Testing of a Mathematical Model of Grain Porosity

Numerous researchers from the field of agricultural engineering use mathematical models for the description of processes. Because of the existing many systems and processes, there is a possibility of making different types of models. Their systematic may be found in the Pabis [1985] and Powierża [1997] books. Once the form of a model is fixed, what remains is the testing of the correctness of the model based on experimental data. Regression models are frequently employed in engineering studies. Commonly used as a measure of efficient suitability of such a model to experimental data is the coefficient of determination R. This index is excellent in the case of linear models and of non-linear models that are intrinsically linear (i.e. can be reduced to linear through suitable transformations). However, for non-linear and intrinsically non-linear models [Dobosz 2001]) complications appear. For example, in a logistic model [Bochniak and Wesołowska-Janczarek 2006] the coefficient of determination R may assume negative values. In such a case it loses its natural interpretation. This paper presents a review of several statistical tests available in literature, that can be applied for testing of the correctness of non-linear regression models on the basis of experimental data. The statistical methods under presentation are illustrated by means of results of experimental studies concerned with oat grain porosity [Kusińska 2007, Bowszys and Tomczykowski 2007].