Two families of statistical models of increasing statistical complexity are presented which generalize global confinement expressions to plasma profiles and local transport coefficients. The temperature or diffusivity is parameterized as a function of the normalized flux radius, y, and the engineering variables u = (Ip,Bt,n,q95). The log-additive temperature model assumes that ln[T(y, u)]= fo (y) + fI(y)In[lp]+ fB(y)ln[Bt]+ fn (y)ln[n]+ fq In[q95] The unknown fi (y) are estimated using smoothing splines. The Rice selection criterion is used to determine which terms in the log-linear model to include. A 43 profile JET Ohmic data set from the Joint European Torus is analyzed and its shape dependencies are described. Our best fit has an average error of 152eV which is 10.5% percent of the typical line average temperature. The average error is less than the estimated measurement error bars. Our second class of models is log-additive diffusivity models where ln[c(y, u)]= g0 (w) + gI(y)In[Ip]+ gB(y)ln[Bt]+ gn (y)ln[n]. These log-additive diffusivity models are useful when the diffusivity is varied smoothly with the plasma parameters. We describe a penalized nonlinear regression technique to estimate the gi (y). The physics implications of the two classes of models, additive log-temperature models and additive log-diffusivity models, are different. The additive log-diffusivity models adjust the temperature profile shape as the radial distribution of sinks and sources. In contrast, the additive log-temperature model predicts that the temperature profile depends only on the global parameters and not on the radial heat deposition.