## 6 Relationship Among Variables in the Dataset  
To evaluate the relationships between continuous variables in the dataset, the cor() function was utilized in R. This function accepts input in the form of a matrix or data frame and outputs a correlation matrix. The computed correlations between all continuous variables are illustrated in Figure 8 and detailed in Table 10.  
Figure 8 and Table 10 together illustrate the interrelationships among key clinical and functional variables relevant to COPD. Figure 7 visually depicts the strength and direction of correlations using a matrix format, while Table 10 provides the exact Pearson correlation coefficients, enabling more precise interpretation. A key observation is the limited role of AGE and PackHistory, which show weak and mostly negative correlations with other variables. While both are tra \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **AGE** & **PackHistory** & **MWT1 Best** & **FEV1** & **FVC** & **SGRQ** \\ \hline AGE & \(1\) & \(-0.0079\) & \(-0.23\) & \(-0.096\) & \(-0.14\) & \(-0.13\) \\ \hline PackHistory & \(-0.0079\) & \(1\) & \(-0.25\) & \(-0.13\) & \(-0.088\) & \(0.036\) \\ \hline MWT1 Best & \(-0.23\) & \(-0.25\) & \(1\) & \(0.47\) & \(0.45\) & \(-0.53\) \\ \hline FEV1 & \(-0.096\) & \(-0.13\) & \(0.47\) & \(1\) & \(0.82\) & \(-0.31\) \\ \hline FVC & \(-0.14\) & \(-0.088\) & \(0.45\) & \(0.82\) & \(1\) & \(-0.23\) \\ \hline SGRQ & \(-0.13\) & \(0.036\) & \(-0.53\) & \(-0.31\) & \(-0.23\) & \(1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Correlation for the dataset. Figure 8: COPD factors correlation matrix. COPD, their weak linear associations with functional outcomes, like lung function (FEV1, FVC) and exercise tolerance (MWT1 Best), suggest that once the disease is established, these variables may not directly reflect the severity of current physiological impairment. In contrast, MWT1 Best, a measure of exercise capacity shows moderate positive correlations with FEV1 (r = 0.47) and FVC (r = 0.45). This finding supports the notion that patients with better-preserved lung function tend to have higher physical performance. More notably, MWT1 Best is moderately negatively correlated with SGRQ (r = \(-\)0.53), indicating that reduced symptom burden and better health-related quality of life are associated with greater functional capacity. This highlights MWT1 Best as a potentially integrative marker of overall disease impact, spanning both objective and subjective domains. FEV1 and FVC show a strong positive correlation (r = 0.82), consistent with their shared physiological basis as indicators of pulmonary function. This relationship is further visualized in Figure 9, where the linear association is evident. FEV1 also correlates positively with MWT1 Best and negatively with SGRQ (r = \(-\)0.31), suggesting that lung function is not only linked to physical capacity but also to patients' perceived health status. Interestingly, SGRQ is negatively correlated with all functional variables (FEV1, FVC, MWT1 Best), reinforcing its role as a subjective measure that captures the overall burden of disease as experienced by patients. Lower SGRQ scores (indicating better health status) are associated with better lung function and greater walking distance, emphasizing the interplay between objective and subjective disease dimensions. A closer examination of FEV1 reveals moderate positive associations with MWT1 Best and AGE, a weak negative correlation with PackHistory, and a strong positive correlation with FVC. This strong relationship is visualized in Figure 9, which depicts a scatter plot demonstrating the linear association between FEV1 and FVC. Establishing the correlation between FEV1 and FVC is particularly important, as FEV1, the forced expiratory volume in one second, is a critical measure of pulmonary function and is expected to be associated with FVC. These measures collectively reflect the volume of air a patient can forcefully exhale, making their interdependence clinically and statistically relevant.