The temperature and density profiles of the Joint European Torus (JET) are parametrized using log additive models in the control variables. Predictive error criteria are used to determine which terms in the log linear model to include. The density and temperature profiles are normalized to their line averages (n and T). The normalized ohmic density shape depends primarily on the parameter n/Bt, where Bt is the toroidal magnetic field. Both the low mode (L mode) and the edge localized mode-free (ELM-free) high mode (H mode) temperature profile shapes depend strongly on the type of heating power, with ion cyclotron resonant heating (ICRH) producing a more peaked profile than neutral beam injection (NBI). Given the heating type dependence, the L mode temperature shape is nearly independent of the other control variables. The H mode temperature shape broadens as the effective charge, Zeff, increases. The line average L mode temperature scales as Bt0.96 (power per particle)0.385. The L mode normalized density shape depends primarily on the ratio of line average density, n, to the edge safety factor, q95. As n/q95 increases, the profile shape broadens. The current, Ip, is the most important control variable for the normalized H mode density. As the current increases, the profile broadens and the gradient at the edge sharpens. Increasing the heating power, especially ICRH, or decreasing the average density, peaks the H mode density profile slightly