# Predictive Modeling of VO2 max Based on 20 m Shuttle Run Test for Young Healthy People
## 4 Discussion

Table 4: Mathematical models with variable selection. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Group** & **Method** & **Equation** \\ \hline Female & OLS (bidirectional) & \(y=61.27+0.02\cdot x_{1}-0.16\cdot x_{7}-0.21\cdot x_{20}\) \\ Male & OLS (forward) & \(y=47.51+0.01\cdot x_{1}-0.36\cdot x_{9}+19.37\cdot x_{14}+1.05\cdot x_{17}-8.50 \cdot x_{19}\) \\ All & OLS (forward) & \(y=72.31+1.94\cdot x_{0}+0.01\cdot x_{1}-0.21\cdot x_{7}-0.23\cdot x_{20}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: VO\({}_{2}\)max linear predictive equations. X-ray Absoptiometry), it is a gold standard method, as there is a high level of agreement [64]. Simple use, lack of radiation and the relatively low cost of bioelectric impedance suggests that it is a feasible analysis for body fat measurement, especially in large populations [65]. Besides a common model for females and males, this paper determines separate models for each group. It may be observed that the models for females are characterised by a significantly smaller error as compared to those for men. The RBF neural network with eight neurons in the hidden layer turned out to be the most accurate. It generates an error of \(RMSE_{CV}=4.07\) [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]. [PERSON] [66] presented similar studies in his paper. He described a multiple regression model whose prediction error amounted to 1.27 [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)] (Table 6). The model used speed and body height as predictors. Other studies concerning prediction among females were published by [PERSON] [23], who calculated a model generating an error of 0.53 [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]. The model used only the maximum speed. When the errors obtained in this paper are compared with errors obtained by other authors, it may be concluded that their errors were significantly smaller. It shall be emphasized that the population analysed in the study was much larger and more diversified for the VO\({}_{2}\)max level (\(44.9\pm 7.0\) [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]). Moreover, cross-validation was used in the paper for evaluation, while in the papers discussed the model quality was evaluated by means of standard errors. That is why direct comparisons are impossible. The model calculated for women has the simplest structure and includes: distance (20 m SRT) (\(x_{1}\)), body height (\(x_{7}\)) and body fat (\(x_{20}\)). The model contains the same variables as the model for all participants save for sex, which is a constant. Similarly to the female group, the RBF network turned out to be the best model for males, whereby in the male group the optimal network consists only of two neurons in the hidden layer. The network generates an error level of \(RMSE_{CV}=5.30\) [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]. Comparing the obtained results with other papers where models were calculated only for males, it may be observed that the parameter value does not deviate significantly from the published results (Table 6). The optimal model for males calculated in the study generated greater errors than the models presented by [PERSON] and [PERSON] [67] (4.10 [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]) and [PERSON] [68] (1.41 [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]). The error obtained is still smaller than the error generated using the [PERSON] model [69] (7.20 [mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)]). When comparing the errors of the calculated models, it should be emphasized that a direct comparison of the errors obtained in the studies is valid only when the same maximal test is used and when a similar study sample is employed [70]. Therefore, it seems that the results obtained may only be compared with models which use 20 m SRT and are developed based on a population of healthy people aged 19-27 years, and are cross-validated. Cross-validation does not evaluate the fitness error but a generalisation error.