Investigating the Correlation between Air Pollution and Housing Prices in Seoul, South Korea: Application of Explainable Artificial Intelligence in Random Forest Machine Learning

Abstract

South Korea’s Particulate Matter (PM) concentration is among the highest among Organization for Economic Cooperation and Development (OECD) member countries. However, many studies in South Korea primarily focus on housing characteristics and the physical built environment when estimating apartment prices, often neglecting environmental factors. This study investigated factors influencing apartment prices using transaction data for Seoul apartments provided by the Ministry of Land, Infrastructure, and Transport (MOLIT) in 2019. For this purpose, the study compared and analyzed a traditional hedonic price model with a machine learning-based random forest model. The main findings are as follows: First, the evaluation results of the traditional hedonic price model and the machine learning-based random forest model indicated that the random forest model was found to be more suitable for predicting apartment prices. Second, an importance analysis using Explainable Artificial Intelligence (XAI) showed that PM is more important in determining apartment prices than access to education and bus stops, which were considered in this study. Finally, the study found that areas with higher concentrations of PM tend to have higher apartment prices. Therefore, when proposing policies to stabilize apartment prices, it is essential to consider environmental factors. Furthermore, it is necessary to devise measures such as assigning PM labels to apartments during the home purchasing process, enabling buyers to consider PM and obtain relevant information accordingly.

1. Introduction

Approximately 90% of the world’s population resides in areas where the air quality exceeds the standards set by the World Health Organization (WHO) [1]. Air pollution poses a global risk, leading to high rates of disease and mortality [2], and damages various economic sectors, such as manufacturing, agriculture, and transportation [3]. Moreover, global deaths attributable to air pollution exposure have increased by 51% since 1990, and without more appropriate measures, they are estimated to double by 2050 [4,5]. As such, air pollution is recognized as a very serious problem worldwide. Among these, particulate matter (PM) is more harmful to human health than other air pollutants. Prolonged exposure to high PM levels increases the risk of respiratory diseases and diabetes [6,7]. Long-term exposure to PM_2.5 significantly increases the risk of cancer as well as cardiovascular and respiratory diseases [8,9]. Therefore, the International Agency for Research on Cancer, a WHO subsidiary, has classified PM as a Group 1 carcinogen [10]. PM concentrations in South Korea are extremely high. As of 2019, South Korea’s annual average PM₁₀ concentration was 42 μm/m³, which is approximately 2.8 times higher than the WHO standard of 15 μm/m³. PM_2.5 recorded a level of 23 μm/m³, which is more than 4 times higher than the WHO standard of 5 μm/m³. Therefore, urgent efforts to reduce PM emissions in South Korea are crucial.

In South Korea, with improvements in income and education levels alongside economic growth, there is a growing demand for pleasant residential environments, and people are showing an increasing interest in neighborhood environments. Air quality significantly affects the choice of residence and housing [3]. Considering the importance of housing as a fundamental form of consumption and the largest single component of most family assets, residents worldwide are sensitive to all factors that may affect the convenience value of housing and its market capitalization [11]. Consequently, when choosing residential areas, people also pay attention to local facilities that affect air quality and the ripple effects of air pollution [12,13]. Thus, environmental factors play a crucial role in determining an individual’s quality of life, making them important considerations when selecting residential areas [14]. Though there are many studies focusing on estimating housing prices based on factors related to house characteristics and the physically built environment in South Korea, the studies that consider PM from an environmental perspective are very limited.

However, it is challenging to represent the factors that linearly influence housing market prices in the real world. This is because it is difficult to capture all the characteristics that affect the housing market. Modeling based on machine learning techniques can complement traditional regression methods, and such approaches can be applied to investigate the linear or non-linear relationships between dependent and independent variables and the hierarchical structure of housing price determinants [15]. In particular, there have been many recent studies using machine learning-based random forest models to estimate housing prices [16,17,18,19]. However, in analyses utilizing machine-learning models, the focus is mostly on predictive capability. This is because the typical artificial intelligence models possess a black box, meaning that they only provide conclusions based on their own judgment without revealing the mechanisms behind the conclusions. Therefore, in most studies utilizing black-box models in the housing market, researchers have pursued the goal of achieving better predictive accuracy while sacrificing model interpretability [15,20,21]. A methodology called Explainable Artificial Intelligence (XAI) has emerged that can ensure both explanatory power and predictive power between variables to a certain extent in the field of artificial intelligence. XAI is a class of systems that provides visual insights into how artificial intelligence systems make decisions, predict, and execute tasks [22].

This study aims to examine the relationship between apartment prices and PM, an area that has rarely been studied in South Korea. In addition, it compares the results of the traditional hedonic price model and the machine learning-based random forest model, which is known for its excellent predictive power. Additionally, the study intends to apply XAI to uncover the explanatory power between variables that have not been elucidated owing to the limitations of black box models in the traditional artificial intelligence field. Through this approach, the objective is to provide more insights into not only the predictive capability of housing prices but also the relationship between variables.

Maslow proposed that human needs can be categorized into five levels of needs in relative priority order: physiological, safety, love, esteem, and self-actualization [23]. In this theory, higher-order needs emerge when people feel that their lower-level needs have been sufficiently satisfied. Owning a home is a major demand to meet these needs, as it not only provides a space to rest but also privacy [24]. Accordingly, the characteristics of structure, dwelling, and the built environment in studies estimating housing prices are common not only in South Korea but also around the world.

