Magnetogram data are analyzed to study daily variations of tilt angles of the magnetic axes of active regions defined by magnetic fields measured with the Mount Wilson magnetograph. The period covered by this daily data set is 1967 through April 9, 1990. It is found that on average regions with positive tilt angles (leading portions of the regions equatorward of following portions) show average negative daily tilt angle changes (decreases in tilt angle) and regions with negative tilt angles show average positive daily tilt angle changes. Generally the larger the tilt angle of either sign, the larger is the average daily tilt angle change. Although at times some young regions are observed to rotate their magnetic axes rapidly as they are formed, or shortly thereafter, age does not seem to be an important factor in distinguishing (among those regions that have large tilt angles) between those that rotate their tilt angles rapidly and those that do not. Other characteristics were also investigated without success to see if they provided such a distinguishing factor. These were: net magnetic flux, total magnetic flux, and magnetic polarity separation. One characteristic that does provide such a distinction is cycle phase: large daily tilt angle changes are clustered around solar maximum. A clear correlation is found between polarity axis rotation and latitude: polarity axis rotation rates are larger at higher latitudes up to about 20 deg. Another parameter that is correlated with large tilt angle change is rotation rate (about the rotation axis of the Sun). Regions with large tilt angle rotation rates tend to rotate by 1-2 deg day-a faster than do those regions that show slow tilt angle twist. These results may be related to characteristics of the subsurface connection of the magnetic flux tubes that form the regions.