## 5 Results and Analysis
### Correlation Analyses
#### 5.4.2 Biweekly Correlation Analysis  
To evaluate the correlation between the biweekly features from sensor data and clinical data, both need to be available in a biweekly format. Combining the biweekly features from the sensor data and the clinical data collected on a biweekly basis, we had a resulting csv file with 90 columns (53 features (5 position features, 5 motion features, 4 heart rate features, 11 sleep features, 5 step features, 23 acceleration features), 9 SIS measurement, 13 Oxford Hip Score, 13 Oxford Knee Score, and 2 physical tests features). Next, the correlation analysis is done following the same steps as listed in Section 5.4.1, for biweekly clinical and sensor features. The resulting biweekly correlation values after removing the redundancies are presented in this section. Table 11 lists the strong biweekly correlations between SI and sensor data. The results from this table show that SIS questions about sense of belonging (questions 4-6) have the most number of correlations with the biweekly sensor data. The strongest positive correlation is between the duration of sleep and the participant's perception of how much time they spend engaged in social activities (SIS, question 6). Notably, SIS questions about belonging have strong positive correlations with total step count, distance traveled from home, and several sleep metrics. This means that as the participant's SI level decreases (SIS belonging increases), their movement, activity outside their home, and sleep duration increase. This relationship can be observed in Figure 4. Moreover, there is a strong negative correlation between duration of sleep and the number of face-to-face interactions the participant has (SIS, question 1). This indicates that as the participant's in-person interactions increase, the amount of time it takes them to fall asleep decreases. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable 1** & **Variable 2** & **Correlation Value** \\ \hline
30 s chair stand & hr-average & 0.36 \\ \hline TUG & snoring & 0.35 \\ \hline TUG & motion-sum & 0.35 \\ \hline TUG & wakeupcount & \(-\)0.31 \\ \hline TUG & duration/tosleep & \(-\)0.31 \\ \hline TUG & lights/keep/duration & \(-\)0.33 \\ \hline TUG & step-sum & \(-\)0.36 \\ \hline
30 s chair stand & snoring & \(-\)0.38 \\ \hline
30 s chair stand & motion-ratio & \(-\)0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Daily moderate correlations between physical tests and sensor data for 8 participants. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable 1** & **Variable 2** & **Correlation Value** \\ \hline Oxford Knee Score—Q10 & step-ratio & 0.32 \\ \hline Oxford Knee Score—Q10 & _l2_-n-sign-changes & 0.32 \\ \hline Oxford Knee Score—Q7 & step-mean & 0.32 \\ \hline Oxford Knee Score—Q4 & wakeupcount & 0.30 \\ \hline Oxford Knee Score—Q3 & acceleration-sum & 0.30 \\ \hline Oxford Knee Score—Q8 & lights/keep/duration & 0.30 \\ \hline Oxford Knee Score—Q7 & motion-sum & \(-\)0.30 \\ \hline Oxford Knee Score—Q3 & _l2_-svd-entropy & \(-\)0.32 \\ \hline Oxford Knee Score—Q10 & snoring & \(-\)0.32 \\ \hline Oxford Knee Score—Q9 & motion-ratio & \(-\)0.38 \\ \hline Oxford Knee Score & motion-ratio & \(-\)0.44 \\ \hline Oxford Knee Score—Q7 & motion-ratio & \(-\)0.49 \\ \hline Oxford Knee Score—Q11 & motion-ratio & \(-\)0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._The results of strong correlations between Oxford Hip Score, Oxford Knee Score, and the two physical tests are displayed in Tables 12-14. Table 12 shows that question 11 (\"Can you do the household shopping on your own?\") on the Oxford Hip Score has several strong correlations with the sleep, motion, and heart rate features. Notably, the strong correlation of question 11 on the Oxford Hip Score with three heart rate metrics (average heart rate during sleep, average heart rate during the day, and maximum heart rate during sleep) can indicate an overall relationship between the activities of daily living and the heart rate of the participants.