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Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single molecule experimental techniques and give insight into biologically relevant processes {\em{in vivo}}. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit, and leverage the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance., Comment: This resubmission corrects some incorrect statistics in the simulations in an earlier version, includes numerous new figures and text to clarify the paper, and removed some aspects of inference of transverse statistics from longitudinal observations. The mathematics and analysis in the paper is identical to the first version, but quantitative aspects of the paper have changed