  Shape deformations and charge radii, basic properties of atomic nuclei, are
influenced by both the global features of the nuclear force and the nucleonic
shell structure. As functions of proton and neutron number, both quantities
show regular patterns and, for nuclei away from magic numbers, they change very
smoothly from nucleus to nucleus. In this paper, we explain how the local shell
effects are impacting the statistical correlations between quadrupole
deformations and charge radii in well-deformed even-even Er, Yb, and Hf
isotopes. This implies, in turn, that sudden changes in correlations can be
useful indicators of underlying shell effects. Our theoretical analysis is
performed in the framework of self-consistent mean-field theory using
quantified energy density functionals and density-dependent pairing forces. The
statistical analysis is carried out by means of the linear least-square
regression. The local variations of nuclear quadrupole deformations and charge
radii, explained in terms of occupations individual deformed Hartree-Fock
orbits, make and imprint on statistical correlations of computed observables.
While the calculated deformations or charge radii are, in some cases,
correlated with those of their even-even neighbors, the correlations seem to
deteriorate rapidly with particle number. The statistical correlations between
nuclear deformations and charge radii of different nuclei are affected by the
underlying shell structure. Even for well deformed and superfluid nuclei for
which these observables change smoothly, the correlation range usually does not
exceed $\Delta N=4$ and $\Delta Z=4$, i.e., it is rather short. This result
suggests that the frequently made assumption of reduced statistical errors for
the differences between smoothly-varying observables cannot be generally
justified.
