INFLUENCE OF LEARNING PROCESS ON THE RELATION BETWEEN CHOSEN ANTHROPOMETRIC DIMENSIONS VIA LINEAR, PARABOLIC AND CUBIC RELATION MODEL

Abstract

       The aim of this paper was to compare, analyze and explain the change in linear, parabolic and cubic models of the relation between two chosen anthropometric soft tissue variables through a learning process implemented as a kinesiological treatment. A homogenous sample which homogenised further as the learning process advanced was used for the purpose of this research. In accordance with this, the linear model, the parabolic model and the cubic model which has never been used before depicting the relation between the thigh skinfold criterion variable and the upper arm circumference predictor variable were observed at 4 points in time. The convergence of statistically insignificant nonlinear models to statistically significant nonlinear model was observed and explained, providing a new methodological tool for quantitative analysis of the success of the learning process.
The research has shown that the cubic model is the most appropriate one at the highest point of sample homogenization. It also suggests the introduction of a mathematical expression for an interval of numbers which encompasses those predictor variable values for which it is reasonable to calculate the criterion variable value – the domain of the (non) linear regression model. Furthermore, the process of calculating the extreme points of the general nonlinear model was mathematically described and applied.
      Key words: anthropometry, cubic regression, education, methodology, nonlinear regression
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      Cilj ovog rada bio je usporediti, analizirati i objasniti promjenu linearnog, paraboličnog i kubičnog modela povezanosti dvije odabrane antropometrijske varijable mekih tkiva, kroz proces učenja implementiranog kao kineziološki tretman. Pritom je korišten homogen uzorak koji se procesom učenja dodatno homogenizira. U skladu s tim, promatrani su linearni, parabolični i do sada nekorišteni kubični model povezanosti kriterijske varijable kožnog nabora natkoljenice i prediktorske varijable opsega nadlaktice u 4 vremenske točke. Uočena i objašnjena je konvergencija statistički neznačajnih nelinearnih modela prema statistički značajnom nelinearnom modelu, što nam daje novi metodološki alat za kvantitativnu analizu uspješnosti procesa učenja. Pritom je pokazano da je kubični model najprikladniji kod najvišeg stupnja homogenizacije uzorka. Također je predložen matematički izraz za interval brojeva koji obuhvaća one vrijednosti prediktorske varijable za koje je smisleno izračunavati vrijednost kriterijske varijable - domenu (ne)linearnog regresijskog modela. Nadalje, matematički je opisan i primijenjen postupak izračuna ekstremnih točaka općeg nelinearnog modela.
      Ključne riječi: antropometrija, edukacija, kubična regresija, metodologija, nelinearna regresija