We test the mutual consistency between the baryon acoustic oscillation measurements from the eBOSS SDSS final release, as well as the Pantheon supernova compilation in a model independent fashion using Gaussian process regression. We also test their joint consistency with the $Lambda$CDM model, also in a model independent fashion. We also use Gaussian process regression to reconstruct the expansion history that is preferred by these two datasets. While this methodology finds no significant preference for model flexibility beyond $Lambda$CDM, we are able to generate a number of reconstructed expansion histories that fit the data better than the best-fit $Lambda$CDM model. These example expansion histories may point the way towards modifications to $Lambda$CDM. We also constrain the parameters $Omega_k$ and $H_0r_d$ both with $Lambda$CDM and with Gaussian process regression. We find that $H_0r_d =10030 pm 130$ km/s and $Omega_k = 0.05 pm 0.10$ for $Lambda$CDM and that $H_0r_d = 10040 pm 140$ km/s and $Omega_k = 0.02 pm 0.20$ for the Gaussian process case.
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