Considering precision of experimental data in construction of optimal regression models

Construction of optimal (stable and of highest possible accuracy) regression models comprising of linear combination of independent variables and their non-linear functions is considered. It is shown that estimates of the experimental error, which are most often available for engineers and experimental scientists, are useful for identifying the set of variables to be included in an optimal regression model. Two diagnostical indicators, which are based on experimental error estimates, are incorporated in an orthogonalized-variable-based stepwise regression (SROV) procedure. The use of this procedure, followed by regression diagnostics, is demonstrated in two examples. In the first example, a stable polynomial model for heat capacity is obtained, which is ten times more accurate than the correlation published in the literature. In the second example, it is shown that omission of important variables related to reaction conditions prevents reliable modeling of the product properties.