The dependence of electron density in the polar F region ioniation hole on solar activity, universal time (UT), magnetic activity, season, and hemisphere is studied using data from the Langmuir probes on Atmosphere Explorer C and Dynamics Explorer 2. The AE-C data were obtained during solar minimum when the 3-month average 10.7-cm solar flux index varied from 70 to 140; the DE 2 data were obtained near solar maximum when the 10.7-cm solar flux index varied from 120 to 220. The polar hole is a region on the nightside of the polar cap where reduced ionization exists because of the long transport time of ionization from the dayside across the polar cap. The behavior of this region as a function of 10.7-cm solar flux (F10.7). UT, and Kp is statistically modeled for equinox, summer, and winter conditions for each hemisphere separately. The strongest dependencies are observed in F10.7 and UT; the Kp dependence is weak because it poorly represents the complexities of convection across the polar cap. A strong hemispherical difference due to the offset of the magnetic poles from the Earth's rotation axis is observed in the UT dependence of the ionization hole: there is a density minimum at about 20.3 hours UT in the south and at about 4.8 hours UT in the north; the minimum to maximum UT density variation is about a factor of 8.9 in the south and about a factor of 2.1 in the north. There is a seasonal variation in the dependence of ion density (Ni) on solar flux (F10.7). Use of the relationship (Ni~F10.7D yields values of D of approximate unity (1.) in the summer polar hole and about 2.1 during equinox. There is an overall asymmetry in the density level between hemispheres; it was found that the winter hole density is about a factor of 10 greater in the north than in the south. The Utah State University time dependent ionosphere model gives similar UT behavior to that found in the AE-C and DE 2 data.