  The Proton Radius Puzzle refers to the ~7{\sigma} discrepancy that exists
between the proton charge radius determined from muonic hydrogen and that
determined from electronic hydrogen spectroscopy and electron-proton
scattering. One possible partial resolution to the puzzle includes errors in
the extraction of the proton radius from ep elastic scattering data. This
possibility is made plausible by certain fits which extract a smaller proton
radius from the scattering data consistent with that determined from muonic
hydrogen. The reliability of some of these fits that yield a smaller proton
radius was studied. We found that fits of form factor data with a truncated
polynomial fit are unreliable and systematically give values for the proton
radius that are too small. Additionally, a polynomial fit with a
\chi^2_{reduced} ~ 1 is not a sufficient indication for a reliable result.
