Inferential variables are often used in process industries in place of direct on-line measurement of controlled variables where direct measurement is expensive, unreliable or adds significant delay. Simplified fundamental models are often not available for inferential control; therefore, empirical models must be used. The procedures currently used for building empirical inferential models are based on standard statistical methods and are generally limited to only a few preselected variables. This work investigates the use of a multivariate regression method, Partial Least Squares or Projection to Latent Structures (PLS). It is shown that PLS provides a general method for building inferential models when one has data on a large number of process variables and when these variables are highly correlated with one another. By not overfitting the data PLS provides models with good predictive power, and through its very efficient handling of missing data, it provides inferential models that are extremely robust to sensor failure. Since empirical models are usually developed directly from process data, the nature of the data set is extremely important. The data set must capture typical variation in all input variables and process disturbances. Furthermore, the data collection must be designed according to the end use intended for the model. If the model is to be used in an inferential control scheme, then it is shown that open-loop process data cannot usually be used. Rather, it is important that the data be collected under a feedback scheme that resembles the final scheme as closely as possible. Two case studies from distillation column control are used to demonstrate the general development of inferential models via PLS, and to illustrate these points.