Regression analysis of expanded polystyrene properties

Own measurements examine the tensile strength of expanded polystyrene (EPS) depending on its bulk density. 30 samples were used to calculate the correlation coefficients between these two properties. In addition to the standard Pearson coefficient, we also calculate the rank correlation coefficients, Spearman´s and Kendall´s. By testing the hypotheses, we verify the correlation of the entire population. After finding a relatively close correlation (0.6 - 0.8), we apply different regression models, especially polynomial, but also exponential. We evaluate the properties of parameters in models, their point estimates and confidence intervals. Based on the characteristics of each of the seven regressions, we found the best exponential form of the dependence, before the linear polynomial. The complexity of a mathematical model does not always mean that it is also a more accurate approximation. On the other hand, a simple model makes it possible, in addition to its ease of use, to more closely reflect the examined dependence.