# Prediction of Cardiorespiratory Fitness Level of Young Healthy Women Using Non-Exercise Variables
## 4 Discussion  
The main contribution of this study was to calculate models for the prediction CRF among healthy and young women using the non-exercise variables. The presented regression models for predicting VO\({}_{2}\)max, which is the best indicator of CRF, based on non-exercise variables. Predictive models of VO\({}_{2}\)max based on non-exercise data applied to apparently healthy individuals have their limitations; however, they allow rapid assessment of CRF without the need for a maximal exercise test. Such models are inexpensive, require no specialized equipment, and are time-efficient and feasible for large groups in epidemiological and population-based studies [28]. Non-exercise regression models give relatively accurate results and are a convenient way to predict VO\({}_{2}\)max in both adult men and women [51]. Comparing the errors of calculated models with those of other presented solutions in the literature is difficult and in some cases impossible. This is due to the fact that direct comparison of errors is possible only when the same maximum test was used, models were calculated for a similar sample of subjects, and using cross-validation for evaluation predictive ability [52]. All models in this study were developed and cross-validated using data from 154 healthy young women. The models obtained were compared with models presented in other studies. The models determined by the other authors are calculated from a sample that includes men and women. Gender is differentiated by the input variable. Thus, there are models for both men and women, which allows comparison with the model calculated in this work. Direct comparison of the calculated model with other authors' models is very difficult. The models presented in Table 5 are models for which a different evaluation criterion was used. For most of the models, the SSE or SE fitting error was calculated, \begin{table}
\begin{tabular}{l r r r r r} \hline \hline
**Method** & **OLS Ridge (\(\lambda=190\))** & **LASSO (\(s=1\))** & **OLS-FS** & **Ridge-FS (\(\lambda=10\))** \\ \hline Intercept & 225.8640 & 55.3396 & 225.8640 & 65.9761 & 64.6133 \\ \(x_{1}\)—Age & \(-0.0432\) & 0.1527 & \(-0.0432\) & 0 & 0 \\ \(x_{2}\)—BW & \(-0.8807\) & \(-0.0195\) & \(-0.8807\) & 0 & 0 \\ \(x_{3}\)—BH & \(-0.5568\) & \(-0.0080\) & \(-0.5568\) & 0 & 0 \\ \(x_{4}\)—WC & 1.3967 & \(-0.0435\) & 1.3967 & \(-0.3098\) & \(-0.2897\) \\ \(x_{5}\)—HC & 0.8201 & \(-0.0485\) & 0.8201 & 0 & 0 \\ \(x_{6}\)—FAT & \(-1.7537\) & \(-0.0459\) & \(-1.7537\) & 0 & 0 \\ \(x_{7}\)—FFM & 6.2698 & 0.0247 & 6.2698 & 0 & 0 \\ \(x_{8}\)—TBW & \(-10.7272\) & 0.0327 & \(-10.7272\) & 0 & 0 \\ \(x_{9}\)—BMI & 2.7528 & \(-0.0870\) & 2.7528 & 0 & 0 \\ \(x_{10}\)—WHtR & \(-464.4435\) & \(-7.3139\) & \(-464.4435\) & 0 & 0 \\ \(x_{11}\)—WHR & 118.3648 & \(-2.4083\) & 118.3648 & 0 & 0 \\ \(x_{12}\)—MLTPAQ\({}_{L}\) & \(-3.0242\) & 0.0003 & \(-3.0242\) & 0 & 0 \\ \(x_{13}\)—MLTPAQ\({}_{M}\) & \(-3.0240\) & 0.0003 & \(-3.0240\) & 0 & 0 \\ \(x_{14}\)—MLTPAQ\({}_{H}\) & \(-3.0238\) & 0.0004 & \(-3.0238\) & 0 & 0 \\ \(x_{15}\)—MLTPAQ\({}_{T}\) & 3.0250 & 0.0003 & 3.0250 & 0.0012 & 0.0011 \\ \hline RMSE\({}_{CV}\) & 12.54 & 6.37 & 12.54 & 6.21 & 6.20 \\ \hline \hline \end{tabular} \(\overline{\text{OLS}}\)—ordinary least squares regression; \(\lambda\)—Ridge regression parameter; \(s\)—LASSO regression parameters; Ridge–FS—Ridge regression model with input variables calculated by forward regression; RMSE\({}_{CV}\)—root mean squared error.  
\end{table} 
Table 4: Weights and RMSE\({}_{CV}\) errors for models based on anthropometric parameters and MLTPAQ. while in the present study, a critical approach was taken by evaluating the models with the LOOCV cross-validation. The exception is the model presented in work [53], where the same criteria and the same database were used, except that the model was based on the maximum test. However, when comparing these two models, it is noted that the use of non-exercise variables results in an error gain of only 2.13 (mL\(\cdot\)kg\({}^{-1}\cdot\)min\({}^{-1}\)).