Among structural characteristics, area is one of the most commonly considered variables. Generally, it has been found that housing prices tend to be higher as the area increases [25,26,27,28,29,30], and similarly, higher floors are associated with higher housing prices [3,31,32,33,34,35]. Additionally, factors such as the number of rooms and bathrooms are frequently taken into account, and overall, it has been observed that housing prices tend to be higher with a greater number of rooms and bathrooms [36,37,38,39,40].

While structural characteristics include the individual attributes of housing, dwelling characteristics, which encompass the concept of housing communities, have also been extensively studied. Building age is one of the most commonly considered variables in dwelling characteristics. In general, people who buy real estate tend to prefer comfortable new homes, so housing prices are found to fall over time [30,41,42,43,44,45]. However, in South Korea, the most representative type of housing, apartments, exhibit a U-shaped relationship with age, where prices initially decline due to aging but then rise again at a certain point due to expectations of reconstruction, where older apartments are demolished and replaced with newly constructed apartments. Therefore, there are cases where age and its square are used together for apartment prices to consider non-linear relationships. In fact, studies conducted targeting Seoul and its surrounding areas found that the square of age had a positive effect on housing prices [28,46,47]. Therefore, it was argued that the prices of apartments in South Korea would increase again after a certain point. South Korea has a very high population density. High-rise multifamily housing, in the form of apartments in which multiple households live in one building, is the most common housing type. Therefore, the number of households in apartment complexes and the number of parking lots are among the dwelling characteristics frequently considered in South Korea. In general, the more households and parking lots, the higher the housing price [48,49,50].

Finally, factors related to the built environment significantly influence housing prices. Among the variables commonly used in previous studies, prominent ones include locational factors such as proximity to the Central Business District (CBD), parks, transportation, schools, and amenities. In general, housing prices appear to decrease as the distance to the CBD increases. This shows mostly the same results regardless of the study area [44,45,51,52,53,54]. Parks also significantly influence housing prices. It has been observed that housing prices tend to decrease as the distance from parks increases [33,35,43,55]. Factors related to transportation are also frequently considered for their effects on housing prices. Access to subway stations, in particular, is found to increase housing prices as accessibility improves [27,28,36,52,55,56]. Moreover, some studies [18,34,38,57] argue that proximity to bus stops leads to higher housing prices. However, there is also the consistent argument that housing prices decrease in closer proximity to bus stops [30,32]. Regarding accessibility to schools, it has been observed that housing prices tend to decrease as the distance from schools increases [34,39,45,56].

PM consists of solid and liquid particles emitted from various sources, such as vehicle emissions, domestic and industrial emissions, forest fires, and smoke [58]. In addition to these various sources of emissions, PM also varies in size. PM₁₀ refers to PM with a diameter of 10 μm or less, while PM_2.5 refers to PM with a diameter of 2.5 μm or less. Among these, PM_2.5 has a significant impact on human health, visibility, ecosystems, weather, and climate [59]. Due to the severity of PM_2.5, previous studies on housing prices and PM have also focused more on PM_2.5. Zhang et al. [60], investigating the impact of air quality on house prices, found that both PM₁₀ and PM_2.5 concentrations were associated with a decrease in housing prices. They argue that urban residents with the financial capacity to afford real estate prices might be willing to pay the cost of avoiding exposure to pollution, thereby increasing the possibility of migration. Also, Xue et al. [61] examined the relationship between PM_2.5 and housing prices. The findings revealed that as PM_2.5 concentrations increased, housing prices tended to decrease. Since PM_2.5 generally has ripple effects, the government should optimize environmental governance systems and promote regional cooperation in governance, according to the study. Borja-Urbano et al. [62], conducted in Quito and focusing on the impact of air pollution on housing prices, found that not only PM_2.5 but also concentrations of CO, O₃, and NOx are associated with lower housing prices. The study suggested that policymakers should consider various strategies when designing rational air pollution control policies. Zou et al. [63], exploring the non-linear impact of air pollution on housing prices, claimed that while PM₁₀ does not have a significant impact on housing prices, PM_2.5 leads to a decrease in housing prices at higher concentrations. Additionally, Chen et al. [64], utilizing the spatial Durbin model to investigate the ripple effects of air pollution on housing prices, argued that housing prices and PM_2.5 concentrations have an inverse relationship.

However, other studies have argued that housing prices and PM concentrations are positively correlated. Sun and Yang [65] divided China into southern and northern regions and investigated the asymmetric and spatially nonstationary effects of particulate air pollution using geographically weighted quantile regression. The results indicate that, in the southern region of China, housing prices decrease with higher PM_2.5 concentrations, whereas in the northern region, prices tend to rise with higher concentrations. It has been suggested that the northern region is significantly affected by industrial pollution and that rapid urban economic development has led to the sacrifice of environmental health. Although economic development has brought about a real estate boom, it is deemed unsustainable. Therefore, raising resident awareness of environmental protection is crucial, and governments must emphasize green development. Additionally, it was argued that encouraging social management of PM_2.5 pollution and enhancing support for sustainable industries are necessary to promote sustainable economic growth. Furthermore, Dai et al. [66] investigated the relationship between environmental risk and housing prices and claimed that housing prices increase with higher PM_2.5 concentrations. Air pollutants are closely related to human activities and mainly occur in areas with high population densities. Because housing prices are more likely to rise in areas where human activities are concentrated due to high-density development in cities, the relationship between housing prices and air pollution tends to be positive (+). Thus, while the overall relationship between housing prices and PM tends to be inverse, there are instances in which they exhibit a proportional relationship depending on the spatial scope or location.

