# An Octahedric Regression Model of Energy Efficiency on Residential Buildings
## 4 Discussion  
The proposed methodology has been compared with other machine learning methods applied to the estimation of energy loads in building from dataset in reference [8]. In the heating load problem, the results for the complete datasets are discrete, in the complete and reduced variables cases. For the separated study of building depending on its floors, the result for one floor is between the median value for the different ML techniques (see Table 4). However, the results for the two floors buildings are again discrete. The results are, in general better for MAPE than for MAE indicators. In the case of the cooling load problem, the results are lightly worse, something that also happens in most of the ML methods presented in Table 4. However, this worsening is relatively minor, obtaining in general results in order with the median of the techniques. Figure 18: Results of the cooling load reduced problem for the full and restricted models with the parameter selection \(h=\omega=0.02\). (**a**) Estimated vs experimental values for 1_floor model with five variables; (**b**) REC curve for the full, restricted and null (mean) 1_floor model; (**c**) Estimated vs experimental values for 2_floors model; (**d**) REC curve for the full, restricted, and null (mean) 2_floors model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **All Variables** & **Reduced Variables** & **1\_floor** & **2\_floors** \\ \hline Number Points & 768 & 768 & 384 & 384 \\ MAE & 1.113 (2.175) & 1.538 (2.892) & 0.603 (1.206) & 1.210 (2.419) \\ MSE & 2.731 (10.453) & 4.774 (16.859) & 0.688 (2.748) & 3.109 (12.426) \\ MAPE & 4.554\% (8.885\%) & 6.058\% (11.360\%) & 3.646\% (7.289\%) & 3.661\% (7.320\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Quality parameters for the mixed and restricted models of the cooling load problem. The effect of the additional variables on the results can be seen on Tables 7 and 8, where the quality parameters are better in all the categories for the complete against the reduced models. Using variables correlated between them can deteriorate the performance of ML methods and detecting and treating the associated overfitting is a difficult problem. The proposed methodology shows a relative stability front the effect of these spurious predictors. Also, an interesting characteristic of the method is the capability of estimating the overfitting at cheap computational cost through the full and restricted models. A compromise between both values is taken as the output of the predictive process. However, more in-depth research must be done in order to adequately evaluate the behaviour and fitness of the octahedric regression technique. For example, the characteristics of the computational algorithm make it an ideal candidate for the use of parallel computing versions. Measurements of the speedups obtained using some benchmarking datasets will be one of the future developments. Another promising characteristic of the methodology is that it is derived of the geometrical properties of the octahedral. The spatial distributions of the symmetry axes allow studying the effect of different orientations on the partial calculation of the estimation. The way this property can be implemented to select the principal components of the dataset is another field of research. With respect to the problem of energy efficiency of buildings, two main lines of study open from this paper. First, the existence of different models far from the considered number of floors could be deduced from the behaviour of the error in Figures 5 and 13. The origin and causes of this different behaviour should be studied in more depth. Related with this problem, the second aspect to consider is the existence of additional variables not related with those in Table 5 that could affect the way the software Ecotect calculates the heating and cooling loads and is not considered in the present study.