## 3 Results
### Correlation Analysis
#### 3.2.3 Relationship between Interior Space Area and Total Floor Area in Buildings  
Figure 7 shows the average floor area if each floor were divided into the first floor as 48.70 M\({}^{2}\), the second floor as 46.10 M\({}^{2}\), the third floor as 45.36 M\({}^{2}\), the fourth floor as 41.63 M\({}^{2}\), and the roof floor 21.63 M\({}^{2}\). Floor area gradually decreases as floors increase. The overall average proportions of space in the building are as follows: bathrooms account for 8.7%, stains for 13.1%, and habitable rooms for only 78.2%. The average proportion of bathroom space is highest on the third floor at 13.5% and lowest on the first floor at 6.4%. The average proportion of stair space is highest on the fourth floor at 14.4% and lowest on the first floor at 8.2%. The average proportion of habitable room space is highest on the first floor at 85.3% and lowest on the fourth floor at 72.7%. Figure 7 also shows that the average proportion of bathroom space on the first floor is 6.4%, and the average proportion of stair space is 8.2%, both of which are the lowest among all floors. Consequently, the first floor has the highest proportion of habitable room space at 85.3%. This is because the first floor of a terraced house typically serves as the starting point for the stairs, resulting in a smaller stair area. This floor is often designed for vehicle parking with limited living space, and the bathrooms usually have no shower facilities, which contributes to a larger habitable room area. The fourth floor has the highest proportions of stair and bathroom space at 14.4% and 13.5%, respectively. Therefore, the average proportion of habitable room space on this floor is only 72.7%, the lowest among all floors. This is primarily because the total floor area of the fourth floor is reduced rather than an increase in the stair and bathroom areas. As shown in Figure 8, the coefficient of determination (R\({}^{2}\)) between the total stair area and the total floor area is 0.0666, which is greater than 0.5, indicating a weak linear relationship. Additionally, Table 3 shows a correlation coefficient (\(r\)) of \(-0.26\) between the total stair area and the total floor area, demonstrating a low negative correlation. This implies that as the total floor area of the building increases, the stair area does not increase correspondingly but tends to decrease. The area of the stairs is determined by the number of steps, tread depth, stair width, and landing area. The number of steps is decided by the floor height. In typical townhouses, the floor height of the living and dining room level is generally higher than that of other floors, ranging from 3.4 to 3.6 m, while other floors are around 3.0 to 3.2 m. Consequently, the number of steps varies between 15 and 23 steps. The  
Figure 7: Proportion of main space and average floor area. tread depth and stair width are regulated by building codes, with little variation beyond the minimum requirements. The landing area is crucial in determining the type and size of the stairs. Therefore, the stair area does not increase with the total floor area but is determined by the stair design. When the building's total floor area increases due to wider or deeper plots, ample space may allow for staircases without intermediate landings or changes in stair design, directly connecting different floors and reducing the proportion of the stair area. Hence, as the total floor area increases, the proportion of the stair area decreases. As shown in Figure 8, the coefficient of determination (R\({}^{2}\)) between the total habitable room area and the total floor area is 0.9162, which is greater than 0.5. Additionally, Table 3 shows a correlation coefficient (\(r\)) of 0.96 between the total habitable room area and the total floor area, indicating a strong positive linear relationship between the two variables. This means that the total habitable room area increases with the total floor area.