# RECORD 0b9eefecd90b818651be4c57fe476bab87958359 # TITLE: Determining Factors on Housing Price in Beijing Using Regression Analysis # YEAR: 2025.0 VENUE: Advances in Economics, Management and Political Sciences DOI: 10.54254/2754-1169/2024.ld19187 # AUTHORS: Yoshiki Hayashi # PAGES: 10 CANDIDATE TABLE PAGES (1-based): [4, 6, 7] # ABSTRACT: This paper investigates the correlation between the characteristics of the houses and their prices using Multiple Linear Regressions. Using datasets from Lianjia, this study reveals factors including total housing area, proximity to subways, number of drawing rooms, and community average price, with robust standard errors confirming the reliability of these results. In the initial Ordinary Least Square (OLS) Regression, multicollinearity was not detected by the VIF test, while heteroskedasticity was detected by the White test so robust standard error is used. To address potential endogeneity issue, Two-Stage Least Squares (2SLS) regression with appropriate instrumental variables is further applied. Notably, the results show a negative relationship between housing size and its price, indicating a demand for smaller, centrally located properties, driven by high housing prices and preferences of younger buyer. As a persuit for accuracy, variables bathroom and followers are used in combination as IVs for the potentially endogenous variable square. The conclusion that socio-economic factors, urban development, and access to subway station play significant roles in determining housing prices in Beijing is drawn from the regressions. ===== PAGE 1 (score 11, numeric-paren 0, table-words 1, var-words 9) ===== Determining Factors on Housing Price in Beijing Using Regression Analysis Yoshiki Hayashi1,a,* 1Guangdong Experimental High School, Guangzhou, Guangdong, China a. yoshiki.hys10@gmail.com *corresponding author Abstract: This paper investigates the correlation between the characteristics of the houses and their prices using Multiple Linear Regressions. Using datasets from Lianjia, this study reveals factors including total housing area, proximity to subways, number of drawing rooms, and community average price, with robust standard errors confirming the reliability of these results. In the initial Ordinary Least Square (OLS) Regression, multicollinearity was not detected by the VIF test, while heteroskedasticity was detected by the White test so robust standard error is used. To address potential endogeneity issue, Two-Stage Least Squares (2SLS) regression with appropriate instrumental variables is further applied. Notably, the results show a negative relationship between housing size and its price, indicating a demand for smaller, centrally located properties, driven by high housing prices and preferences of younger buyer. As a persuit for accuracy, variables bathroom and followers are used in combination as IVs for the potentially endogenous variable square. The conclusion that socio- economic factors, urban development, and access to subway station play significant roles in determining housing prices in Beijing is drawn from the regressions. Keywords: Beijing housing prices, OLS regression, 2SLS regression, endogeneity, urban development. 1. Introduction This paper analyzed the factors that affect housing prices in Beijing. Nowadays, mainly attributing to increasing modernization and economic breakthrough, the housing prices surges in especially large cities in China. Although current researches have revealed significant insight toward the factors that affect the property values in Beijing or other China’s large cities, there are few that only used quantitative data, and also that most of them are using relatively old data, which limits their predictability of constantly changing housing prices. This paper aimed to study the factors that affect Beijing’s housing prices solely using quantitative data from an econometric scope, allowing for more subjective and data-based statistical analysis. The research is significant on its usage of regression analysis and quantitative data, as well as the dataset obtained from the period in which Beijing’s undulation and movements in housing prices are relatively large. The large data size also contribute to a relatively accurate estimate. Fang et al. conducted a large-scale investigation based on dataset from China Commercial Bank about mortgage loan from 2003 to 2013, using hedonic price regressions [1]. The research reveals the price surge was especially significant in first-tier cities (Beijing, Shanghai, Shenzhen, and Guangzhou) Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 © 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/). 