applied research, multivariable models, particularanalysis, PISA, regression interactions, statistical estimations

In the frame of applied mathematical modeling, a wide spectrum of that approximations of real processes has been proposed and used. The specifics of the quantitative research techniques can be suitably utilized in favour of real situations. In the case of an analysis of a big data set, the consequences between mathematical models can be interesting in the selection of appropriate models. Particularly in a regression analysis, the spectrum of model structures has been widely offered depending on the expert approach or regarding the quality criteria. The quality of the model may not be generally the priority whether on other aspects is a mathematical model focused. For purposes of description of various situations that occurred due to setting the appropriate structure of mathematical models, their fitting behavior is identified progressively in this paper. In this contribution, the selected type of models can be classified as multivariable regression models. The partial dependences of Cardinal- Variables’ Dependences are analysed steeply from onedimensional cases to multidimensional models. The applied research, in which the results can be particularly utilized regarding the progressively changed structure of model, the research within frame of PISA monitoring (OECD’s Programme for International Student Assessment) is presented.