## Modeling and Analyzing the Energy Efficiency Using the Proposed Approach
### Modeling the Energy Efficiency in Each Cluster
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cluster** & **Row** & \multicolumn{2}{c}{**Rule**} & \multicolumn{2}{c}{**Result**} \\ **Label** & **Row** & \multicolumn{2}{c}{**(Energy Efficiency)**} & **Percentage** \\ \hline Low-consumption cluster & 1 & The home structure is a bungalow and uses economy 7 & & & \\  & & & electricity meters and has installed a boiler. & D & 80\% \\  & & & The home structure is mid-terrace and the built-year is & & \\  & & 2 & between 1950 and 1966, the floor area is less than 51 m\({}^{2}\) & F & 75\% \\  & & & and it uses economy 7 electricity meters. & & \\  & & & The home is in region 2 and the floor area is between 51 & & \\  & & 3 & m\({}^{2}\) and 100 m\({}^{2}\), the built-year is between 1950 and 1966 & D & 71.50\% \\  & & & and it uses economy 7 electricity meters. & & \\  & & 4 & The home structure is detached houses built before 1930. & G & 66.70\% \\  & & & Hornes built after 1996, having cavity walls, and whose & & \\  & & 5 & floor area is between 51 m\({}^{2}\) to 100 m\({}^{2}\) and which do not & A and B & 54.90\% \\  & & & use economy 7 electricity meters. & & \\ \hline Medium-consumption cluster & 6 & The home structure is detached and was built before 1930, does not have a cavity wall, and the floor area is & E & 100\% \\  & & & more than 151 m\({}^{2}\), it uses economy 7 electricity meters. & & \\  & & & The region is Wales, and the home structure is & & \\  & & 7 & semi-detached and built before 1930 and has a boiler & C & 100\% \\  & & & installed. & & \\ Medium-consumption cluster & 8 & The home structure is detached and built before 1930 and & & \\  & & & does not have a cavity wall, the floor area is more than & F & 80\% \\  & & 151 m\({}^{2}\) and it does not use economy 7 electricity meters. & & & \\  & & & The home structure is a flat built after 1996, does not & & \\  & & 9 & have a cavity wall and does not use economy 7 & A and B & 67.90\% \\  & & & electricity meters. & & \\  & & & The home structure is detached, semi-detached, & & \\  & & & mid-terrace, and end-terrace, built after 1996, does not & C & 65.70\% \\  & & & have a cavity wall and does not use economy 7 & & \\  & & & electricity meters. & & \\  & & & & & \\ High-consumption cluster & 13 & The home structure is a flat, built after 1996 and the floor area is between 51 m\({}^{2}\) and 100 m\({}^{2}\). & A and B & 100\% \\  & & & 14 & Houses built after 1996, and the structure is mid-terrace. & C & 81.40\% \\  & & & The home structure is detached and the region is 4, 5 and & & \\  & & & 9, it was built in 1983 01995, a boiler was installed in & C & 80\% \\  & & & 2010 and it does not use economy 7 electricity meters. & & \\  & & & The home structure is mid-terrace, it was built between & C & 78.80\% \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\  & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The corresponding rules of the C5.0 tree in each cluster separately. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Household Characteristic** & \multicolumn{4}{c}{**Energy Efficiency Group**} \\  & **A\_B** & **C** & **D** & **E** & **F** & **G** \\ \hline The small homes which have tariff 7 & 6.92\% & 40.34\% & 32.54\% & 13.51\% & 5.47\% & 1.50\% \\ \hline The small homes which do not have tariff 7 & 12.74\% & 51.23\% & 26.51\% & 6.73\% & 2.23\% & 0.68\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The percentages of homes located in different energy efficiency groups. * In Wales, houses which have a detached structure, are old (built before 1930) and which have installed boilers have an energy efficiency group C (rule 7). In the high-consumption cluster:
* The good performance of boiler installation in the residential houses of this cluster is evident. In the 12 th, 16 th and 17 th rules, the homes are not newly-built, but are located in the energy efficiency group C. The existence of a boiler in these houses, structured as mid-terrace and end-terrace, has diminished the role of the built-year.