People are increasingly concerned about the impact of local facilities on air quality and the ripple effects of air pollution when choosing a place of residence. As a result, studies that consider factors influencing housing prices include not only structural characteristics, dwelling characteristics, and built environment characteristics around houses, but also air pollution characteristics. However, South Korea stands out among the organizations for economic cooperation and development countries for having the most severe air pollution exposure [67]. In particular, Seoul’s average PM₁₀ concentration is 42 μm/m³, more than twice the WHO standard, and PM_2.5 is 25 μm/m³, which is five times higher than the WHO standard. Meanwhile, Seoul is the most expensive region in South Korea, with housing prices more than twice as high as the average apartment price in all of South Korea. Accordingly, the city of Seoul is in urgent need of efforts to both reduce air pollution and stabilize housing prices. However, studies estimating housing prices have mainly focused on structural, dwelling, and built environment characteristics, limiting the consideration of air pollution characteristics. Furthermore, as evidence continues to show that machine-learning methods outperform traditional hedonic models in terms of predictive power, studies utilizing machine learning to estimate housing prices are rapidly increasing. However, the use of artificial intelligence methods based on machine learning only provides conclusions, such as predictive power, based on its own judgment without revealing the mechanisms through which individual variables lead to these conclusions, which is a significant limitation [29,68,69].

This study aims to investigate the impact of air pollution, specifically PM, the most serious pollutant in Seoul, South Korea, on apartment prices. Employing a machine-learning-based random forest model, this study seeks to address the limitations of traditional artificial intelligence black box models by leveraging XAI. Through XAI, the goal is not only to improve the predictive capability of the machine learning-based model but also to forecast the influence of individual variables. This approach provides more precise and varied insights into housing policies.

2. Materials and Methods

2.1. Study Area

This study investigates the factors influencing housing prices, focusing on Seoul, the capital of South Korea, as shown in Figure 1. Seoul has an area of 605.21 km² and a population of 10,010,983, making it a city with a fairly high population density.

2.2. Materials

To investigate the factors influencing apartment prices in Seoul, this study categorized the variables into three main categories: structural, dwelling, and built environment characteristics, as shown in

Table 1. Variable description.

Classification		Values	Descriptions
Dependent variable	Price	Numerical	Apartment transaction prices
Structure characteristics	Area	Numerical	Area of transacted apartment
	Floor	Numerical	Floor of transacted apartment
	Entrance	Categorical	Entrance of transacted apartment (1: Stair 0: Otherwise)
	Room	Numerical	Number of rooms in transacted apartment
	Bath	Numerical	Number of baths in transacted apartment
Dwelling characteristics	Age	Numerical	Age of transacted apartment
	Age2	Numerical	Square of the age of transacted apartment
	Household	Numerical	Number of households in transacted apartment
	Parking lot	Numerical	Parking lots per household in transacted apartment
	Heating	Categorical	Heating type of transacted apartment (1: individual 0: Otherwise)
	Brand	Categorical	Construction ranking of transacted apartment (1: Top 10 0: Otherwise)
PM characteristics	PM2.5	Numerical	Average PM2.5 concentration within a 400 m radius of transacted apartment
	PM10	Numerical	Average PM10 concentration within a 400 m radius of transacted apartment
Accessibility characteristics	CBD	Numerical	Distance from the transacted apartment to the CBD
	Han river	Numerical	Distance from the transacted apartment to the Han river
	Park and green	Numerical	Distance from the transacted apartment to the park and green area
	Bus stop	Numerical	Distance from the transacted apartment to the bus stop
	Subway exit	Numerical	Distance from the transacted apartment to the subway exit
	Kindergarten	Numerical	Distance from the transacted apartment to the kindergarten
	Elementary school	Numerical	Distance from the transacted apartment to the elementary school
	High school	Numerical	Distance from the transacted apartment to the high school
Location characteristics	Longitude	Numerical	Longitude of transacted apartment
	Latitude	Numerical	Latitude of transacted apartment

. Built environment characteristics were further subdivided into PM, accessibility, and location.

2.2.1. Apartment Prices

To investigate the factors influencing apartment prices in Seoul, this study utilized the 2019 apartment transaction data provided by Ministry of Land, Infrastructure and Transport (MOLIT) [70]. This dataset includes information such as address, date, price, area, floor, and construction year of the transactions. In 2019, 78,084 apartment transactions were conducted in Seoul. Among these, transactions with incorrect values recorded in the MOLIT-provided data or those in which the location information of the transactions was unclear were excluded. Additionally, structural and dwelling information could not be obtained, and these cases were excluded. Through these processing steps, 71,716 apartment transaction records were analyzed.

2.2.2. PM Concentrations

In South Korea, the characteristics of housing properties and the built environment characteristics of neighborhoods are mainly considered factors for predicting apartment prices, and cases in which PM is considered from an environmental perspective are very limited. Accordingly, spatial interpolation was performed to measure PM concentrations in Seoul using PM data for each of the 40 air monitoring stations installed in Seoul (Figure 2). Spatial interpolation is a method of estimating the observed value of the point to be obtained from the actual observed value of surrounding points. There are several methods for this interpolation, such as Inverse Distance Weighted (IDW) and kriging. Among them, IDW practically assumes that the ratio of correlation and similarity between neighbors is proportional to the distance between neighbors [71]. Therefore, in this study, IDW interpolation was used to construct PM data, and the PM concentration estimated through interpolation was represented as a raster with a size of 50 m × 50 m to ensure analysis accuracy. Meanwhile, PM concentration data were measured based on a 400 m radius from each transacted apartment point. Because 400 m is generally used as the appropriate walking distance in studies related to walkability [72,73,74,75].

