## 3 Parametric Cost Estimation Model for Use in the Architectural Planning Stage
### Construction Cost Estimation Model  
To improve the accuracy of construction cost estimation in the pre-design phase, a parametric prediction model was developed in this study, rather than the commonly used method of cost calculation by unit area. Among the 907 construction project cases in the dataset, the data from 10 cases were utilized for verification, and the rest were employed to develop the cost prediction model. For validation, it was necessary to construct a cost prediction model using the existing method, use it as a control, and compare the evaluation metrics obtained from the control and proposed methods. The predictive performance of the model was evaluated based on the mean squared error (MSE) and mean absolute error (MAE) that are commonly employed for model evaluation, to construct the parametric model and conventional prediction model and to compare the performance between the two models.  
The following modeling process is commonly applied to construction cost estimation models for validation. First, using a box plot, data outside the range 1.5 times the interquartile range (IQR) are considered as outliers and removed. If some fields in the dataset have missing values, KNNImputer in the scikit-learn package is applied to replace the data to reflect the similarity between the data. In order for the linear model to reflect each field in the same unit, the StandardScaler module of the scikit-learn package is used to standardize  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Column Name** & **Cor.coef** & **Abs.cor.coef** \\ \hline
0 & floor\_area & 0.93396 & 0.93396 \\
1 & building\_area & 0.82752 & 0.82752 \\
2 & construction\_period & 0.56663 & 0.56663 \\
3 & number\_of\_parking & 0.54187 & 0.54187 \\
4 & max\_number\_of\_floors & 0.53205 & 0.53205 \\
5 & max\_height & 0.49949 & 0.49949 \\
6 & landscaping\_area & 0.47655 & 0.47655 \\
7 & type\_id & 0.46966 & 0.46966 \\
8 & max\_number\_of\_underground\_floors & 0.31536 & 0.31536 \\
9 & year & 0.30109 & 0.30109 \\
10 & site\_area & 0.27924 & 0.27924 \\
11 & base\_floor\_height & \(-\)0.12921 & 0.12921 \\ \hline \hline \end{tabular} Note. This table shows correlations between the 12 factors and dependent variable (total construction cost). Cor.coef. = correlation coefficient; Abs.cor.coef = absolute value of correlation coefficient.  
\end{table}
Table 4: Correlation coefficient for each factor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Column Name** & **Cor.coef** & **Abs.cor.coef** \\ \hline
1 & Type\_9 & 0.42858 & 0.42858 \\
2 & Type\_3 & \(-\)0.39388 & 0.39388 \\
3 & Type\_7 & 0.23916 & 0.23916 \\
4 & Type\_6 & \(-\)0.18417 & 0.18417 \\
5 & Type\_10 & 0.12561 & 0.12561 \\
6 & Type\_8 & 0.09533 & 0.09533 \\
7 & Type\_5 & \(-\)0.06559 & 0.06559 \\
8 & Type\_1 & \(-\)0.05243 & 0.05243 \\
9 & Type\_2 & \(-\)0.03731 & 0.03731 \\
10 & Type\_4 & \(-\)0.01295 & 0.01295 \\
11 & Type\_11 & 0.01065 & 0.01065 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Correlation coefficient for Building Type_ID.  
the mean to 0 and the variance to 1 to construct the two models. The overall process of modeling and validation can be summarized as shown in Figure 3.  
Figure 3: Cost prediction modeling process.