# Machine Learning Models for Ecofriendly Optimum Design of Reinforced Concrete Columns
## 3 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **R\({}^{2}\)** & **NRMSE** & **NMAE** & **NMSE** \\ \hline Foundational & & & & \\ Linear Regression & 0.550 & 245.971 & 202.094 & 170,863.191 \\ Decision Tree Regressor & 0.996 & 29.915 & 16.465 & 2505.221 \\ Elastic Net & 0.546 & 243.435 & 204.567 & 166,992.364 \\ K Neighbors Regressor & 0.617 & 154.277 & 104.274 & 54,986.445 \\ SVR & 0.016 & 406.631 & 286.463 & 371,551.833 \\ Ensemble & & & & \\ Random Forest Regressor & 0.998 & 17.777 & 10.162 & 840.449 \\ Hist. Gradient Boosting Regressor & 0.997 & 20.212 & 12.456 & 1090.250 \\ Gradient Boosting Regressor & 0.995 & 33.965 & 22.829 & 3406.932 \\ Voting & & & & \\ Combinations & & & & \\ Triple combinations & & & & \\ hgbr,rfr,gbr & 0.998 & 19.921 & 12.868 & 1211.681 \\ hgbr,gbr,rfr & 0.998 & 20.408 & 13.191 & 1123.193 \\ rrf,hgbr,gbr & 0.998 & 20.565 & 13.153 & 1133.298 \\ rrf,gbr,hgbr & 0.998 & 19.952 & 12.862 & 1156.364 \\ gbr,hgbr,rfr & 0.998 & 20.170 & 13.120 & 1160.247 \\ gbr,rfr,hgbr & 0.998 & 19.849 & 13.196 & 1155.065 \\ Quad combinations & & & & \\ lm,dtr,knr,svr & 0.738 & 177.226 & 137.481 & 74,641.302 \\ lm,dtr,ent,knr & 0.790 & 148.851 & 120.047 & 59,889.432 \\ lm,svr,rfr,hgbr & 0.852 & 150.574 & 117.956 & 56,440.011 \\ lm,rfr,hgbr,gbr & 0.969 & 66.7835 & 53.160 & 12,304.705 \\ dtr,lm,hgbr,ent & 0.886 & 123.958 & 102.064 & 43,174.734 \\ dtr,rfr,hgbr,gbr & 0.998 & 19.608 & 12.668 & 1155.584 \\ ent,rfr,hgbr,gbr & 0.968 & 62.278 & 53.828 & 12,587.107 \\ knr,rfr,hgbr,gbr & 0.975 & 45.830 & 31.108 & 5089.051 \\ svr,lm,hgbr,rfr & 0.852 & 151.568 & 118.307 & 56,129.966 \\ svr,dtr,ent,gbr & 0.851 & 153.118 & 119.770 & 57,176.112 \\ lm,rfr,knr,ent & 0.790 & 149.798 & 120.438 & 60,492.775 \\ lm,ent,knr,svr & 0.786 & 232.016 & 184.786 & 135,143.241 \\ lm,knr,svr,rfr & 0.788 & 178.366 & 137.091 & 75,001.233 \\ knr,svr,lm,dtr & 0.785 & 179.431 & 137.158 & 75,382.651 \\ knr,svr,ent,hgbr & 0.787 & 177.944 & 137.468 & 74,679.626 \\ gbr,hgbr,rfr,ent & 0.969 & 66.271 & 53.565 & 12,658.159 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance results of the model. When the accuracy metrics of the regression algorithms were examined, it was shown that random forest regressor provided the best results, followed by decision tree. The R\({}^{2}\) value of random forest was 0.9984, the NRMSE value was 17.7774, the NMAE value was 10.1621, and the NMSE value was 840.4499. The closest result to these results was obtained with the decision tree. The R\({}^{2}\) value was 0.9984, the NRMSE value was 29.9151, the NMAE value was 16.4650, and the NMSE value was 2505.2210. The best accuracy was achieved with the random forest algorithm. The decision tree model follows the random forest model in terms of overall accuracy rate. Decision tree has the highest correlation coefficient determination coefficients (R\({}^{2}\)) and lowest NRMSE, NMAE, and NMSE values among foundational models. Among the different regression techniques, the worst result is obtained with the SVR model. In the results obtained with the support vector regressor, the result is 0.0168 for R\({}^{2}\). When the NRMSE value is examined, the highest error value also belonged to support vector regressor as 416.6314. In the next stage, we tested different base estimator combinations in voting and stacking algorithms. The highest R\({}^{2}\) in voting models was achieved with the triple combination of gradient boosting, histogram-based gradient boosting, and random forest. The lowest R\({}^{2}\) in voting was obtained from the quintet combination of linear model, decision tree, elastic net, K neighbors, and support vector. In stacking, R\({}^{2}\) was usually very high (more than 99%). The highest R\({}^{2}\) in stacking was achieved at octal combination of gradient boosting, histogram-based gradient boosting, random forest, elastic net, linear model, decision tree, K neighbors, and support vector has