## 4 Data Preparation and Statistics  
In this study, we used the dataset taken from [[https://cml.ics.uci.edu/](https://cml.ics.uci.edu/)]([https://cml.ics.uci.edu/](https://cml.ics.uci.edu/)), based on research by [PERSON] and [PERSON] [32]. Eight input parameters, including relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area, and glazing area distribution of a residential building, (named as X1, X2,..., X8, respectively) and two response parameters, including heating load (HL) and cooling load (CL) (named as Y1 and Y2, respectively) of the proposed building construct the mentioned dataset. Figure 4 shows a graphical description from data preparation procedure. Considering twelve different buildings, four glazing areas, five distribution scenarios, and four orientations, 768 buildings were modelled and analyzed by using Ecotect computer software [43]. The basic assumptions and the characteristics of the considered building are well described in Reference [32]. Additionally, Table 1 denotes the results of the statistical analysis of both independent and dependent variables. To better understand the issue, the relationship between the inputs and output variables is demonstrated in this section. To do so, the 3D distribution of each independent parameter (i.e., input variables) against both response variables is depicted in Figure 5. In this regard, each diagram shows the X1, X2,..., X8 on the x-axis, versus Y1 and Y2 on the y and z axes. Figure 3: Taking possession of the weakest colony during the imperialistic competition (after Reference [42]). Figure 4: Graphical view of data preparation. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multirow{2}{*}{**No. of Possible**} & \multirow{2}{*}{**Label**} & \multicolumn{8}{c}{**Descriptive Index**} \\  & & & \multicolumn{1}{c}{**Mean**} & \multicolumn{1}{c}{**Standard**} & \multicolumn{1}{c}{**Median**} & \multicolumn{1}{c}{**Mode**} & \multicolumn{1}{c}{**Standard**} & \multicolumn{1}{c}{**Sample**} & \multicolumn{1}{c}{**Skewness**} & \multicolumn{1}{c}{**Minimum**} & \multicolumn{1}{c}{**Maximum**} & \multicolumn{1}{c}{**Count**} \\  & & & & & & & & & & & & & & \\ \hline Relative & & & & & & & & & & & & & & \\ Compactness & 12 & X1 & 0.76 & 0.00 & 0.75 & 0.98 & 0.11 & 0.01 & 0.50 & 0.62 & 0.98 & 768 \\ Surface Area & 12 & X2 & 671.71 & 3.18 & 673.75 & 514.50 & 88.09 & 7759.16 & \(-\)0.13 & 514.50 & 808.50 & 768 \\ Wall Area & 7 & X3 & 318.50 & 1.57 & 318.50 & 294.00 & 43.63 & 1903.27 & 0.53 & 245.00 & 416.50 & 768 \\ Roof Area & 4 & X4 & 176.60 & 1.63 & 183.75 & 220.50 & 45.17 & 2039.96 & \(-\)0.16 & 110.25 & 220.50 & 768 \\ Overall Height & 2 & X5 & 5.25 & 0.06 & 5.25 & 7.00 & 1.75 & 3.07 & 0.00 & 3.50 & 7.00 & 768 \\ Orientation & 4 & X6 & 3.50 & 0.04 & 3.50 & 2.00 & 1.12 & 1.25 & 0.00 & 2.00 & 5.00 & 768 \\ Gazing Area & 4 & X7 & 0.23 & 0.00 & 0.25 & 0.10 & 0.13 & 0.02 & \(-\)0.06 & 0.00 & 0.40 & 768 \\ Gazing Area & 6 & X8 & 2.81 & 0.06 & 3.00 & 1.00 & 1.55 & 2.41 & \(-\)0.09 & 0.00 & 5.00 & 768 \\ Heating load & 586 & Y1 & 22.31 & 0.36 & 18.95 & 15.16 & 10.09 & 101.81 & 0.36 & 6.01 & 43.10 & 768 \\ Cooling load & 636 & Y2 & 24.59 & 0.34 & 22.08 & 21.33 & 9.51 & 90.50 & 0.40 & 10.90 & 48.03 & 768 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistical analysis of energy-efficient design on ten features of the efficient building. Figure 5: _Cont._  
Moreover, the frequency of output data has been calculated and depicted in the form of histogram charts by using IBM SPSS software. These diagrams are available in Figure 6a,b. Furthermore, according to the Figure 6c, the high correlation between the values of Y1 and Y2 (R\({}^{2}\) = 0.9523) portends a meaningful accommodation between these two variables. It shows that HL is positively correlated with CL. In other words, the input samples that produce low/high values of HL, give low/high values of CL, too.