron skin. By adding the information on the neutron radius to the pool
of observables determining the energy functional, we show how precise
experimental determination of the neutron radius in $^{208}$Pb would reduce
theoretical uncertainties on the neutron matter equation of state.
