## 6 Result
### Stepwise Multivariate Linear Regression  
A total of 57 datasets were employed as training sets for regression purposes, the following models were tested: (i) incorporating features from both subjects' signals, (ii) exclusive use of subject 1's data, and (iii) exclusive use of subject 2's data. Subsequently, the corresponding models underwent evaluation, using all available windows from (i) subject 1 and 2, (ii) subject 1 alone, and (iii) subject 2 alone as testing sets. This evaluation employed leave-one-out cross-validation. Furthermore, the models built with training sets that contained information from only one of the subjects were also assessed using the data of the other subject. This assessment aimed to confirm the presence of any bias within the models, specifically whether they exhibited inferior performance when estimating SBP and DBP values for the subject not included in their training set. The results demonstrated were worse when estimating SBP and DBP values of the subject excluded from the training set (Table 2). In each of these evaluation scenarios, metrics such as the mean absolute error (MAE), standard deviation (STD), and root mean Squared error (RMSE) were computed to quantify performance. The function _trapz.m in MATLAB_ was used to extract the features that were placed under the PPG curve based on the trapezoidal rule approximation method by integrating the input curve between specified points numerically. As described in the method section, the windows that were generated previously from the signals are fed into the _FeatureExtraction.m_ function as an input, and we implemented functions to extract features at various  
Figure 6: Projection of each subject data point onto the plane defined by the first two PCs and projection of features onto their different plane. steps. At each step, these windows pass through quality control, and if they do not carry any interpretable signal, then they are rejected, which means the well-documented features of each signal are absent. This is a crucial advance in our implementation because, even if we tried to remove maximum noise and large amplitude artifacts, there may remain some low-amplitude artifacts that corrupt the samples. In Table 3, the features excluded or chosen by our stepwise linear regression algorithm are displayed, and their selection varies depending on the training dataset and the target variable, either SBP or DBP. Notably, when focusing on subject 2's subset, we observed a larger number of features that were considered statistically insignificant for the regression model. This observation might be attributed to the high variance shown by this patient, as previously mentioned, in contrast to the data from subject 1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Training Set**} & \multirow{2}{*}{**Testing Set**} & \multicolumn{3}{c}{**Systolic Blood Pressure (mmHg)**} & \multicolumn{3}{c}{**Diastolic Blood Pressure (mmHg)**} \\ \cline{3-8}  & & **MAE** & **STD** & **RMSE** & **MAE** & **STD** & **RMSE** \\ \hline Subject 1 & Subject 2 & 13.32 & 10.87 & 17.00 & 9.20 & 6.33 & 11.18 \\ \hline Subject 2 & Subject 1 & 36.80 & 7.00 & 37.45 & 22.40 & 3.62 & 22.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSEs, standard deviation (STD), and MAEs of the linear regression models with alternating training and testing sets.