Molecular oxygen (O 2 ) paired with a reducing gas is regarded as a promising biosignature pair for the atmospheric characterization of terrestrial exoplanets. In circumstances when O 2 may not be detectable in a planetary atmosphere (e.g., at mid-IR wavelengths) it has been suggested that ozone (O 3 ), the photochemical product of O 2 , could be used as a proxy to infer the presence of O 2 . However, O 3 production has a nonlinear dependence on O 2 and is strongly influenced by the UV spectrum of the host star. To evaluate the reliability of O 3 as a proxy for O 2 , we used Atmos, a 1D coupled climate and photochemistry code, to study the O 2 -O 3 relationship for "Earth-like" habitable zone planets around a variety of stellar hosts (G0V-M5V) and O 2 abundances. Overall, we found that the O 2 -O 3 relationship differed significantly with stellar hosts and resulted in different trends for hotter stars (G0V-K2V) versus cooler stars (K5V-M5V). Planets orbiting hotter host stars counter-intuitively experience an increase in O 3 when O 2 levels are initially decreased from 100% Earth's present atmospheric level (PAL), with a maximum O 3 abundance occurring at 25-55% PAL O 2 . As O 2 abundance initially decreases, larger amounts of UV photons capable of O 2 photolysis reach the lower (denser) regions of the atmosphere where O 3 production is more efficient, thus resulting in these increased O 3 levels. This effect does not occur for cooler host stars (K5V-M5V), since the weaker incident UV flux does not allow O 3 formation to occur at dense enough regions of the atmosphere where the faster O 3 production can outweigh a smaller source of O 2 from which to create O 3 . Thus, planets experiencing higher amounts of incident UV possessed larger stratospheric temperature inversions, leading to shallower O 3 features in planetary emission spectra. Overall it will be extremely difficult (or impossible) to infer precise O 2 levels from an O 3 measurement, however, with information about the UV spectrum of the host star and context clues, O 3 will provide valuable information about potential surface habitability of an exoplanet.