# Influence of Social Overhead Capital Facilities on Housing Prices Using Machine Learning
## 3 The Proposed Scheme
### Modeling Process
#### 3.3.1 Multicollinearity and Its Mitigation  
As we progress through the modeling process, it is imperative to ensure the validity and reliability of the model. One potential pitfall in multiple regression models that can compromise model reliability is the presence of multicollinearity. Multicollinearity is a phenomenon observed in multiple regression analysis when several independent variables are highly correlated with each other. In models burdened with high multicollinearity, deciphering the distinct influence of each independent variable becomes intricate, potentially leading to unreliable coefficient estimates [65,66]. Such scenarios can inflate the standard errors of the regression coefficients, rendering it very challenging to attain statistically significant results.  
To address the issue of multicollinearity in our analysis, we employed the Variance Inflation Factor (VIF). The VIF calculates the magnitude of multicollinearity among independent variables. Specifically, it sets each independent variable as the dependent variable and conducts a regression analysis against other variables, using the \(R^{2}\) value for its computation. Typically, a VIF value exceeding 10 indicates significant multicollinearity between the variable in question and others.  
Utilizing the statsmodels.api library in Python, VIF values for all independent variables were determined. The computed VIF values for the modeling input variables are depicted in Figure 4. However, after performing one-hot encoding (OHE) on the original 'HUS_TP' variable, we observed potential multicollinearity. Considering the inherent nature of OHE, which transforms a single variable into multiple binary columns, it is not uncommon to encounter high multicollinearity among the generated features. Recognizing this, we excluded the highly correlated variables and re-evaluated the VIF. Upon inspecting the revised VIF values for each feature, all variables demonstrate a VIF less than 10.  
\begin{table}
\begin{tabular}{l l} \hline
**Feature** & **Feature Description** \\ \hline WTD\_SUBW\_RANK & Ranking of subway stations based on weighted passenger volume \\ NEAR\_SUBW\_DIST & Distance between the property and the nearest subway station \\ INC\_BY\_REG & Ranked region based on weighted average income \\ PLC\_RATE & Policy interest rate corresponding to the contract date \\ ELET\_SCH & Number of elementary schools \\ MDL\_SCH & Number of middle schools \\ CNT\_PART & Number of parks \\ CNT\_LIB & Number of libraries \\ FLR & Floor Information \\ XUAR & Exclusive Area (m\({}^{2}\)) \\ COMP\_NM & Branded construction company status \\ HUS\_TP\_APT & Apartment status \\ HUS\_TP\_STD & Studio status \\ HUS\_TP\_MUTF & Multi-Family status \\ LOG\_PRICE & Log-transformed sale price \\ AGE\_BLDG & Building age \\ \hline \end{tabular}
\end{table}
Table 3: Summary of input features utilized in the modeling process after complete preprocessing.  
Figure 4: Variance Inflation Factor (VIF) values for all features, assessing multicollinearity among input variables in the modeling process.