## 4 Model Development
### Target (Energy Consumption) vs. Input Variable Correlations  
The purpose of the target vs. input variable correlations analysis was to investigate the correlation between the model output, which was the school energy consumption, and the model input variables. The analysis computed the strength relationship or \"correlation coefficient value\" between all the model inputs and the output (target). This analysis could have led to two conclusions. The first one was that there would be a correlation close to one, which indicates that a single target was correlated with a certain single input and/or there would be no relationship between a certain input and the target variable, as given by the value being close to zero. Table 9 indicates that the strongest correlation of 0.970322 was between the input variable of AC capacity in ton of refrigeration (TR) and the predicted energy consumption. This finding agrees with a previous finding revealed in [PERSON] and [PERSON] [13]. It is interesting to note that the age of the school building had a weak relationship with all other variables, including the model output \"energy consumption.\" This is a good indication that the schools were operating in good condition due to a good maintenance plan, even though the minimum age of the schools was 11 years, while the oldest school was 58 years, with a mean of 32.82 years.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Variables** & **Type** & \multicolumn{3}{c}{**Energy Consumption**} \\  & & & & & & & & & & \\ AC capacity (TR) & Linear & & & & & & & & \\ Total roof area (sqm) & Linear & & & & & & & & \\ Total built area—all floors (sqm) & Linear & & & & & & & & \\ City & Linear & & & & & & & & \\ Number of floors & Linear & & & & & & & & \\ Number of students & Linear & & & & & & & & \\ Number of classrooms & Linear & & & & & & & & \\ Total air-conditioned area (sqm) & Linear & & & & & & & & \\ Number of staff & Linear & & & & & & & & \\ Age of building & Linear & & & & & & & & \\ Type of school & Linear & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 9: Correlations of the model target vs. input variables.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline City & 1 & \(-\)0.3 & \(-\)0.27 & \(-\)0.25 & 0.11 & \(-\)0.37 & \(-\)0.24 & \(-\)0.057 & \(-\)0.3 & \(-\)0.31 & \(-\)0.35 \\ Number of floors & & 1 & 0.65 & 0.29 & \(-\)0.14 & 0.3 & 0.28 & 0.042 & 0.28 & 0.26 & 0.36 \\ Total built area—all Floors (sqm) & & & 1 & 0.86 & \(-\)0.066 & 0.38 & 0.37 & 0.1 & 0.36 & 0.37 & 0.43 \\ Total roof area (sqm) & & & & 1 & 0.018 & 0.34 & 0.28 & 0.065 & 0.3 & 0.31 & 0.58 \\ Type of school & & & & & 1 & 0.19 & \(-\)0.23 & 0.081 & 0.12 & 0.15 & \(-\)0.015 \\ Number of students & & & & & & & 1 & 0.7 & 0.086 & 0.88 & 0.9 & 0.3 \\ Number of staff & & & & & & & & & & & \\ Age of building & & & & & & & & & & & \\ Number of classrooms & & & & & & & & & & \\ Total air-conditioned area (sqm) & & & & & & & & & & & \\ AC capacity & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Model input variables correlation.  
Figure 4 shows the reliance of the predicted energy consumption with the input variables of the model. The figure also represents the concept of a \"Pareto chart,\" or what is called the 80/20 rule, where 80% of the problem or opportunity of improvement was due to 20% of the reasons. In this case, as can be seen in Figure 4, improving the existing AC system and retrofitting the existing roof could improve the energy consumption (55% opportunity of improvement). It should be noted that such an analysis could have been more representative if the architectural elements were included in the study, such as the walls, windows, and insulations. This can be done for private schools in Saudi Arabia because of the variation in the architectural design, construction material, and differences in AC and lighting systems.