2.3. Methods

2.3.1. Hedonic Price Model

This study seeks to evaluate which model is more suitable for predicting housing prices using a traditional linear regression model and a machine learning-based random forest model. In this regard, an analysis was conducted on the factors influencing apartment prices using the most commonly used ordinary least squares-based hedonic price model in real estate valuation studies. Among the various hedonic models, the semi-log is the most widely used [26,42,66,76], and the equation for the semi-log-based hedonic price model is as follows [52]:

$$lnY=\alpha +\beta X+e$$

(1)

where $lnY$ represents apartment prices, $\alpha$ is the mean constant, $\beta X$ is the coefficient for each independent variable, and $e$ is the residual error term. This hedonic price model has the advantage of being able to intuitively interpret how much each characteristic affects housing prices. However, this model not only assumes a linear relationship between independent and dependent variables but also has limitations in capturing complex non-linear relationships.

2.3.2. Random Forest

Random forest is an integrated machine learning approach that can be used for both classification and regression, based on a tree-based ensemble method [77]. It combines many decision trees using a bagging method called bootstrap aggregation [78]. This approach involves individually training several different trees and then aggregating the predictions of multiple decision trees, resulting in more reliable predictions than a single decision tree [29]. In addition, random forest algorithms such as decision trees can be very useful in housing value analysis because they can capture non-linear relationships between dependent and independent variables [79] and have the advantage of high model accuracy [80]. However, unlike the hedonic price model, this model has a complex structure due to the inclusion of multiple decision trees, and there is also the limitation that learning and prediction may take longer as the amount of data increases.

2.3.3. Model Evaluation

To compare the analysis results of the traditional hedonic price model and machine learning-based random forest, this study utilized R-Squared (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) [63].

$$R^2=1-\frac{{\sum }_{i=1}^M{\left(\widehat{y}-y_i\right)}^2}{{\sum }_{i=1}^M{\left(y_i-\overline{y}\right)}^2}$$

(2)

$$RMSE=\sqrt{\frac{{\sum }_{i=1}^M{\left(y_i-\overline{y}\right)}^2}{M}}$$

(3)

$$MAE=\frac{1}{M}{\sum }_{i=1}^M\left|y_i-\right.\left.{\widehat{y}}_i\right|$$

(4)

where y_i represents observed values, ${\widehat{y}}_i$ signifies predicted values, $\overline{y}$ denotes the mean of observed values, and M represents dataset size. RMSE and MAE indicate the disparities between predicted and actual housing price values, while R² offers insight into the model’s goodness of fit. A higher R² and lower RMSE and MAE values indicate greater predictive accuracy. Therefore, this study aims to select the model, whether the traditional hedonic model or the machine learning-based random forest, with a higher R² and lower RMSE and MAE values as the final model.

2.3.4. Explainable Artificial Intelligence

Currently, artificial intelligence is increasingly used to make predictions and facilitate decision making [81]. However, artificial intelligence lacks the clarity and interpretability of machine learning solutions because it is a black box in which it is unknown how individual variables affect the prediction results [82]. To address these issues, XAI frameworks emphasizing accountability, transparency, ethics, and reliability [83] have been proposed. Various approaches exist for implementing XAI, and a noteworthy method is SHapley Additive exPlanations (SHAP) [84]. SHAP is used for machine learning model interpretation and can visually express not only the important characteristics of the XAI model but also whether each input characteristic makes a positive or negative contribution [83,85]. SHAP can be divided into a global and local explanation. The global explanation aims to estimate the general contribution of each conditioning factor to understand the factors that affect house prices [86]. In another aspect, a local explanation highlights factors that significantly contributed to the prediction by allowing the impact of each factor to be identified at the individual pixel level [87,88].

3. Results and Discussions

3.1. Spatial Distribution of PM Concentrations

The spatial distribution of PM types in Seoul in 2019, as determined by interpolation, is shown in Figure 3a,b. PM_2.5 and PM₁₀ exhibited similar distributions. Regardless of the type, the concentration of PM was generally high in the southwestern area of Seoul, whereas it was relatively low in the northern area. More closely, PM_2.5, appeared to be more locally concentrated than PM₁₀. Compared with Figure 1, it can be seen that PM concentrations are generally higher in areas where apartment prices are high.

3.2. Descriptive Statistics

Table 2. Descriptive statistics.

