  Scientists often try to incorporate prior knowledge into their regression
algorithms, such as a particular analytic behavior or a known value at a
kinematic endpoint. Unfortunately, there is often no unique way to make use of
this prior knowledge, and thus, different analytic choices can lead to very
different regression results from the same set of data. To illustrate this
point in the context of the proton electromagnetic form factors, we use the
Mainz elastic data with its 1422 cross section points and 31 normalization
parameters. Starting with a complex unbound non-linear regression, we will show
how the addition of a single theory-motivated constraint removes an oscillation
from the magnetic form factor and shifts the extracted proton charge radius. We
then repeat both regressions using the same algorithm, but with a rebinned
version of the Mainz dataset. These examples illustrate how analytic choices,
such as the function that is being used or even the binning of the data, can
dramatically affect the results of a complex regression. These results also
demonstrate why it is critical when using regression algorithms to have either
a physical model in mind or a firm mathematical basis
