# Sustainable Building Tool by Energy Baseline: Case Study
## 2 Methodology
### Statistical Models  
Statistical regression methodologies have recurrently served as instrumental tools for the extrapolation of trend data and the prognostication of forthcoming performance. In the realm of estimating energy baseline (EnBL) and prognosticating energy consumption within architectural domains, the preponderance lies in the deployment of linear regression models. Eminent scholars, including [PERSON] and [PERSON] [31], [PERSON] and [PERSON] [32], [PERSON] and [PERSON] [33], [PERSON] and [PERSON] [34], and [PERSON] et al. [35], among others [36; 37; 38; 39; 40], have significantly advanced this line of inquiry. Nevertheless, a cohort of researchers, as exemplified by [PERSON] et al. [41], diverge in their approach, opting for the utilization of nonlinear regression models. Numerous investigations have been conducted to approximate the energy baseline (EnBL), employing both univariate and multivariate regression models. Rigorous examinations of these models have been undertaken to ensure compliance with a battery of statistical assumptions requisite for the validation of the regression framework. [PERSON] [42] adeptly utilized this methodology to prognosticate energy consumption levels within the United Kingdom, leveraging it as a strategic instrument in the formulation of energy policies. [PERSON] et al. [43], in a parallel vein, harnessed the baseline model to foresee Japan's energy requisites for the year 2030, meticulously incorporating climatic variables and socio-economic facets of the nation. The outcome of their investigation illuminated an upward trajectory in the building sector's energy consumption juxtaposed with a concomitant downturn in industrial usage. [PERSON] et al. [44], [PERSON] et al. [45], and [PERSON] et al. [46] assert that the construction of an EnBL serves as a pivotal precursor to comprehending the energy demands of urban landscapes benefit of benchmarks for building energy consumption. This lacuna in knowledge complicates decision-making concerning building stock management, given the absence of knowledge pertaining to both extant and achievable energy performance. [PERSON] et al. [47], in a noteworthy observation, contend that extant models for predicting EnBLs in buildings frequently neglect occupancy as a variable, which is an oversight considered to be pivotal in antecedent research [48]. Regression methodologies, as applied in this context, scrutinize the formulation of models elucidating the interdependence between a dependent variable (\(\gamma\)) and explanatory variables (\(X\)). These models typically adopt either univariate or multivariate configurations. The univariate instantiation is explicated by Equation (4). \[Y=\beta_{0}+\beta_{1}X_{1} \tag{3}\]  
The multivariable model is defined by Equation (4). \[Y=\beta_{0}+\beta_{1}X_{1}+\beta_{2}X_{2}+\cdots+\beta_{n}X_{n} \tag{4}\]  
Typically, the assessment of regression models hinges upon the proportion of variance in the dependent variable that can be explained by the independent variables. This elucidation is encapsulated by the coefficient of determination, denoted as R\({}^{2}\), which is a metric ranging from 0% to 100%. Consequently, an elevated R\({}^{2}\) value signifies the heightened accuracy of the model in accordance with the available data. Nevertheless, the mere attainment of a lofty R\({}^{2}\) value within a regression model does not unequivocally ensure optimal predictive efficacy. It is imperative, therefore, to adhere to a suite of statistical assumptions to substantiate the validity of the model. The necessary statistical assumptions that regression models are required to satisfy Linearity, Normality, Homoscedasticity, Independence, and Multicollinearity (Only for the multi-variable model) [49; 50; 51; 52]. Table 2 shows the statistical assumptions that regression models must fulfill. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **Definition** & **Validation** \\ \hline \multirow{3}{*}{Linearity} & \multirow{3}{*}{The relation between the variables is linear.}