Classification		Units	Min	Max	Mean	Std. Dev
Dependent variable	Price	10,000 ₩/m2	163.19 ($1394.79)	4336.95 ($37,067.95)	1036.15 ($8855.98)	506.65 ($4330.34)
Structure characteristics	Area	m2	10.78	273.82	78.38	30.41
	Floor	Number	1	67	9.51	6.26
	Entrance	Dummy	0	1	0.70	0.46
	Room	Number	1	8	2.91	0.738
	Bath	Number	1	4	1.62	0.51
Dwelling characteristics	Age	Number	0	51	18.11	9.509
	Age2	(Number)2	0	2601	418.42	381.60
	Household	100 households	0.05	95.10	10.95	11.87
	Parking lot	Number	0.02	11.96	1.12	0.52
	Heating	Dummy	0	1	0.65	0.48
	Brand	Dummy	0	1	0.37	0.48
PM characteristics	PM2.5	μg/m3	22.17	29.53	25.47	0.96
	PM10	μg/m3	34.80	49.17	43.47	2.11
Accessibility characteristics	CBD	100 m	2.05	154.05	63.82	32.55
	Han river	100 m	0.54	147.97	42.19	34.24
	Park and green	100 m	0.00	11.22	1.65	1.37
	Bus stop	100 m	0.08	5.60	1.28	0.68
	Subway exit	100 m	0.12	31.03	5.20	3.76
	Kindergarten	100 m	0.00	19.51	3.04	2.21
	Elementary school	100 m	0.22	17.60	3.27	1.56
	High school	100 m	0.40	29.16	6.00	3.51
Location characteristics	Longitude	degree	126.81	127.18	127.00	0.09
	Latitude	degree	37.43	37.69	37.55	0.06

presents the descriptive statistics for the variables used in this study. The average transaction price per square meter for apartments in Seoul in 2019 was 1.036 million won ($8856). Meanwhile, the average transaction price per square meter for apartments in Seoul exhibits a significant deviation, ranging from a minimum of 0.163 million won ($1395) to a maximum of 4.337 million won ($37,068).

The PM characteristics considered in this study showed that the average concentrations of PM_2.5 are 25.47 μg/m³ and PM₁₀ are 43.47 μg/m³. These values significantly exceed the WHO standards of 5 μg/m³ for PM_2.5 and 15 μg/m³ for PM₁₀. Even at their minimum values, PM_2.5 records 22.17 μg/m³, and PM₁₀ records 34.80 μg/m³, still exceeding the WHO standards. This indicates that Seoul is highly vulnerable to PM_2.5 and PM₁₀, highlighting the urgent need for efforts to mitigate PM pollution citywide.

3.3. Model Evaluation Comparison

The adequacy of the traditional hedonic price model and machine learning-based random forest analysis are presented in

Table 3. Model evaluation.

Classification	Hedonic Price Model	Random Forest
R2	0.676	0.962
MAE	0.195	0.059
RMSE	0.253	0.083

. The R² value for the hedonic price model is 0.676, whereas it improves significantly to 0.962 in the random forest model, indicating a substantial enhancement in the model’s explanatory power. Both the MAE and RMSE were lower in the random forest model than in the hedonic price model. This finding suggests that the random forest model is more suitable than the traditional hedonic price model for estimating apartment prices in Seoul. Therefore, in this study, a machine learning-based random forest model was adopted.

3.4. Regression Analysis

Before explaining the results of the random forest analysis through the verification of model suitability, the results of the hedonic price model analysis are presented in

Table 4. Hedonic price model.

Classification			Coef.	Std Err.	t
Intercept			−90.783 ***	1.991	−45.589
Apartment characteristics	Structure characteristics	Area	−0.004 ***	0.000	−58.327
		Floor	0.003 ***	0.000	21.553
		Entrance	0.027 ***	0.003	9.529
		Room	0.041 ***	0.002	18.157
		Bath	0.006	0.003	1.842
	Dwelling characteristics	Age	−0.035 ***	0.000	−98.170
		Age2	0.001 ***	0.000	92.040
		Household	0.004 ***	0.000	37.715
		Parking lot	0.099 ***	0.003	38.688
		Heating	−0.263 ***	0.002	−111.493
		Brand	0.107 ***	0.002	48.947
Built environment characteristics	PM characteristics	PM2.5	0.062 ***	0.001	42.373
		PM10	−0.013 ***	0.001	−17.936
	Accessibility characteristics	CBD	−0.005 ***	0.000	−89.823
		Han river	−0.002 ***	0.000	−31.026
		Park and green	−0.010 ***	0.001	−14.317
		Bus stop	0.044***	0.001	29.906
		Subway exit	−0.014 ***	0.000	−50.700
		Kindergarten	0.004 ***	0.000	8.578
		Elementary school	−0.009 ***	0.001	−13.081
		High school	−0.006 ***	0.000	−19.608
	Location characteristics	Longitude	1.094 ***	0.013	83.650
		Latitude	−1.104 ***	0.027	−40.427

*** p < 0.001.

. The main results are as follows. Among the variables considered, the number of baths was the only one that did not appear to have any effect on apartment prices. This is believed to reflect the fact that most apartments in South Korea have two bathrooms, regardless of apartment size. In addition, age has a negative (−) relationship with apartment prices, but age-squared has a positive (+) relationship with apartment prices. This can be interpreted to mean that the price of apartments in Seoul decreases as buildings age but starts to rise again at a certain point due to expectations for reconstruction. In addition, the closer the accessibility to most facilities, excluding bus stops and kindergartens, the higher the apartment prices.

3.5. Machine Learning Algorithm

3.5.1. Hyperparameter Tuning

For the random forest analysis in this study, the train-test data ratio was 7:3. In addition, random search was employed for hyperparameter tuning. For the random search, the number of estimators was specified between 1 and 100; the maximum features were chosen from auto, sqrt, and log2; and the maximum depth was set to be within the range of 1 to 20. Moreover, to derive the optimal hyperparameter values through random search, the number of iterations for the random search was set to 100. The final hyperparameter values obtained from these steps are listed in

Table 5. Hyperparameter values.

