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Scientists often try to incorporate prior knowledge into their regressionalgorithms, such as a particular analytic behavior or a known value at akinematic endpoint. Unfortunately, there is often no unique way to make use ofthis prior knowledge, and thus, different analytic choices can lead to verydifferent regression results from the same set of data. To illustrate thispoint in the context of the proton electromagnetic form factors, we use theMainz elastic data with its 1422 cross section points and 31 normalizationparameters. Starting with a complex unbound non-linear regression, we will showhow the addition of a single theory-motivated constraint removes an oscillationfrom the magnetic form factor and shifts the extracted proton charge radius. Wethen repeat both regressions using the same algorithm, but with a rebinnedversion 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, candramatically affect the results of a complex regression. These results alsodemonstrate why it is critical when using regression algorithms to have eithera physical model in mind or a firm mathematical basis

How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering Cross Section Data