## 3 Results
### Correlation Analysis
#### 3.2.2 Width, Depth, and Total Floor Area Ratio Correlation  
In Figure 5, the coefficient of determination (R\({}^{2}\)) between the building width and total floor area is 0.0018; it indicates that there is no significant linear relationship between the building width and total floor area. Furthermore, the correlation coefficient (\(r\)) between the building width and total floor area, as shown in Table 3, is \(-0.04\), reflecting a low negative correlation with no significant association. The primary reason for this weak correlation is that the design of townhouses typically starts with the building lot layout. The building width is mainly influenced by factors such as the economic conditions of the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & \(-\sigma\) & \(x\) & **+2\(\sigma\)** \\ \hline Width & 4.1 m & 4.86 m & 6.38 m \\ Depth & 7.67 m & 9.34 m & 12.68 m \\ Total floor area & 136.02 m\({}^{2}\) & 154.81 m\({}^{2}\) & 192.39 m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Building floor area, facade width, and depth range.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**r** & **Width** & **Depth** & \begin{tabular}{c} **The Total Area** \\ **of the Staircase** \\ \end{tabular} & \begin{tabular}{c} **Total Area of** \\ **Baths and Toilets** \\ \end{tabular} & \
\begin{tabular}{c} **Habitable Total** \\ **Area of the** \\ **Habitable Room** \\ \end{tabular} &
\begin{tabular}{c} **Total Floor** \\ **Area** \\ \end{tabular} \\ \hline Width & \(1.0\) & - & - & - & - & - \\ Depth & \(-0.51\) & \(1.0\) & - & - & - \\ The total area of the staircase & \(0.43\) & \(-0.26\) & \(1.0\) & - & - \\ Total area of baths and toilets & \(0.13\) & \(0.16\) & \(0.09\) & \(1.0\) & - \\ The total area of the the habitable room & \(-0.14\) & \(0.75\) & \(-0.43\) & \(0.14\) & \(1.0\) & - \\ Total floor area & \(-0.04\) & \(0.75\) & \(-0.26\) & \(0.39\) & \(0.96\) & \(1.0\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Correlation coefficients.  
era, regional land prices, and building lot conditions, resulting in a low correlation with the total floor area.  
Figure 5 demonstrates that the coefficient of R\({}^{2}\) for the correlation between the depth and total floor area is 0.5571, indicating a strong linear relationship. Additionally, Table 3 shows that the correlation coefficient (\(r\)) between the depth and total floor area is 0.75, representing a high positive correlation. This implies that the total floor area of townhouses increases with the depth. This phenomenon may be attributed to the depth of townhouses is influenced by the width, plot area, and building coverage ratio. With a minimum acceptable width of 4.0 for townhouses, further reduction is not feasible. Consequently, in cases where the depth of the plot is extensive and nearing saturation to optimize the coverage ratio, the increased plot depth results in a larger ground floor area, which subsequently increases the total floor area. Furthermore, the preference of Taiwanese residents for townhouses with a greater depth further strengthens the positive correlation between the depth and total floor area in such buildings.  
The relationship between the building width and depth, as shown in Figure 6, has a coefficient of R\({}^{2}\) of 0.2604, which is less than 0.5, indicating a weak linear relationship. Table 3 displays the correlation coefficient (\(r\)) between the width and depth as \(-0.51\), suggesting a moderate negative correlation. This implies that the depth of a townhouse decreases as the width increases. The reason for this trend is that townhouses, typically three to four floors in Taiwan, have their width and depth determined by factors such as layout plans, site conditions, and construction costs. Each floor has a specific range of area, so when the width increases, the depth is usually reduced to keep the total floor area within a controlled range.  
Figure 5: Correlation between building width, depth, and total floor area.  
Figure 6: Correlation between building width and depth.