Two families of statistical models 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, $\barψ$, and the engineering variables, ${\bf u} = (I_p,B_t,\bar{n},q_{95})^\dagger$. The log-additive temperature model assumes that $\ln [T(\barψ, {\bf u})] =$ $f_0 (\barψ) + f_I (\barψ)\ln[I_p]$ $+ f_B (\barψ) \ln [B_t]$ $+ f_n (\barψ) \ln [ \bar{n}] + f_{q}\ln[q_{95}]$. The unknown $f_i (\barψ)$ are estimated using smoothing splines. A 43 profile Ohmic data set from the Joint European Torus is analyzed and its shape dependencies are described. The best fit has an average error of 152 eV which is 10.5 \% percent of the typical line average temperature. The average error is less than the estimated measurement error bars. The second class of models is log-additive diffusivity models where $\ln [ χ(\barψ, {\bf u})] $ $=\ g_0 (\barψ) + g_I (\barψ) \ln[I_p]$ $+ g_B (\barψ) \ln [B_t ]$ $+ g_n (\barψ) \ln [ \bar{n} ]$. These log-additive diffusivity models are useful when the diffusivity is varied smoothly with the plasma parameters. A penalized nonlinear regression technique is recommended to estimate the $g_i (\barψ)$. 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.