## 3 Results
### Principal Component Analysis and K-Means Clustering  
The combination of PCA and K-means clustering is a practical approach for classifying ACU power consumption, facilitating both dimensionality reduction and effective pattern recognition. This enables the analysis of key variables--such as temperature, humidity, and occupancy--while preserving the relationships that drive power consumption. K-means clustering complements PCA by grouping similar data points into clusters, defined by their proximity in the reduced feature space. Theoretically, PCA ensures that \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predictor 1** & **Predictor 2** & **Correlation Coefficient** & **Basis of Selection** \\ \hline Indoor CO\({}_{2}\) Level & Indoor TVOC Level & 0.999325835 & Indoor CO\({}_{2}\): represents indoor occupancy. \\ Indoor Dry Bulb Temperature & Indoor Heat Index & 0.929435058 & None: Has correlation with Wet Bulb Temperature \\ Indoor Relative Humidity & Indoor Wet Bulb Temperature & 0.860634623 & None: Has correlation with Wet Bulb Temperature \\ Indoor Dry Bulb Temperature & Indoor Wet Bulb Temperature & 0.897239755 & None: Has correlation with Wet Bulb Temperature \\ Indoor Heat Index & Indoor Wet Bulb Temperature & 0.968497618 & Indoor Wet Bulb Temperature: Combined temperature and humidity to represent felt \\ Indoor Heat Index & Indoor Wet Bulb Temperature & 0.999325835 & Indoor Wet Bulb Temperature: Combined temperature and humidity to represent felt \\ Outdoor CO\({}_{2}\) Level & Outdoor TVOC Level & 0.999999291 & CO\({}_{2}\) Level: Represents ventilation quality \\ Outdoor Dry Bulb & Outdoor Heat Index & 0.922516068 & Outdoor Bulb Temperature: Combined temperature and humidity to represent felt \\ Temperature & Outdoor Heat Index & 0.922516068 & Combined temperature and humidity to represent felt \\ Indoor Relative Humidity & Differential Indoor and Outdoor Humidity & \(-\)0.833722982 & Outdoor Humidity: Represents both indoor and outdoor conditions \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Highly correlated predictors for office rooms. the most informative features are retained, while K-means clustering identifies distinct operational patterns, such as differences in power consumption during high versus low occupancy periods or extreme versus moderate outdoor conditions. This synergy is particularly valuable in HVAC applications, where segmentation of operational scenarios informs targeted strategies for energy optimization and comfort management. The feature selection process for determining ACU setpoint decisions focused on retaining predictors with strong correlations (\(R\geq 0.5\)) to ACU power consumption, as summarized in Table 10. This method ensured that the model prioritized impactful variables while discarding less significant features. Key predictors such as the outdoor heat index (OHI), relative humidity (RH), and dry bulb temperature (T) consistently showed high correlation values, underscoring their critical roles in power consumption. Conversely, features such as CO and CO\({}_{2}\) were excluded across most room types due to negligible correlations, thus simplifying the model without compromising performance. The TVOC feature covers a wide range of air pollutants (e.g., acetone, benzene, ethylbenzene, formaldehyde, and toluene) deriving from cleaning agents, laboratory chemicals, or electronic equipment present inside each room. The TVOC feature was significantly correlated with ACU power consumption in computer rooms only. In instructional rooms, RH emerged as the most influential predictor, displaying the highest correlation values in classrooms (R = 0.6954) and laboratory rooms (R = 0.6134). This highlights its importance in spaces with variable occupancy and activity levels, where humidity directly affects cooling needs. OHI demonstrated strong correlations in laboratories (R = 0.5724) and computer rooms (R = 0.5733), emphasizing the role of outdoor conditions in determining ACU load.