## 5 Results and Analysis
### Correlation Analyses
#### 5.4.2 Biweekly Correlation Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable 1** & **Variable 2** & **Correlation Value** \\ \hline Oxford Knee Score—Q5 & motion-max & 0.81 \\ \hline Oxford Knee Score—Q11 & hr-average & 0.78 \\ \hline Oxford Knee Score—Q10 & distance travelled from home & 0.67 \\ \hline Oxford Knee Score—Q10 & 12-mean & 0.67 \\ \hline Oxford Knee Score & hr-average & 0.67 \\ \hline Oxford Knee Score—Q10 & motion-sum & 0.63 \\ \hline Oxford Knee Score—Q10 & 12-peaks & 0.63 \\ \hline Oxford Knee Score—Q9 & hr-max & 0.62 \\ \hline Oxford Knee Score—Q7 & heart rate-mean & 0.62 \\ \hline Oxford Knee Score & motion-max & 0.60 \\ \hline Oxford Knee Score—Q10 & acceleration-sum & 0.59 \\ \hline Oxford Knee Score—Q10 & step-ratio & 0.59 \\ \hline Oxford Knee Score—Q12 & step-sum & 0.53 \\ \hline Oxford Knee Score—Q11 & step-max & 0.52 \\ \hline Oxford Knee Score—Q10 & durationtosleep & 0.51 \\ \hline Oxford Knee Score & durationtowakeup & 0.51 \\ \hline Oxford Knee Score & motion-ratio & \(-0.54\) \\ \hline Oxford Knee Score—Q11 & motion-ratio & \(-0.61\) \\ \hline Oxford Knee Score—Q7 & motion-ratio & \(-0.71\) \\ \hline \hline \end{tabular} The different items/questions in the Oxford Knee Score are illustrated in Appendix A in this paper.  
\end{table} 
Table 13: Biveekly strong correlations between Oxford Knee Score and sensor data for 8 participants. Figure 4: Scatter plot of bi-weekly strong correlation between (**a**) SIS (Belonging) and total step count, (**b**) SIS (Belonging) and wake up count during sleep, (**c**) SIS (Belonging) and distance traveled from home. The analysis reveals a strong biweekly correlation between Oxford Knee Score and the sensor data. Specifically, Table 13 indicates that items 10 and 11 on the Oxford Knee Score have the strongest correlations with the sensor data (7 and 4, respectively). Question 10 (\"Have you felt your knee might suddenly give away or let you down?\") from this questionnaire has a strong positive correlation of 0.67 with distance traveled from home and \(l2\)-mean. This relationship demonstrates that the higher the score on question 10 (lower physical health), the farther the participants traveled from home and the higher their magnitude of acceleration during the day. However, the destination/sites the participants visited were not recorded; therefore, we were unable to determine the cause of the relationship between lower physical health and the distance traveled. Question 11 on this questionnaire refers to the participant's ability to do household shopping on their own  
Figure 5: Scatter plot of bi-weekly strong correlation between (**a**) question 11 on Oxford Hip Score and average heart rate during sleep, (**b**) question 11 on Oxford Hip Score and average heart rate during the day, (**c**) question 11 on Oxford Hip Score and maximum heart rate during sleep. (bpm = beats per minute). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable 1** & **Variable 2** & **Correlation Value** \\ \hline
30 s chair stand & hr-max & 0.55 \\ \hline TUG & step-sum & \(-\)0.50 \\ \hline
30 s chair stand & motion-ratio & \(-\)0.52 \\ \hline TUG & totalsleepduration & \(-\)0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Biweekly strong correlations between physical tests and sensor data for 8 participants. (similar to question 11 on the Oxford Hip Score) with respect to their knee, which also has a strong positive correlation with average heart rate during sleep, maximum step count, and the time it takes the participant to wake up (durationwaveup). Lastly, Table 14 displays the biweekly strong correlations between the physical tests and the sensor data. Strong negative correlations exist between TUG and total sleep duration and total step count. This finding shows that participants who take longer to complete the TUG, indicating poorer functional mobility, tend to have shorter sleep durations and lower step counts.