Classification	Hyperparameter Values
Estimators	83
Max features	auto
Max depth	19
Cross validation	5
Iteration	100

. The number of estimators was 83, maximum features were auto, maximum depth was 19, cross-validation was 5, and the number of iterations for the random search was 100.

3.5.2. Importance of Features

Figure 4 presents the importance of the features from highest to lowest based on the XAI. The variables influencing apartment prices in Seoul were ranked in the following order of importance: distance to the Han River; type of heating; distance to the CBD; number of households; and longitude, area, and latitude. This indicates that apartment characteristics and the built environment play a complex role in estimating apartment prices.

Accessibility to the Han River was significantly more important than other features. This is likely attributable to the Han River’s prominent role as a natural recreational space traversing the center of Seoul and being perceived as one of the most representative leisure spots in the city.

However, in terms of location characteristics, the longitude appears to be more important than the latitude. This suggests that the east-west position may be more crucial than the north–south position in determining apartment prices in Seoul. However, in reality, Seoul’s main housing policy is implemented by dividing Seoul into northern and southern areas based on the Han River. Nevertheless, the analysis results show that the importance of the east and west is actually higher than that of the north and south. Thus, it is necessary to divide Seoul into east and west to estimate the degree of change and imbalance in apartment prices and consider appropriate housing supply and management measures.

Additionally, the number of households is an important factor in determining apartment prices. As apartments in large complexes are large, they tend to maintain relatively stable price fluctuations compared with those that are not, even during times of high economic volatility. Therefore, in the case of large apartment complexes, there is a strong tendency to prefer them because of their ability to provide more stable asset protection than other apartments. Moreover, large apartment complexes often have well-established security systems, ensuring residents’ safety and offering various amenities such as fitness centers, swimming pools, and parks because of their large number of households. Therefore, the number of households plays a crucial role in determining apartment prices.

In contrast, both PM₁₀ and PM_2.5 were ranked in the intermediate category of importance. In particular, it was revealed that PM concentration has a more significant impact on apartment prices than on educational facility accessibility. This suggests that air pollution contributes to apartment prices in Seoul, to a certain extent. Therefore, it suggests the necessity for housing policies in South Korea to consider environmental factors such as PM, in addition to the attributes of apartments and the physical location environment, when estimating apartment prices in Seoul.

3.5.3. Effect of Features

Figure 5 shows the results of applying SHAP to visualize the impact of each feature on predicting apartment prices in Seoul as positive (+) and negative (−) effects in order of importance. Before explaining the analysis results, among the variables considered in this study, the number of rooms, PM₁₀ concentration, and distance to the kindergarten had different influences from the analysis results of the existing traditional hedonic price model. Similar findings were also observed in a study on the real estate market in Rotterdam, Netherlands [89]. Potrawa and Tetereva [89] claimed that there were variables that caused differences in the influence between the OLS and random forest models. Therefore, the random forest algorithm can more accurately capture the non-linear relationship between the dependent and independent variables.

Prior to the analysis of the results of individual variables, it was found that overall, the lower the value of the structure characteristics, the higher the apartment price. However, for the dwelling characteristics, it was found that the higher the value for all variables except age, the higher the apartment price. In addition, in the built environment characteristics, the higher the level of the PM characteristics, the higher the apartment price, and for variables related to accessibility, it was found that the better the accessibility, the higher the apartment price.

Accessibility to the Han River, which was shown to be the most important factor affecting apartment prices in Seoul, decreased as the distance increased. In fact, Figure 1 shows that apartment prices along the Han River are notably high. The Han River is Seoul’s main open space that runs through the center of Seoul and provides great views of apartments along the Han River. In addition, people’s preference for waterside spaces, where various outdoor activities such as jogging and biking are possible, is believed to be the main reason for high apartment prices.

In the case of heating type, apartment prices were lower when individual heating was used compared with district heating. Compared with individual heating, district heating has a higher thermal efficiency [90], and residents tend to prefer it because the energy costs are lower. Therefore, South Korea prioritizes district heating for the reconstruction and development of new cities [91]. This means that the policy of prioritizing district heating is supported by consumers who want to purchase apartments.

The apartment prices increased as the distance to the CBD decreased. This result aligns with many studies that have attempted to estimate housing prices in the CBD [44,45,51,52,53,54]. A study analyzing housing price determinants in Beijing, China Duan et al. [40] claimed that housing prices are higher because of supply shortages in downtown areas, where land use regulations are strict and developable land is relatively scarce. Additionally, Hussain et al. [45], argued that living near the CBD can reduce transportation costs to reach workplaces and enhance convenience, resulting in higher housing prices near the CBD. In fact, Seoul has recently attempted to solve the problem of housing supply within the city center through the construction of high-rise apartments by introducing a plan to relax floor area ratio restrictions when apartment construction and redevelopment proceed in areas near the CBD. In addition, there is a need to create an environment in which people can fully enjoy accessibility to amenities such as transportation, medical care, childcare, and culture, which are concentrated in the CBD, even within the neighborhood rather than the CBD.

The apartment prices increased as the number of households within an apartment increased. Apartments with a large number of households tend to have a more active housing market and thus provide stability in the real estate market. Therefore, compared with apartments with fewer households, apartments with a larger number of households can more effectively protect assets, leading to a higher preference among the public for large apartment complexes. Additionally, large apartment complexes often have well-established security systems that enhance residents’ safety, as well as various lifestyle amenities, such as fitness centers, cultural facilities, and parks within the complex, which are considered factors that contribute to increasing apartment prices.

