# Predictive Modeling of VO2 max Based on 20 m Shuttle Run Test for Young Healthy People
## 4 Discussion  
The paper presents mathematical models for the prediction of VO\({}_{2}\)max based on a 20 m SRT and anthropometric parameters. All models were developed and cross-validated using a sample of 308 healthy young people (aged 19-27). The models obtained are classified as \"maximal models\" [49] and that is why errors in this group of models were compared with errors presented by other authors. The majority of papers with VO\({}_{2}\)max maximal predictive models present a common model for females and males [15; 30; 31]. An analysis of errors for predictive models in which sex was the input variable revealed that the error \(RMSE_{CV}=4.78\) [mL\(\cdot\)kg\({}^{-1}\)\(\cdot\)min\({}^{-1}\)] is a result which does not deviate from errors presented in other papers (Table 6). The calculated model is more accurate than the model proposed by [PERSON] [30] and [PERSON] [15]. It is however less accurate than the models proposed in papers by [PERSON] [31; 50]. The optimal model for the whole group used the following factors for prediction: sex (\(x_{0}\)), distance (20 m SRT) (\(x_{1}\)), body height (\(x_{7}\)) and content of adipose tissue (\(x_{20}\)). In young males and females, regular physical exercise definitely improves CRF by increasing VO\({}_{2}\)max and decreasing body fat percentage, leading to a better quality of life [51; 52; 53; 54]. The VO\({}_{2}\)max level varies significantly among individuals and mainly depends on genetic aspects, sex, age anthropometric properties of health, lifestyle and training status [51; 52; 55; 56; 57; 58; 59]. Reference values may change over time and should be regularly updated/validated [60]. The data may be found in papers analysing the results of cardiac stress tests carried out for large groups of healthy people [8; 60; 61]. Typical values of VO\({}_{2}\)max in young healthy male students amount to about 50 [mL\(\cdot\)kg\({}^{-1}\)\(\cdot\)min\({}^{-1}\)], and in women to about 40 [mL\(\cdot\)kg\({}^{-1}\)\(\cdot\)min\({}^{-1}\)] [62]. CRF in terms of aerobic capacity is affected by the composition of the body. Low CRF in young adults with increased body fat could be a factor in the development of cardiovascular comorbidities later in middle age and old age [63]. Bioimpedance is an alternative method to estimate the percentage of body fat, when compared to DXA (Dual Energy \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Group** & **Predictors** & \(RMSE_{CV}\) & **Parameter** \\ \hline \multirow{4}{*}{Lasso} & All & \(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},x_{9},x_{10},x_{14},x_{17},x_ {19},x_{20}\) & 4.91 & \(s=0.1\) \\  & F & \(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},x_{9},x_{10},x_{13},x_{16},x_ {17},x_{18},x_{19},x_{21}\) & 4.48 & \(s=0.1\) \\  & M & \(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8},x_{12},x_{13},x_{14},x_{16},x_ {18},x_{21}\) & 5.53 & \(s=0.1\) \\ \hline \multirow{4}{*}{OLS (forward)} & All & \(x_{0},x_{1},x_{7},x_{20}\) & **4.78** & — \\  & F & \(x_{1},x_{5},x_{7},x_{20}\) & 4.14 & — \\  & M & \(x_{1},x_{9},x_{14},x_{17},x_{19}\) & **5.35** & — \\ \hline \multirow{4}{*}{OLS (backward)} & All & \(x_{1},x_{6},x_{10},x_{11},x_{12},x_{13},x_{14},x_{15},x_{20},x_{22}\) & 5.30 & — \\  & F & \(x_{1},x_{5},x_{7},x_{8},x_{11},x_{16}\) & 4.20 & — \\  & M & \(x_{1},x_{6},x_{8},x_{9},x_{13},x_{14},x_{16},x_{17},x_{18},x_{21},x_{22}\) & 5.39 & — \\ \hline \multirow{4}{*}{OLS (bidirectional)} & All & \(x_{0},x_{1},x_{7},x_{20}\) & **4.78** & — \\  & F & \(x_{1},x_{7},x_{20}\) & **4.11** & — \\  & M & \(x_{1},x_{19}\) & 5.39 & — \\ \hline \multirow{4}{*}{MLP (best subset)} & All & \(x_{0},x_{1},x_{7},x_{20}\) & 4.94 & \(m=2\) \\  & F & \(x_{1},x_{7},x_{20}\) & 4.26 & \(m=2\) \\  & M & \(x_{1},x_{9},x_{14},x_{17},x_{19}\) & 5.56 & \(m=2\) \\ \hline \multirow{4}{*}{ RBF (best subset)} & All & \(x_{0},x_{1},x_{7},x_{20}\) & 4.80 & \(m=5\) \\  & F & \(x_{1},x_{7},x_{20}\) & 4.07 & \(m=5\) \\ \cline{1-1}  & M & \(x_{1},x_{9},x_{14},x_{17},x_{19}\) & 5.30 & \(m=2\) \\ \hline \hline \end{tabular}
\end{table}