Empirical models fitted to measured data should be used only in the region within which measurements were made, the so-called interpolation region. In cases in which many variables are involved, the determination of the interpolation region is not self-evident and the region is sometimes unexpectedly small. A definition of the interpolation region is presented, to enable some consequences of the use of models with high numbers of parameters to be exemplified. In particular, unreliability close to the boundary of the interpolation region is highlighted by comparison of the predictions of models with different numbers of parameters.