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We have been using the Keck I High Resolution Spectrograph to search for planetary companions in the Hyades cluster. We selected four stars from this sample that showed significant radial velocity variability on short timescales to search for short-period planetary companions. The radial velocities of these four stars were monitored regularly with the Hobby-Eberly Telescope for approximately 2 months, while sparse data were also taken over ∼4 months: we also obtained near-simultaneous photometric observations with one of the automatic photoelectric telescopes at Fairborn Observatory. For three of the stars, we detect photometric variability with the same period present in the radial velocity (vr) measurements, compatible with the expected rotation rates for Hyades members. The fourth star continues to show vr variations and minimal photometric variability but with no significant periodicity. This study shows that for the three stars with periodic behavior, a significant portion of the vr fluctuations are likely due primarily to magnetic activity modulated by stellar rotation rather than planetary companions. Using simple models for the vr perturbations arising from spot and plage, we demonstrate that both are likely to contribute to the observed vr variations. Thus, simultaneous monitoring of photometric (photospheric) and spectroscopic (chromospheric) variations is essential for identifying the cause of Doppler-shifted absorption lines in more active stars.