## 4 Results and Discussions
### Transfer Function Impact  
The transfer function is a singular monotonically increasing and differentiable function used for translating the input data signals to produce the final output signals of a neuron. The transfer function is fundamental to the concrete concept of neural networks mainly for three key reasons. Firstly, without activation functions, the entire organization of the neural network will be similar to an ordinary linear function that cannot learn non-linear relationships. Secondly, transfer function styles face the main computation accomplished by neural networks. Thirdly, transfer functions possess the proclivity to boost the learning rate and formation patterns in datasets. Thus, the choice of the right transfer (activation) function also positively influences the performance of the NN training algorithm. Table 4 presents the list of sigmoid transfer functions employed in this study to ascertain the stability of the proposed neural network model. The performance of sigmoid transfer functions in terms of MAE, MSE, RMSE, R and STD are also displayed in Table 4. The standard deviation (STD) statistics with one, two and three layers of training are given in Figure 7, and the Root Mean Error performance statistics with one, two and three layers of training are shown in Figure 8.  
Figure 5: Overall Performance Error Statistics with MAE, STD and RMSE.  
Figure 6: Overall Performance Error Statistics with R (%) and COE (%).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Testing**} & \multicolumn{2}{c}{**Overall Performance**} & \\ \hline
**Transfer Function** & **MSE** & **R** & **MSE** & **R** & **MAE** & **STD** & **RMSE** & **R** \\ \hline purelin & 19.74 & 0.8614 & 18.29 & 0.8692 & 3.36 & 2.65 & 4.28 & 0.8636 \\ tansig & 6.82 & 0.9366 & 26.07 & 0.7865 & 2.19 & 2.45 & 3.29 & 0.9073 \\ logsig & 4.62 & 0.9594 & 23.09 & 0.7812 & 2.15 & 2.30 & 3.15 & 0.9106 \\ purelin-purelin & 20.33 & 0.8715 & 13.09 & 0.8964 & 3.59 & 2.75 & 4.52 & 0.8637 \\ purelin-tagsig & 7.83 & 0.9325 & 12.20 & 0.8539 & 2.38 & 1.80 & 2.99 & 0.9173 \\ purelin-logsig & 9.18 & 0.9173 & 20.24 & 0.8755 & 2.52 & 2.02 & 3.24 & 0.9026 \\ tansig-tansig & 3.18 & 0.9697 & 20.17 & 0.8643 & 1.82 & 1.89 & 2.63 & 0.9365 \\ tansig-logsig & 3.23 & 0.9697 & 23.65 & 0.8094 & 1.82 & 2.18 & 2.84 & 0.9266 \\ tansig-purelin & 6.39 & 0.7622 & 10.28 & 0.6907 & 2.04 & 1.82 & 2.73 & 0.9315 \\ logsig-logsig & 4.82 & 0.9511 & 10.31 & 0.9382 & 1.76 & 1.63 & 2.40 & 0.9290 \\ logsig-tansig & 3.97 & 0.9669 & 12.96 & 0.8467 & 1.60 & 1.70 & 2.34 & 0.9499 \\ logsig-pureline & 6.01 & 0.9430 & 16.45 & 0.8471 & 2.18 & 1.91 & 2.90 & 0.9222 \\ purelin-purelin & 13.07 & 0.8804 & 18.34 & 0.8413 & 2.93 & 2.39 & 3.78 & 0.8637 \\ purelin-tangsig-tangsig & 5.87 & 0.9487 & 8.89 & 0.9181 & 1.88 & 1.78 & 2.59 & 0.9283 \\ tansig-tansig-purelin & 6.38 & 0.9337 & 17.89 & 0.8607 & 2.17 & 2.06 & 2.76 & 0.9200 \\ tansig-tansig-tossig & 5.11 & 0.9568 & 8.98 & 0.8907 & 1.92 & 1.93 & 2.72 & 0.9318 \\ logsig-logsig-logsig & 7.18 & 0.9358 & 13.86 & 0.9187 & 2.15 & 1.85 & 2.83 & 0.9285 \\ logsig-logsig-purelin & 9.12 & 0.9238 & 98.48 & 0.6384 & 2.91 & 4.03 & 4.97 & 0.8049 \\ logsig-tansig-tansig & 5.34 & 0.9489 & 7.52 & 0.9429 & 2.18 & 1.92 & 2.90 & 0.9245 \\ logsig-tansig-logsig & 6.90 & 0.9428 & 3.97 & 0.9467 & 1.98 & 1.75 & 2.67 & 0.9340 \\ tansig-logsig-tansig & 6.53 & 0.9433 & 3.68 & 0.9468 & 1.97 & 1.56 & 2.47 & 0.9445 \\ logsic-tansig-purelin & 6.92 & 0.9392 & 11.34 & 0.9093 & 2.09 & 2.02 & 2.90 & 0.9222 \\ purelin-logsig-tansig & 25.57 & 0.8583 & 25.94 & 0.8707 & 3.28 & 3.58 & 4.86 & 0.8597 \\ \hline \end{tabular}
\end{table}
Table 4: Transfer Functions used for network training/testing and their performance.  
Figure 7: Standard deviation (STD) statistics with one, two and three layers of training.