## 3 Results
### Prediction of Usable Area in a Test Set for Linear, Non-Linear, and Regularised Models
The mean absolute error indicated an average deviation of 12.8 m\({}^{2}\), whereas the root mean squared error indicated an average deviation of 15.1 m\({}^{2}\). Furthermore, it was observed that half of the errors did not exceed 12 m\({}^{2}\), while the others did not exceed 28 m\({}^{2}\) (the maximum error recorded was 27.7 m\({}^{2}\)). As large errors occur in only 1-2% of cases on the learning set and in 1-2 cases on the test set, such a result can be provisionally accepted. In contrast, the best of the acquired non-linear models, model \(D_{N}\), described in detail in Section 3.2, despite the slightly worse characteristics obtained on the learning data, predicted the usable area in the test sample even better, with a mean absolute error of 12.1 m\({}^{2}\) and a root mean squared error of 14.09 m\({}^{2}\), with a maximum error of 23.8 m\({}^{2}\). These two models will be treated as baseline models for comparison in the following section. Both provided a benchmark of high requirements for subsequent methods. In the next step, the models were simulated with LASSO regularisation, then this scheme was repeated for ridge regression and elastic net. None of these models gave better \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Linear Models 1**} & \multicolumn{2}{c}{**ML and Neural Nets 2**} & \multicolumn{2}{c}{**Hybrid Models 2**} \\  & _Model C_ & _LASSO_ & _XGBoost eb_ & _NN6(10-6)eb_ & _C+ LASSO_ & _LASSO A180C_ & _NN6 A200C_ \\ \hline MAE & 20.95 & 20.43 & 15.94 & 10.81 & 16.65 & 16.95 & 9.99 \\ RMSE & 27.92 & 24.16 & 18.81 & 12.77 & 23.12 & 21.14 & 11.91 \\ \(\max[y-\hat{y}]\) & 55.34 & 39.55 & 30.73 & 20.73 & 47.45 & 39.55 & 20.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Quality of the estimation of the usable area in the test group (N = 5) of the existing buildings data—baseline linear models, best ML (XGBoost and NN) models, and selected hybrid models. Source: 1 [PERSON] et al. [1]: 2 own calculations. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Hybrid Models**} & \multicolumn{2}{c}{**NN5**} & \multicolumn{2}{c}{**NN5**} & \multicolumn{2}{c}{**NN5**} & \multicolumn{2}{c}{**NN6**} & \multicolumn{2}{c}{**NN6**} & \multicolumn{2}{c}{**XGB**} \\  & _A180D\({}_{N}\)_ & _A180D\({}_{N}\)_ & _A180D\({}_{N}\)_ & _90_ & _A180D\({}_{N}\)_ & _90 A180D\({}_{N}\)_ & _90 A180D\({}_{N}\)_ & _90 A180D\({}_{N}\)_ & _+NN6_ \\ \hline MAE & 11.69 & 10.11 & 9.58 & 10.88 & 10.60 & 9.26 & 8.73 & 8.87 \\ RMSE & 13.58 & 12.39 & 11.60 & 14.71 & 12.83 & 12.07 & 11.25 & 11.15 \\ \(\max[y-\hat{y}]\) & 23.06 & 27.73 & 23.06 & 34.95 & 23.06 & 27.73 & 23.06 & 23.06 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{Naming conventions: first part of the name: _LASSO_—the best LASSO model (presented in Table 6), _XGB_—the best XGBoost model, _NN5_—the best neural network with 5 inputs, _NN6_—the best neural network with 6 inputs (all presented in Table 7); subsequent parts of the name: 90—a model in which predictions lower than 90 are replaced by 90, _90D\({}_{N}\)_—a model in which predictions lower than 90 are replaced by predictions from model \(D_{N}\), _A180D\({}_{N}\)_—a model in which predictions for objects with _A\({}_{C}\)_ higher than 180 are replaced with predictions from model \(D/\)model \(D_{N}\), respectively; _XGB + NN6_—a model averaging the predictions from models _XGB A180D\({}_{N}\)_ and _NN6 90 A180D\({}_{N}\)_.  
\end{table} 
Table 8: Quality of the estimation of the usable area in the test group (N = 25) of the design data—selected hybrid models. Source: * [PERSON] et al. [1]: ** own calculation. results than models \(D\) and \(D_{N}\) for the test sample. Subsequently, models with LASSO regularisation were estimated, where the learning sample was reduced by 20 observations (indicated by the expert as potential outliers). The best model in this approach is denoted in Table 5 as LASSO+ Amin = 0.72.