## 2 Materials and Methods
### Well-Being Index  
The proposed Well-Being Index (_WBI_) uses four components. The mathematical formulations for each element were developed, and the appropriate weights were assigned in the final formula. The _WBI_ contains the heart rate component (_HRC_), the physical activity component (_PAC_), the sleep quality component (_SQC_), and the stress component (_SC_). The _HRC_ measures cardiovascular health based on minRate and maxRate relative to the avgRate. The _HRC_ is calculated using Equation (1):  
\[HRC_{i}=0.25\times\left(\frac{maxRate_{i}-minRate_{i}}{avgRate_{i}}\right) \tag{1}\]  
where  
\(HRC_{i}\) is the heart rate component for date \(i\);  
\(avgRate_{i}\) is the average heart rate for date \(i\);  
\(minRate_{i}\) and \(maxRate_{i}\) are minimum and maximum heart rate for date \(i\). The _PAC_ assesses physical condition based on number of steps, walking distance, intense activity distance, and calories burned, and it is calculated using Equation (2):  
Figure 1: Overview of health metrics collected from CWD. \[PAC_{i}=0.25\times(\ln(1+noSteps_{i})+\ln(1+distanceM_{i})+\ln(1+intensActDistance _{i})+\ln(1+burnCalories_{i})) \tag{2}\]  
where  
\(PAC_{i}\) is the psychological activity component for date \(i\);  
\(noSteps_{i}\) is the number of steps for date \(i\);  
\(distanceM_{i}\) is the distance in meters for date \(i\);  
\(intensActDistance_{i}\) is the intense activity distance in meters for date \(i\);  
\(burnCalories_{i}\) is the number of burned calories for date \(i\). The _SQC_ evaluates the quality of sleep relative to shallow sleep and number of wake times (Equation (3)):  
\[SQC_{i}=0.25\times\left(\frac{deepSleep_{i}}{wakeTime_{i}\times shallowSleep_ {i}}\right) \tag{3}\]  
where  
\(SQC_{i}\) is the sleep quality component for date \(i\);  
\(deepSleep_{i}\) is the number of minutes associated with deep sleep for date \(i\);  
\(shallowSleep_{i}\) is the number of minutes associated with shallow sleep for date \(i\);  
\(wakeTime_{i}\) is stress reflected in sleep by analyzing the number of wake-up times for date \(i\). The _SC_ binary based on the stressIdentified parameter, where 1 indicates high stress and 0 is low stress, is computed using Equation (4):  
\[SC_{i}=0.25\times stressIdentified_{i} \tag{4}\]  
where  
\(SC_{i}\) is the stress component for date \(i\);  
\(stressIdentified_{i}\) is stress identified in working hours, computed with Equation (5), for entry \(i\):  
\[stressIdentified_{i}=\left\{ \begin{aligned} & 0,maxRate_{i}\in not\ working\ hours\\ & 1,maxRate_{i}\in working\ hours\end{aligned} \right. \tag{5}\]  
where  
1 indicates that maximum heart rate occurs during working hours, on working days, indicating a potential stress situation;  
0 indicates that maximum heart rate does not occur during the working period, suggesting a potential stress situation outside of working days, which does not concern the employer. The _WBI_ is computed using Equation (6) as the sum of the four indicators, rounded to the nearest integer:  
\[WBI_{i}=ROUND(HRC_{i}+PAC_{i}+SQC_{i}+SC_{i}) \tag{6}\]  
The _WBI_ produces values ranging from 1 to 10, where 1 represents the lowest possible level of well-being. Ideally, this state should never be reached, and 10 signifies excellent physical and mental well-being. The _WBI_ for each of the 605 entries is calculated using Equation (6) and integrated into a classification model. The parameters (_HRC_, _PAC_, _SQC_, and _SC_) and their weights were selected based on their relevance to holistic health and well-being in prior physiological and psychological health metrics studies. Weights were applied uniformly in the experiments, allowing each component to contribute equally to the _WBI_. This approach reflects our hypothesis that, for an employee _WBI_, each of these factors holds approximately equal importance in daily assessments. By balancing these components equally, the _WBI_ calculation ensures that each metric contributes proportionally to the well-being assessment, reflecting physical and mental health equally.