In this study, longitude and latitude were utilized to control for factors influencing apartment prices based on spatial characteristics. Higher longitudes and lower latitudes were associated with higher apartment prices. Therefore, when considering both variables collectively, it can be estimated that apartments located in the southeastern region of Seoul command higher prices. This observation aligns with the distribution of apartment prices in Seoul, as shown in Figure 1, where apartments in the southeastern region of Seoul are clustered at higher prices. This area corresponds to one of the three CBDs in Seoul, known as “Gangnam,” which is one of the most developed and densely populated areas with considerable economic activity. “Gangnam” is not only characterized by a high concentration of job opportunities but also boasts excellent transportation accessibility and a plethora of cultural facilities for leisure activities. In particular, apartment prices are estimated to be high because this area specializes in education, and the demand for living in the area is quite high.

In contrast, smaller apartments tend to have higher prices. Although this result contradicts previous studies, it reflects the characteristics of Seoul, South Korea. South Korea is on the verge of becoming a post-aged society because of a significant decline in population, with Seoul’s birth rate standing at 0.717, which is very low [92]. Therefore, there has been a significant increase in the demand for smaller apartments compared with larger ones. However, prices have increased owing to insufficient supply. Therefore, to stabilize prices, it is necessary to expand the supply of apartments with smaller areas in future apartment constructions.

In terms of apartment age, the prices of newly built apartments were higher. This shows the same results as most previous studies [40,41,42,43,44,45]. In general, real estate often deteriorates over time and its value decreases; therefore, it is believed that the higher the apartment age, the lower the housing price. In particular, in Seoul, as new apartments are built owing to continuous reconstruction and redevelopment, people’s tendency to move to new apartments is believed to affect apartment prices.

However, variables related to accessibility in terms of public transportation, such as distance to subway entrances and bus stops, yielded contrasting results. It was found that the closer the distance to subway entrances, the higher the apartment prices, whereas the farther the distance to bus stops, the higher the prices. Zhang and Dong [56]. found that bus stops tended to decrease housing prices, which was attributed to noise pollution. However, the subway has the advantage of not being exposed to direct noise and exhaust fumes compared with buses and is not affected by traffic congestion during commuting. Additionally, areas around subway stations often provide various amenities owing to commercial development. These results indicate a preference for subways over buses among residents; therefore, proximity to subway stations is associated with higher apartment prices.

The apartment price was higher for the higher number of parking lots per household. Despite Seoul’s high population density and increasing traffic congestion, the number of vehicles owned per household is steadily increasing as vehicle consumption increases because of an increase in household income owing to economic growth and an increase in the working population. Accordingly, the number of parking lots per household is a major factor in the choice of a house. Therefore, parking spaces have become valuable resources and indispensable elements in the development of new communities [36].

The apartment price was higher for the higher floor level. This result aligns with most previous studies [31,32,33,34,35]. Generally, higher floors command a premium owing to the panoramic view they offer, which is considered a factor that contributes to an increase in apartment prices. Indeed, Xiao et al. [33] investigated the impact of landscape proximity based on floor level on housing prices. As a result, housing prices increased at higher floor levels. It has been argued that residing in high-rise apartments is advantageous for maximizing the amenity value of the landscape, allowing residents to enjoy significant benefits from the scenery.

Both PM_2.5 and PM₁₀, which were considered to examine the impact of air pollution on apartment prices, were measured to have an overall positive (+) effect. In other words, areas with higher apartment prices had higher concentrations of PM_2.5 and PM₁₀. Sun and Yang [65] investigated the asymmetric and spatial non-stationary effects of particulate air pollution, and their study showed similar results in northern China, where prices increased as PM concentrations increased. In this regard, the northern regions are experiencing the most significant impact of industrial pollution, and it is argued that health is being sacrificed due to rapid urban economic development. Dai et al. [66] also investigated the relationship between environmental risks and housing prices and argued that the higher the PM concentration, the higher the housing price. This is closely related to human activities, as air pollutants tend to be generated mainly in densely populated areas. In other words, areas where human activities are concentrated because of urban development tend to have higher housing prices; however, the concentration of air pollutants may also increase because of such developments. Indeed, by examining Figure 1 and Figure 3, it can be observed that high-priced apartments in Seoul are mostly located near Gangnam or the three previously mentioned CBDs. These areas are known to have the highest development density in Seoul, resulting in significant traffic volume and elevated PM concentrations from sources such as diesel vehicles and tire wear [93]. Accordingly, there is a need to minimize the impact of PM on apartment prices by considering restricting the entry of old diesel vehicles around the CBD, which has the highest development density in Seoul. However, if the socioeconomic benefits obtained from the non-environmental factors considered in this study outweigh the advantages of living in areas with low air pollution, citizens may choose to reside in areas with high PM concentrations despite the potential adverse effects on their health. Therefore, the government must better coordinate and manage the relationship between urban development and air pollution by optimizing the environmental governance system to minimize exposure to air pollution [61].

