# Predictive Modeling of VO2 max Based on 20 m Shuttle Run Test for Young Healthy People
###### Abstract  
This study presents mathematical models for predicting VO2 max based on a 20 m shuttle run and anthropometric parameters. The research was conducted with data provided by 308 young healthy people (aged 20.6 \(\pm\) 1.6). The research group includes 154 females (aged 20.3 \(\pm\) 1.2) and 154 males (aged 20.8 \(\pm\) 1.8). Twenty-four variables were used to build the models, including one dependent variable and 23 independent variables. The predictive methods of analysis include: the classical model of ordinary least squares (OLS) regression, regularized methods such as ridge regression and Lasso regression, artificial neural networks such as the multilayer perceptron (MLP) and radial basis function (RBF) network. All models were calculated in R software (version 3.5.0, R Foundation for Statistical Computing, Vienna, Austria). The study also involved variable selection methods (Lasso and stepwise regressions) to identify optimum predictors for the analysed study group. In order to compare and choose the best model, leave-one-out cross-validation (LOOCV) was used. The paper presents three types of models: for females, males and the whole group. An analysis has revealed that the models for females (\(RMSE_{CV}=4.07\) mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)) are characterised by a smaller degree of error as compared to male models (\(RMSE_{CV}=5.30\) mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)). The model accounting for sex generated an error level of \(RMSE_{CV}=4.78\) mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\).  
maximal oxygen uptake; cardiorespiratory fitness; predictive modeling; students health 2018 82213 2213 2018 2213 20  
forecasted based on indirect measurements, using predictive models [23; 25; 26]. A 20 m shuttle run test (20 m SRT) is often used to measure cardiovascular fitness [22; 23; 27; 28]. Therefore, it seems reasonable to model the index using various mathematical methods. A predictive model may help to identify the level of CRF without costly equipment and specialised research time. The prediction of the VO2 max parameter may become an important element of health monitoring and fitness improvement in young healthy people.  
In the literature, there are many papers that focus on the prediction of this indicator using, among other factors, the results of resistance tests, anthropometric parameters or physical activity indicators [15; 23; 29]. Therefore, the VO2 max predictive models may be classified as both exercise and non-exercise models. Exercise models make predictions based on the result of an endurance test with maximum or submaximal intensity [15; 23; 30; 31; 32; 33; 34]. In the literature, there are also prediction models based on ergometric tests [35; 36]. The most popular predictors include age, sex and BMI [25]. Most of the published models are based on multiple regression or machine learning methods.  
In this paper, the authors present different models to predict VO2 max based on the result of the 20 m shuttle run test and anthropometric parameters. The aim of the work is to determine the optimal predictive model to estimate VO2 max for young healthy people (students). The models may be used e.g., by a Physical Education teacher for CRF monitoring. To the best of our knowledge, these are the first studies for such a large group (\(n\) = 308) using the direct measurement of oxygen uptake. Data was collected at five large universities in various parts of Poland.