# A Data-Driven Analysis on the Impact of High-Speed Rails on Land Prices in Taiwan
## 4 Data-Driven Analysis
### Determining Factors Affecting Land Prices

Table 3: Descriptive statistics of data set before and after the introduction of HSR. In the regression model represented with Equation (1), ten explanatory variables had a variance inflation factor (VIF) greater than five, indicating multi-collinearity. The estimated correlation matrix (Figure 6) shows the interdependency of each pair of explanatory variables. To eliminate multi-collinearity, the pairs of variables which showed high correlation (\(>\)0.7) were identified, and variables with the highest VIFs were first eliminated. In this step, five variables that were removed were housing-price-to-income ratio (_H5I_), commercial borrowing interest rate (_5 BankIR_), number of companies registered (_NumCom_), energy price index (_Energy_), and road density (_RoadDen_). As the underlying effects of these variables were captured in other variables, their removals do not compromise the model's explanatory power. Eliminating these variables also complies with the principle of model parsimony (Since most existing literature would concur that a dense road network facilitates a fast commute from one location to another and increases the accessibility in a city, a high density road network should, in principle, increases land prices. However, the road network density was found to have dropped out of the set of significant predictors for land prices. This can be explained by the strong link between the advancement of a city's economic and infrastructure developments and the road network. For the same reason, the \"number of companies\" was not within the set of significant predictors for land prices. While the increase in the number of companies will bid up land prices, its effect would have been captured by the presence of the free trade zone (_FTZ_), low interest rates, and favorable exchange regimes that attract foreign direct investment and promote the establishment of companies in the city. As \"energy prices\" are part of the overall \"construction cost\", the former is also excluded to prevent multi-collinearity). Figure 5: Regression analysis outcome for the base model (1). Figure 6: Correlation matrix of the base model (1). A reduced multivariate linear regression model constructed based on the eleven remaining explanatory variables is as follows:  
\[ULPI_{2}=\beta_{0}+\beta_{1}(HSR)+\beta_{3}(GenPop)+\beta_{4}(UnEmp)+\beta_{5}( CPI)+\beta_{6}(Fprex)+\beta_{7}(IRrf)\]  
\[+\beta_{10}(NumGuests)+\beta_{11}(Internet)+\beta_{12}(FTZ)+\beta_{13}(AirDist)+ \beta_{14}(CC)+\varepsilon \tag{2}\]  
In the model represented by Equation (2), all the explanatory variables including \(HSR\) and risk-free interest rate were significant with \(p\)-values less than 0.01. The VIF were all below five (Figure 7). Errors followed a normal distribution as displayed in the histogram and normal probability plot (Appendix A). The \(R^{2}\) value dropped slightly to 78% which is unsurprising, since the five variables that were removed could have caused the \(R^{2}\) value to decrease mathematically [49]. Equation (2) shows that the establishment of a free trade zone (\(FTZ\)), the presence of a high-speed rail (\(HSR\)) station, consumer price index (\(CPI\)), and exchange rate are positively related to land prices in Taiwan. Comparatively, the magnitude of the construction cost, size of the tourism industry, and the distant airport marginally increase land prices. The free-trade zone (\(FTZ\)) and stronger exchange rate contribute to the economic growth by increasing the earnings from trade. The presence of HSR station improves the attractiveness of an area via better accessibility that boosts the demand and pushes up the land prices of an area. Meanwhile, higher \(CPI\) reflects higher inflation rates which will be factored into the market property prices. The same applies to construction cost where higher construction cost translates into higher property prices. Although the presence of an airport boosts intercity and regional/ global connectivity, land prices are found to increase with distance away from an airport.