  We show that single-particle energies in doubly magic nuclei depend almost
linearly on the coupling constants of the nuclear energy density functional.
Therefore, they can be very well characterized by the linear regression
coefficients, which we calculate for the coupling constants of the standard
Skyrme functional. We then use these regression coefficients to refit the
coupling constants to experimental values of single-particle energies. We show
that the obtained rms deviations from experimental data are still quite large,
of the order of 1.1 MeV. This suggests that the current standard form of the
Skyrme functional cannot ensure spectroscopic-quality description of
single-particle energies, and that extensions of this form are very much
required.
