# Artificial Neural Network Model to Predict Final Construction Contract Duration
## 5 Results and Discussions  
Figure 6a,b shows the distribution frequency of the APE for the first and second analyses, respectively. Although the data for APE greater than 35% were deleted in the first analysis, there were some data for APE greater than 35% in the second analysis. In addition, the positive promotes data not only on essential data with high error (APE > 35%) but also on data with low error, as shown in Figure 6b. The trend of APE's frequency decreased with the APE value increase in the second analysis. In the first analysis, some data had a greater difference between the observed and computed _FCCD_ than the observed _FCCD_, as shown in Figure 6a. This difference means that the data may contain a significant number of abnormal data. Figure 5 shows the MAPE of the ten ANN models for the first and second analyses. The MAPE ranged from 27.5% to 32% for the first analysis. On the other hand, it ranged from 9.68% to 15.84% for the ANN models in the second analysis. The percentage removing data that had a significant difference between observed and computed _FCCD_ (APE > 35%) was significant, with minimum and maximum values of 28% and 42%, respectively, as shown in Figure 7. Although the removing data percentage was high, the MAPE value decreased from 29.9% for the first analysis to 12.22% for the second analysis on average, which was close to the MAPE of the high accuracy models (MAPE \(\leq\) 10%), as illustrated by [25; 32; 38]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**NO**} & \multicolumn{5}{c}{**Input**} & \multicolumn{2}{c}{**Output**} \\ \cline{2-7}  & \(\overline{\text{CC}}\) & \(\overline{\text{CD}}\) & **Public** & **Semi-Public** & **Private** & \(\overline{\text{FCCD}}\) \\ \hline
1 & 20.66 & 13.01 & 0 & 1 & 0 & 14.90 \\
2 & 33.08 & 0.05 & 0 & 1 & 0 & 0.04 \\
3 & 20.20 & 12.68 & 0 & 1 & 0 & 10.86 \\
4 & 27.01 & 14.46 & 0 & 1 & 0 & 17.03 \\
5 & 35.23 & 15.22 & 0 & 1 & 0 & 13.85 \\
6 & 22.57 & 14.77 & 0 & 1 & 0 & 15.72 \\
7 & 21.58 & 16.81 & 0 & 1 & 0 & 17.60 \\
8 & 32.86 & 15.92 & 0 & 1 & 0 & 15.82 \\
9 & 34.51 & 14.39 & 0 & 1 & 0 & 17.46 \\
10 & 29.65 & 14.95 & 0 & 1 & 0 & 15.77 \\
11 & 24.43 & 14.77 & 0 & 1 & 0 & 15.04 \\
12 & 30.00 & 14.95 & 0 & 1 & 0 & 16.25 \\.. &. &. &. &. &. \\.. &. &. &. &. &. \\
122 & 33.68 & 16.38 & 1 & 0 & 0 & 16.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Illustrative example of input and output data used in ANN model 2. Figure 6: Frequency of APE of the first and second analysis for ten ANN models. **(a)** for first analysis (**b**) for second analysis. Figure 7: MAPE of the ten ANN models for the first and second analysis and the removing percentage. Figure 8 shows the accumulative frequency of the APE; the data that had APE less than 10% varies from 48% to 65% among the ten ANN models. Moreover, the percentage of data that had APE less than 20% ranged from 75% to 81%. The difference ranges of the accumulative frequency decreased with increasing APE. The MAPE results of the ten models for testing data are shown in Figure 9. The MAPE value ranges from 3.47% (ANN-8) to 26.91% (ANN-3). The average MAPE of the ten models was 14.92%, less than the allowable standard value of 20% [27]. The MAPE of the three types of linear regression models (LR1, LR2, and LR3) was compared with the average MAPE of the ANN models in the first and second analyses. The LR1 represents linear regression performed on the 135 data sets without any transformed functions. LR2 and LR3 are linear regressions on the 135 data sets transformed by the square root and logarithmic function, respectively. The equations for LR1, LR2, and LR3 are shown in Table 3. The results indicate that the LR1 prov  
Figure 8: Accumulative frequencies versus APE of the ten ANN models of the second analysis. Figure 9: MAPE of ANN models for test data. 143%, which indicates a low-accuracy model. On the other hand, the LR2 and LR3 models gave MAPEs of 43.6% and 39.23%, respectively, as shown in Figure 10. The results agreed with the results of [23,39].