4. Conclusions

Air pollution is a significant issue with a serious impact on human health. Therefore, selecting healthy and safe residential areas and houses within the constraints of limited resources is important. However, in densely populated Seoul, the impact on housing prices has been studied primarily by focusing on the characteristics of housing structures and the physical built environment around the complexes owing to the shortage of housing supply. Nevertheless, with increasing interest in health and quality of life, there is growing interest in the impact of environmental factors such as air pollution on the housing market. Therefore, this study applies XAI based on machine learning to investigate the relationship between apartment prices and PM, which is relatively understudied in South Korea. The main findings were as follows:

First, in this study, the predictive power was compared using the hedonic price model and the machine learning-based random forest model to investigate the factors affecting apartment prices. As a result, the machine learning-based random forest was found to be more suitable for predicting housing prices than the hedonic price model.

Second, the importance analysis revealed that the factors affecting apartment prices in Seoul were in the following order: accessibility to the Han River, heating type, CBD accessibility, household, longitude, area, latitude, age, and subway entrance. Meanwhile, PM_2.5 and PM₁₀ were found to be more important than accessibility to educational facilities and apartment brands. This implies that factors related to air pollution also contribute to a certain extent in determining apartment prices. Accordingly, when presenting various policies to stabilize apartment prices, there is a need to propose housing policies that consider environmental factors. Meanwhile, South Korea has considerable interest in PM among air pollutants. Accordingly, Information and Communication Technologies (ICT)-based mobile phone Global Positioning System (GPS) is used to determine PM levels at the current location by using data from the nearest monitoring station. Therefore, given the seriousness of air pollution issues globally, it is necessary to devise measures such as assigning PM labels to apartments during the home purchasing process, enabling buyers to consider PM and obtain relevant information accordingly. Additionally, implementing a certification and evaluation system for PM labels and offering incentives such as tax deductions for buildings with high ratings could be considered. As in Maslow’s theory that spiritual satisfaction can be pursued only when physiological and safety needs are satisfied, all people who own a house, regardless of gender, age, or occupation, should be able to escape the environmental risk of air pollution. This is because satisfying the need for safety when all surrounding factors are equal results in a subjective feeling of safety [94]. In that case, humans will move forward to satisfy their spirits.

Third, the apartment prices were higher for better accessibility to the Han River, Seoul’s representative waterfront space. Therefore, a housing policy is needed to ensure that more apartments are supplied so that more people can enjoy open spaces and to alleviate the increase in apartment prices around open spaces. In addition, there is a need to create a social mix by providing affordable housing in open spaces around the Han River.

Fourth, apartment prices increased with better accessibility to the CBD. The demand for a CBD is high owing to its convenience in facilities and transportation, but its supply is low owing to a lack of developable land and strict regulations. Therefore, there is a need to consider ways to expand supply by relaxing the floor area ratio when constructing apartments near the CBD. Instead, construction companies that receive incentives convert part of the land needed for apartment construction into open spaces that can be used by all citizens, thereby improving the overall quality of life.

Fifth, apartment prices increased when there was no individual heating. The representative heating types for apartments in Seoul include individual and district heating. Among them, district heating has good energy efficiency; therefore, residents have the advantage of lower maintenance costs, and it is believed that apartment prices are high owing to high demand. Therefore, when constructing new apartments in the future, it is necessary to adopt a district heating supply method and manage it to maintain eco-friendly apartment construction.

Sixth, apartment prices were higher in smaller areas. In Seoul, the birth rate is rapidly decreasing, and as a result, the number of family members is also rapidly decreasing. Accordingly, it is believed that the demand for small areas is increasing, rather than for unnecessarily large areas. Therefore, there is a need to further expand the supply of small-area apartments in line with the changes in South Korea’s demographic structure. Meanwhile, globally, countries with higher gross domestic product (GDP) per capita tend to have smaller families. Therefore, in countries with fast-growing economies, it may be necessary to be proactive about the supply of small-sized housing to prevent future small-sized housing shortages from causing prices to rise exponentially.

Finally, apartment prices were higher in areas with higher PM concentrations. This could be associated with human activities, as the areas where human activities are concentrated due to urban development tend to have higher apartment prices. In other words, the quality of life may be high in large cities formed by rapid growth due to the construction of various infrastructures. However, if the socioeconomic benefits obtained from the non-environmental factors considered in this study outweigh the advantages of living in areas with low air pollution, citizens may choose to reside in areas with high PM concentrations despite the potential adverse effects on their health. Therefore, the government must further optimize the environmental governance system to properly regulate and manage the relationship between urban development and air pollution. Real estate developers also need to devise measures to improve the air quality in the vicinity when constructing apartments.

This study had several limitations as well. First, the study utilized transaction data from 2019 to identify the factors influencing apartment prices in Seoul. Conducting a study based on a single year limits the ability to capture time-series changes in the independent variables that affect apartment prices, making it challenging to generalize the findings. Second, apartment prices can be influenced by macroeconomic indicators such as interest rates and economic growth rates. However, as this study focused on a single year, macroeconomic indicators were not incorporated. Therefore, future analyses that consider multiyear data and relevant macroeconomic indicators will provide a more accurate understanding of the causal relationships underlying temporal changes in apartment prices. Third, the interpolation method, which is a method of predicting the value of an unpredicted area through the values measured at actual points, allows for more accurate measurement of the surrounding area as more points are measured. Therefore, it is expected that the accuracy of the interpolation method can be further improved if more air pollution measurement stations are installed in the future. Lastly, in this study, the analysis was conducted using random forest, the most representative regression prediction method among the artificial intelligence methods. However, it is believed that if more diverse artificial intelligence algorithms are used in the future, more appropriate algorithms will be discovered to estimate housing prices.