*5.2. Multiple Regression Analysis*

To develop a formula for predicting villa development, we conducted a multiple regression analysis with the changing rate of increase in the number of villas over 8 years as the object variable, and 26 criteria as explanatory variables (Table 7). We devised the regression formula through repeated parallel implementation of a stepwise selection method and a forward selection method.


**Table 7.** Related criteria for the multiple regression analysis.

The following formula was used to predict villa development according to the increase in the number of villas over 8 years:

Increase in the number of villas over 8 years = 27.724 − 0.02 × (Land price) + 1.296 × (ratio of lots with areas ranging between 300 and 400 m2)

> The coefficients were significant at the 0.01 level, and the Variance Inflation Factors (VIFs) among two criteria (the land price and ratio of lots with area ranging between 300 and 400 m2) all had values under 1.068, and thus satisfied the requirement of being under 10. The Durbin–Watson test yielded a value of 1.750, indicating the independence of the

criteria (Table 8). The adjusted *R*-squared value was 0.391, which explained 39.1% of the number of increased villas over 8 years (Table 8). The standardized coefficients of these two criteria were respectively −0.330 and 0.465, so that the ratio of lots with areas ranging between 300 and 400 m2 was evidently of greater significance than the land price (Table 9). These results indicate that, over the 8-year study period, villa development occurred mainly in lower-priced villa lots having areas ranging between 300 and 400 m2. Thus, the optimal area of the lot for villa development considering purchasing ability is between 300 and 400 m2.

**Table 8.** Summary of model for predicting the increase in the number of villas as an explanatory variable.


Note, Predictors: (constant), land price, ratio of lots having areas that range between 300 and 400 m2.

**Table 9.** Coefficients for the change rate of the number of villas as an explanatory variable.


The following formula was used to predict the net ratio of vacant lots:

Net ratio of vacant lots = 53.368 + 0.011 × (distance between mosque and park) − 0.015 × (total length of roads) + 0.517 × (ratio of lots with areas ranging between 1000 and 1400 m2)

> The coefficients were significant at the 0.01 level, and the VIFs for the three criteria (the distance between a mosque and a park, the total length of roads, and the ratio of lots having areas ranging between 1000 and 1400 m2) were all under 1.154, and thus satisfied the requirement of being under 10. The value obtained for the Durbin–Watson test was 1.821, indicating the independence of the criteria (Table 10). The adjusted *R*-squared value was 0.281. The standardized coefficient values for these three criteria were respectively 0.243, −0.288, and 0.269, revealing that the three criteria were almost equally significant. To reduce the ratio of vacant lots using the above predictive formula would require developing parks near mosques and not increasing the total length of roads. Moreover, the areas of villa lots ranging between 1000 and 1400 m2 would need to be reduced (Table 11).

**Table 10.** Summary of the model used to calculate the net ratio of vacant lots.


Predictors: (constant), distance between mosques and parks, total length of roads, and ratio of lots that range in area between 1000 and 1400 m2.


**Table 11.** Coefficients for the net ratio of vacant lots as an explanatory variable.
