Paramagnetic correlations in the magnetic material Yb2Ti2O7 have been investigated via neutron scattering, revealing a [111] rod of scattering intensity. Assuming interactions between the Yb3+ ions composed of all symmetry-allowed nearest neighbor exchange interactions and long-range dipolar interactions, we construct a model Hamiltonian that allows for an excellent description of the neutron scattering data. Our results provide compelling evidence for significant anisotropic exchange interactions in an insulating magnetic pyrochlore oxide. We also compute the real space correlations leading to the [111] rod of scattering.