4.1. Results Analysis of Traditional Model
Models 1-6 are estimated by OpenGeoDa software, and the results are presented in
Table 4. The results demonstrate that the F value of the traditional Hedonic price model (i.e., Model 1, Model 3 and Model 5) is close to 0, indicating that the model has passed the significance test and that all models are valid. The values of adjusted R-square for the three models are: 0.6316, 0.6428, 0.6284, which indicate that the model has a strong ability to interpret and can explain more than 60% of house price changes. The VIF value of all variables is lower than 7.5, indicating that there is no redundancy in the explanatory variable, and the multi-collinear effects of model variables are controllable. Most of the variables in the input model pass the 5% significance test and only individual explanatory variables are opposite to the expected symbol. In general, the establishment of the model is relatively successful, and most of the water system factors have passed the significance test, indicating that the water system has a significant impact on the housing price in Zhengzhou housing market.
Both Models 1 and 2 are relatively basic model, which explore the influence of a water system on housing price by measuring the distance from the community to a water system. The regression results are shown in
Table 5. According to model 1, it is found that the distance from the community to the water system is significant at the level of 1%, and the regression coefficient is −0.0278, indicating that the distance from the community to the water system increase by 1%, then the housing price of the community will decline by 2.78%.
In Zhengzhou City, the current average price of housing about 15,000 yuan /m2, which indicates that the price of housing near a water system is approximately 300 yuan /m2 higher than that far away from the water system. As expected, water system will have an impact on people’s daily life, and more and more people pay attention to their own living environment, which indicates that people are willing to pay a certain premium for living around the water system. At the same time, the result also indirectly indicates that more and more housing demand is changing from simple rigid demand to environmental improvement demand.
The distance from the residential area to the river and lake, which instead of the variable of the distance to the river system, was added to the Models 3 and 4 to explore the heterogeneity of the influence separately. The regression results are shown in
Table 6. The adjusted R-square of Model 3 (0.6428) is higher than that of Model 1 (0.6316), indicating that Model 3 has more explanatory power and it is more convincing to consider the influence of rivers and lakes on housing prices separately. According to Model 3 and Model 4, the distance from the community to the river and lake all passed the significance test of 1%, indicating that this factor has an impact on the housing price.
However, it can also be seen that the impact of lakes (0.0568) on housing prices in residential areas is about twice as great as that of rivers (0.0231) according to the above results, which indicate that people prefer lakes than rivers. On the one hand, the scarcity leads to people’s chasing behavior because there are fewer lakes than rivers in urban areas. On the other hand, lakes have inherent advantages in terms of the visual field, regional climate influence, and even surrounding environmental facilities due to their aggregation compared with rivers.
Model 5 and Model 6 explore the impact on housing prices from the perspective of the characteristics of the water system without the accessibility variable, and the regression results are shown in
Table 7.
It is noted that the variable of river width passed the 1% significance test and has a positive impact on the housing price from Model 5. The price will increase by 0.23% if the distance from a house to a river increases by 1 km. The variable of river water quality passed the 5% significance test, and every unit reduction in the river’s water quality rating results in a 2.44% drop in the price of housing in the community. It can be seen that the river width and water quality level all have a greater impact on housing prices, and especially the good water quality is a prerequisite for people to pay a premium [
33].
The lake area variable failed to pass the significance test because the analysis in this paper only took into account the physical characteristics and natural factors of the lake, while the external characters assigned by the public, such as the political, economic and cultural factors, were not taken into account. For example, Ruyihu is the smallest lake analyzed in this paper, but the impact of this lake on housing prices is more significant, because this lake is located in the core area of financial center of Zhengzhou city and gathered a large number of high-quality resources around.
4.2. Result Analysis of Spatial Lag Model
Models 2, 4 and 6 are spatial econometric models, which all take into account the autocorrelation of housing prices. The spatial matrix in the model can be better interpreted by the second order of the latter formula according to the multiple fitting experiments. According to the results of the
Table 2, it can be seen that the R-square of three spatial econometric model (i.e., 0.6872, 0.6906, 0.6887) are higher than the traditional Hedonic price model, the LIK values of the spatial econometric model are greater than the traditional model, and the AIC and SC values are less than the traditional model, which demonstrate that the spatial econometric model has more explanatory power than the traditional model and improves the fit degree of the traditional model.
The results of the spatial econometric model are basically consistent with the results of the traditional model, and the distance to water system, river, lake and river water quality variables are all significant at the level of 1%. Considering the spatial effect, the river width variable is significant at the 10% level, while the influence of lake area on housing price is still insignificant. Compared with the regression coefficient of the traditional model, the regression coefficient of variables in the spatial econometric model is reduced to some extent, which indicate that the traditional Hedonic price model does not take into account the spatial autocorrelation effect of housing price and overestimates the influence of water system on housing price in the residential area.
