The recently developed concept of a correlation entropy, S, as a quantitative measure of the correlation strength present in a correlated quantum many-body state is applied to the ground states of the He isoelectronic series He( Z) with varying nuclear charge Z and of the Hooke's law model HLM(omega) with varying oscillator frequency omega. S is constructed from the natural orbital occupation numbers. It vanishes for weak correlation (large coupling constants Z or omega), and increases monotonically with decreasing Z or omega (strengthening correlation). A reduced correlation energy per particle Delta e(corr) and a dimensionless ratio epsilon = \E-corr/E\ are introduced which vanish asymptotically in the weak correlation limit in contrast to E-corr and e(corr) = E-corr/N. These two intensive quantities, Delta e(corr) and epsilon, are compared with s = S/N. For both model systems, d Delta e(corr)/ds greater than or equal to 0 and d epsilon/ds greater than or equal to 0 (which modifies Collins' conjecture that \E-corr\similar to S).