  [Background] The proton charge radius extracted from recent muonic hydrogen
Lamb shift measurements is significantly smaller than that extracted from
atomic hydrogen and electron scattering measurements.
  [Purpose] In an attempt to understand the discrepancy, we review
high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon
and Stanford.
  [Method] We make use of stepwise regression techniques using the $F$-test as
well as the Akaike information criterion to systematically determine the
predictive variables to use for a given set and range of electron scattering
data as well as to provide multivariate error estimates.
  [Results] Starting with the precision, low four-momentum transfer ($Q^2$)
data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression
of the Maclaurin series using the $F$-test as well as the Akaike information
criterion justify using a linear extrapolation which yields a value for the
proton radius that is consistent with the result obtained from muonic hydrogen
measurements. Applying the same Maclaurin series and statistical criteria to
the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the
stepwise regression tends to favor a radius consistent with the muonic hydrogen
radius but produces results that are extremely sensitive to the range of data
included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select
functions which extrapolate to high $Q^2$, we find that a Pad\'e ($N=M=1$)
statistical model works remarkably well, as does a dipole function with a 0.84
fm radius, $G_E(Q^2) = ( 1 + Q^2/0.66\,\mathrm{GeV}^2)^{-2}$.
  [Conclusions] From this statistical analysis, we conclude that the electron
scattering result and the muonic hydrogen result are consistent. It is the
atomic hydrogen results that are the outliers.