4.3. Results Analysis of GWR Model
Combining with Model 7, three geologically weighted regression models were constructed to explore the spatial heterogeneity of the influence of water system on housing price from the three aspects of water system accessibility, river and lake accessibility and water system property. The spatial statistics toolbox of ArcGIS is used to estimate the model. In order to avoid the setting error of local multiple generality of variables, the selected explanatory variables were estimated iteratively, and some of them are selected under the condition of ensuring enough explanatory variables and better explanatory effect. The basic variables include building age, plot ratio, property fee, greening rate, total number of buildings, distance to CBD, distance to the nearest top three hospital, distance to the nearest business circle, number of junior high within 1 km, number of supermarket within 500 m, and Whether there is key school nearby, while the water system variables are still the six variables mentioned above.
The estimated results of the global parameter of the above three models are shown in
Table 8, which indicate that the fitting effect of the three models are relatively good, and the spatial heterogeneity effect of the water system can be analyzed through the constructed model.
In order to make the results more intuitive, the regression results for each model are presented in the form of maps.
Figure 3 is the p-value and the local regression coefficient diagram of the distance variables to water system. From the p-value diagram in
Figure 3a, it can be found that the
p-value of this variable at all observation points has passed the significance test of 1%, indicating that it is valid within all observation ranges and further proving that the water system has a significant impact on the housing price. As can be seen from
Figure 3b, the regression coefficient of the distance variable to the water system is all negative in the whole research area. In addition, the coefficient distribution gradually creases from northwest to southeast, reaching a peak value of −0.0357 in the southeast.
The above analysis results show that there are differences in the spatial distribution of the effect of the water system on the housing price in Zhengzhou. The influence in the east is greater than that in the central and western regions. The reasons for this can be explained from two aspects. Firstly, according to
Figure 4, it can be observed that the distance between the western urban area and the water system is farther than the other areas. The fact of the matter is that the water resources of the eastern urban areas are more abundant than in the western urban areas, and the landscape of water system is also better, so the impact of the water system on the eastern urban area is more significant. Secondly, the housing of the main central urban area is mostly built in the last century and the building age of central urban area is earlier than the surrounding area. The residents of this area are mostly rigid demand users and they pay little attention to the surrounding natural environment, so the impact of the water system is not significant compared to the eastern district. At the same time, the poor river environment and less green space in this area are also found to be reasons.
P-value test chart of the river and lake accessibility is shown in
Figure 5a,b, and all observation points pass the 1% significance test, indicating that the accessibility of rivers and lakes has a significant impact on housing prices.
Figure 6a,b and show the corresponding coefficient distribution diagram, which is roughly the same as the accessibility of the water system. The coefficients in the study area are all negative and distributed in a crease pattern of reaching their peaks in the southeast of the city, respectively in −0.0265 and −0.0580. It can be seen that the influence effect of lakes was still greater than that of rivers, and the influence of accessibility of rivers and lakes on the eastern urban area was greater than that of the central and western urban area, which show that the spatial distribution of the influence effect of rivers and lakes on housing prices is not uniform, and the influence effect of lakes is greater than that of rivers.
The regression results of GWR model for river system properties (i.e., river width, lake area and river water quality) are likewise measured.
Figure 7a–c are the p-values of the three variables, and
Figure 8a–c are the corresponding regression coefficients of the three variables. From the
p-value diagram of the width of the river (in
Figure 7a), only a few observation points in the northwest are unable to pass the significance test of 5%, while observation points in the rest of the region all pass the test. It can be seen from the distribution diagram that all the coefficients (in
Figure 8a) are positive and the distribution is still decreasing from southeast to northwest, which show that the influence of river width factor on housing price exists in most areas, and the influence of river width factor on housing price in the eastern area is greater because most rivers in the eastern area are wider than those in the central and western areas.
From the
p-value diagram of the lake area in
Figure 7b, only observation points in the western urban area pass the significance test of 5%, indicating that the variable of lake area only has a significant impact in this region. According to the coefficient distribution map (in
Figure 8b), the effect of lake area on housing price is all positive and decreases gradually from southwest to northeast, and the main influence areas are located close to Xiliuhu. The analysis results of this variable show that the increase of lake area will drive up the housing price in the western part of the city, but not significantly in the eastern part. The reason may be that social, cultural and economic attributes attaching to a lake are often overlooked.
It can be observed from the p-value distribution map of river water quality (in
Figure 7c) that the areas that pass the 5% significance test are distributed in the eastern region bounded, namely Zhengdong new district. In addition, water quality does not get a significant impact on housing prices elsewhere. According to the regression coefficient distribution diagram as shown in
Figure 8c, the regional regression coefficient that has passed the significance test is negative, and the influence effect increases gradually from southwest to northeast. The analysis results of water quality variables show that the river water quality is good in the Zhengdong new district, which has a significant impact on the housing prices in the area.