The authors apply a two-step tokamak regression procedure to L-mode confinement data. The resulting scaling expression for τE: is similar to other published scaling expressions. Using the random coeffcient model, tokamak-to-tokamak variations are included in the estimate of the uncertainty. The uncertainty factor in the predicted confinement times is calculated to be 19% for ITER and 35% for CIT. The confinement uncertainties are dominated by the propagation of uncertainties arising from the tokamak-to-tokamak variation in scalings with q and n to the second-step regression and, for CIT, by the lack of high magnetic field, moderate size devices in the L-mode database.