## 3 Results  
The number of original samples and the number of samples considered reliable after pre-processing are reported in Table 2. After pre-processing, 2409 out of 2421 samples (99.5%) were considered reliable. Distributions of predictors for wearable-device data and reference instrumentation data are reported in Table 3; no statistical differences were observed between HRWD and HRREF (\(p\)-value \(>\) 0.05) and between BRWD and BRREF (\(p\)-value \(>\) 0.05). The final formulation of the model is described by the following equation:  
\[\widehat{\text{TV}_{\text{WD}}}=0.30\cdot\text{Age}+0.39\cdot\text{BMI}\ -\ 0.02\cdot\text{HR}_{\text{WD}}+0.17\cdot\text{BR}_{\text{WD}}-0.12\cdot\text{ Age}\cdot\text{HR}_{\text{WD}}-0.46\cdot\text{Age}\cdot\text{BR}_{\text{WD}}\]  
\[+0.20\cdot\text{BMI}\cdot\text{HR}_{\text{WD}}-4.80\cdot\text{BMI}\cdot \text{BR}_{\text{WD}}-0.35\cdot\text{HR}_{\text{WD}}\cdot\text{BR}_{\text{WD}} -11.46\]The values of the model parameters obtained by applying the stepwise linear regression approach are reported in Table 4; the \(R^{2}\) value for model formulation is equal to 0.71. [PERSON] plots and results of the linear regression analysis for the comparison between both \(\widehat{\text{TV}_{\text{WD}}}\) and \(\widehat{\text{TV}_{\text{REF}}}\) predictions and breath-by-breath TV are represented in Figure 1. Bland-Altman analysis confirmed very good \(\widehat{\text{TV}_{\text{WD}}}\) estimations (confidence intervals: [\(-\)0.01; 0.01] L), and \(\widehat{\text{TV}_{\text{REF}}}\) estimations (confidence intervals: [0.05; 0.08] L). The data division for the leave-one-subject-out cross-validation procedure is reported in Table 2. The results of the leave-one-subject-out cross-validation procedure in terms of \(R^{2}\), Pearson's correlation coefficients, and predicted tidal volume using either wearable-device data (\(\widehat{\text{TV}_{\text{WD}}}\)) or reference instrumentation data (\(\widehat{\text{TV}_{\text{REF}}}\)) are reported in Table 5. Values of \(R^{2}\) and correlation coefficients confirmed the goodness of fit. The results of the test of equivalence revealed a substantial equivalence between \(\widehat{\text{TV}_{\text{WD}}}\) and TV and between \(\widehat{\text{TV}_{\text{REF}}}\) and TV (Table 5), with an equivalence margin equal to 70% of a standard deviation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Subject** & **Original** & **Reliable** & **Training** & **Testing** \\ \hline
1 & 200 & 199 & 2210 & 199 \\
2 & 271 & 271 & 2138 & 271 \\
3 & 239 & 233 & 2176 & 233 \\
4 & 278 & 273 & 2136 & 273 \\
5 & 285 & 285 & 2124 & 285 \\
6 & 238 & 238 & 2171 & 238 \\
7 & 288 & 288 & 2121 & 288 \\
8 & 348 & 248 & 2061 & 348 \\
9 & 274 & 274 & 2135 & 274 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of original samples, number of samples considered reliable after pre-processing and data division for the leave-one-subject-out cross-validation procedure. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Subject**} & \multirow{3}{*}{\
\begin{tabular}{c} **Age** \\ **(years)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **BMI** \\ **(kg/m2)** \\ \end{tabular} } & \multicolumn{3}{c}{**Wearable**} & \multicolumn{3}{c}{**Reference**} \\  & & & & **Device** & **Instrumentation** \\ \cline{3-6}  & & & & & **HRWD** \\
5 & 53 & 22.7 & 128 \(\pm\) 26 & 31 \(\pm\) 7 & 129 \(\pm\) 27 & 34 \(\pm\) 12 \\
6 & 46 & 22.3 & 146 \(\pm\) 32 & 26 \(\pm\) 9 & 147 \(\pm\) 32 & 29 \(\pm\) 12 \\
7 & 27 & 21.0 & 149 \(\pm\) 25 & 30 \(\pm\) 7 & 150 \(\pm\) 24 & 32 \(\pm\) 10 \\
8 & 27 & 24.1 & 164 \(\pm\) 26 & 38 \(\pm\) 9 & 160 \(\pm\) 27 & 39 \(\pm\) 14 \\
9 & 40 & 24.1 & 134 \(\pm\) 31 & 29 \(\pm\) 9 & 130 \(\pm\) 30 & 30 \(\pm\) 9 \\ \hline All & 41 \(\pm\) 10 & 22.8 \(\pm\) 1.3 & 145 \(\pm\) 28 & 30 \(\pm\) 10 & 144 \(\pm\) 29 & 32 \(\pm\) 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Distributions of the predictors.