We explore the connection between two recently introduced notions of
non-Markovian quantum dynamics and the validity of the so-called
quantum regression theorem. While non-Markovianity of a quantum
dynamics has been defined looking at the behavior in time of the
statistical operator, which determines the evolution of mean values,
the quantum regression theorem makes statements about the behavior of
system correlation functions of order two and higher. The comparison
relies on an estimate of the validity of the quantum regression
hypothesis, which can be obtained exactly evaluating two-point
correlation functions. To this aim we consider a qubit undergoing
dephasing due to interaction with a bosonic bath, comparing the exact
evaluation of the non-Markovianity measures with the violation of the
quantum regression theorem for a class of spectral densities. We
further study a photonic dephasing model, recently exploited for the
experimental measurement of non-Markovianity. It appears that while a
non-Markovian dynamics according to either definition brings with
itself violation of the regression hypothesis, even Markovian dynamics
can lead to a failure of the regression relation.