# Influence of Age on the Technical Wear of Tenement Houses
## 3 Discussion
The multi-criteria analysis of the proposed mathematical models, which describe the observed states of the technical wear of 10 elements of downtown residential buildings, allowed for the formulation of the following conclusions:  
* Regarding mathematical modelling when using nonlinear regression:
* from the four proposed mathematical models, which were tested using the non-linear regression method, and which describe the observed states of the technical wear of the elements of downtown tenement houses, none of the power models (Y = AX\({}^{\text{B}}\)) represent the nature of the determined trend of the wear process over time (a very low coefficient of determination R\({}^{2}\));
* analysis of the theoretical wear function \(Zt=f(T)\) shows a much better representation of the modelled trend by the exponential relationships (Y = exp(A + BX)) and hyperbolic relationships (1/Y = A + BX), and slightly worse by linear functions (Y = A + BX);
* when assuming that the measure of adjustment of mathematical models to the observed states is the coefficient of determination R\({}^{2}\), then only in the case of three elements--the roof structure (Z10), window joinery (Z13) and facade (Z20)--was the value of the wear differentiation of these elements (observed in the test) explained by their partial regression (up to 30%) in relation to the age of the analyzed buildings; this observation was confirmed by the acquisition of the largest amount of current data concerning the age of these elements;
* Regarding the analysis of the residual component, and also the assumed parabolic models with regards to the assumed durability \(T\) of the elements of downtown residential buildings:
* durability \(T\), which is defined as the residue variance parameter \([d(\xi)]^{2}\), and which reaches the minimum at the point of the sought \(T\), takes much greater values than the literature durability \(T\);
* the regularity of the results is surprising due to the fact that the variability range of \(T\) is narrow and varies from 153 years (for the roof structure Z10) to 177 years (for the massive ceilings above the cellars Z4); for comparison, their literature values are taken as \(T\) = 75 years (Z10) and \(T\) = 150 years (Z4);
* the reliability of the obtained results of the durability \(T\) in the analysis of the variance of the residual component was confirmed by the analysis of exponential and hyperbolic models, in which durability \(T\) (understood as the period of depletion of the function of the serviceability value (Z = 100%)) assumes values that are similar to those obtained in the analysis of the variance of the residues (this dependence is valid only for elements with a significant coefficient of determination R\({}^{2}\)). The correctness of the assumptions and results of the research in relation to the examined representative group of downtown residential buildings with a traditional construction (erected at the turn of the 19 th and 20 th centuries) allows for the following statements:  
* The age of the elements of an old residential building with a traditional construction:
* is of secondary importance in the process of the intensity of the loss of its service-ability value;
* is not a fundamental quantity that determines the course of their technical wear. The nonlinear regression method indicates that, in some specific building elements and with the proposed mathematical models, at best no more than 30% of the damage of elements is explained by the passage of time. Therefore, with the proposed mathematical models, it seems that the age does not determines completely the course of the technical wear of the analyzed building elements. * The degree of the technical wear of the elements of an old residential building is determined by the conditions of its maintenance and use.