164 ===== PAGE 4 (score 35, numeric-paren 0, table-words 14, var-words 3) ===== 𝑦= 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽4𝑥4 + 𝛽5𝑥5 + 𝛽6𝑥6 + 𝛽7𝑥7 + 𝜀 (1) However, to address potential possibility of endogeneity issue, Two-Stage Least Squares (2SLS) Regression Analysis is applied. 𝑦= 𝛽0 + 𝛽1･ 𝐸(𝑥1) + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽4𝑥4 + 𝛽5𝑥5 + 𝛽6𝑥6 + 𝛽7𝑥7 + 𝜀 (2) 3. Results and Discussion 3.1. Results of the OLS Regression Table 2 shows the results of the OLS Regression. The p-values for all of the coefficients are less than 0.05, and none of the 95% confidence interval contains 0; both facts indicate that all of the listed independent variable have statistically significant correlation with the independent variable - price. The coefficient of square is negative meaning that as the total housing area of a typical home increases, the price will decrease, which is apparent regardless of other factors. Other variables’ coefficients are all positive. The coefficient for ladderRatio is especially large (as ladderRatio increase by one unit, price will increase 2716.725), followed by drawingRoom and subway. Table 2: OLS Regression Results Price SE t-statistics p-value [95% CI] square 4.82445 -12.38 0.000 -69.20572 -50.28691 livingRoom 251.5072 2.16 0.031 49.4778 1035.749 drawingRoom 327.9339 6.08 0.000 1350.025 2636 ladderRatio 838.3254 3.24 0.001 1073.002 4360.448 elevator 333.727 2.53 0.012 189.0831 1497.775 subway 326.3123 2.97 0.003 328.9668 1608.582 communityAverage 0.0063315 133.34 0.000 0.8318034 0.8566321 Constant 637.0295 -6.15 0.000 -5165.927 -2667.852 As shown in Table 3, the p-value associated with F-statistic is 0.00, suggesting that there is convincing evidence against the null hypothesis that all coefficients are zero. In other words, overall F-test for the model is highly significant and the model is significant. Table 3 also shows that the R- squared value is 0.8689. This means that 86.89% of the variation in price (dependent variable) can be explained by variation in the independent variables, validating the fitness of the regression. Table 3: Other Statistics Associated with the OLS Regression Statistics Value F-statistic 2964.85 P-value 0.0000 R-squared 0.8689 Adjusted R-squared 0.8686 Subsequently, to test whether the independent variables have high correlation with one another, VIF test is applicated. The results (Table 4) show that all of the VIF are less than 5. This means that there is multicollinearity issue but it is not serious. Additionally, since the mean VIF is close to 1, it can be concluded that multicollinearity is very mild. Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 167 ===== PAGE 5 (score 15, numeric-paren 0, table-words 6, var-words 1) ===== Table 4: Results for the VIF Test Constant VIF 1/VIF 𝑥1 3.35 0.298482 𝑥2 2.69 0.371829 𝑥3 1.86 0.537082 𝑥4 1.33 0.750873 𝑥5 1.20 0.835150 𝑥6 1.16 0.863709 𝑥7 1.12 0.892681 Mean 1.82 - Next, to test if the linear regression model fits in the correlation between variables, residual plot is made. As shown in Figure 1, the plot showed mild pattern. Figure 1: Residual Plot Therefore, residual test (one sample t-test) with “the mean of the residuals is zero” as the null hypothesis is conducted. The p-value of 1.00 foretells that there is no convincing evidence that the residual mean is different from zero. Since the errors are centered around zero, the regression model is fit on average in terms of residual behaviors. 3.2. Robust Regression Results To test heteroskedasticity and avoid unreliable estimates, the White test was conducted. The Chi- square test statistic value is 422.70, degree of freedom is 33, and the p-value is 0.0000, confirming the presence of heteroskedasticity. To address heteroskedasticity issue and better promote accuracy of the estimate, the subsequent regressions will use robust standard errors. Adjusted to the robust standard errors, p-value for the livingRoom coefficient increased to 0.063 (0.063<0.05). Yet, it is lower than the significance level of 0.1, so the effect of number of living rooms on the house’s price still can be said significant (Table 5). Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 168 ===== PAGE 6 (score 23, numeric-paren 0, table-words 4, var-words 11) ===== Table 5: OLS Regression with Robust Standard Errors Price coefficient Robust SE t-statistics p-value [95% CI] square -59.74631 5.937107 -10.06 0.000 -71.38733 -48.1053 livingRoom 542.6135 291.935 1.86 0.063 -29.78979 1115.017 drawingRoom 1993.013 351.7496 5.67 0.000 1303.329 2682.696 ladderRatio 2716.725 932.9369 2.91 0.004 887.4948 4545.954 elevator 843.4289 327.006 2.58 0.010 202.2612 1484.597 subway 968.7746 315.3396 3.07 0.002 350.4814 1587.068 communityAverage 0.8442177 0.0078306 107.81 0.000 0.8288642 0.8595713 Constant term -3916.89 769.663 -5.09 0.000 -5425.985 -2407.795 3.3. Endogeneity Issue Although the regression has overall high fitness on the estimate, there is another concern: endogeneity. The conventional one-step OLS regression may render endogeneity issue considering theoretical contexts. It can be alleviated by using a 2SLS; when Ou et al. is studying about how PM2.5 levels play a role on urban cities’ housing prices, suggesting its usefulness in analyzing housing prices determining factors [9]. The variable square may be correlated with error term, resulting in such an issue. Firstly, simultaneity may exist. The size of the house may influence the price, and vice versa - higher prices may be a incentives for developers to build larger houses, seeking for the expected higher selling prices. Such an mutual influence can make the variable square and error term correlated, inducing endogeneity issue. Secondly, there may be omitted variable bias. Square could be correlated with unobserved factors such as neighborhood quality or demand fluctuations, proximity to amenities, or school districts. The study by Shi et al. have pointed out that the choice of the size of the house to live in should vary largely, depending on the buyer’s income level and social background [5]. Putting this into mind, the size of the house that a family wants to live in is definitely larger than that of a young person living alone (square is larger). Economic conditions of people with families are definitely better than those of freshmen, fore instance. Thus, they can afford higher price. This mutually effecting relationship, in other words, reverse causation, precludes us from drawing causal relationship between price and the variables, especially square. The housing prices-to-income ratios are calculated by Fang et al. [1]. In the sampled Chinese cities, price-to-income ratio is in the range of 6 to 10. In 2016, the price of a house with 90 square meters in Shanghai or Beijing is 25 times the average income of households [2]. Based on the viewpoint of this ratio, since people living in larger houses tend to hold families and thus a higher disposable income than freshmen. This makes the payment for buying houses occupy a smaller portion of the disposable funds for those holding families than the young; thus, their demand for buying the house is more elastic. When taking into account the economic conditions of the people who have demand for this house and the elasticities for their demand, it is possible that those omitted variables positively influencing housing prices, rather than square directly causing the price increase. The study also reveals that most Chinese buyer of houses are middle-aged people or above, largely attributing to their more stable savings than youngers. The motivations for them to purchase houses includes to use real estate as an investment or saving for retirement, or for their children’s marriage. The few chances of investment and expected relatively low returns of investment on finance products are driving people with abundant income or saving to devote their money into buying houses (Table 6). Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 169 ===== PAGE 7 (score 34, numeric-paren 1, table-words 10, var-words 8) ===== Table 6. Possible Choices for Instrumental Variable Variable Meaning Cid community ID kitchen the number of kitchen bathroom the number of bathroom DOM active days on market. followers the number of people follow the transaction Yet, 2SLS using Cid as an instrument variable (IV) yields multicollinearity issue, so it is not suitable as an IV. This may be because the ID number in some way is correlated with other variables. Also, when kitchen is used as an IV for square, the p-values for all regressors are larger than any possible significance level. This makes the correlation not statistically significant, so using kitchen as an IV for square is not suitable. Other variables alone were not suitable as well, either because it disqualifies the correlation between independent variables and dependent variable or because the endogeneity test had a small p-value. Thus, several variables need to be combined as IVs for square. 3.4. Results of the 2SLS Regression The results of the 2SLS regression using bathroom and follower as IVs is shown in Table 7. The p- values for square, drawingRoom, ladderRatio, subway, communityAverage are less than 0.05, suggesting there is statistically significant correlation between these variables and price. Coefficient of square is -52.274343. This indicates that for each additional one unit of square meter of the house, the price will decrease by 52 units; in other words, larger houses tend to have slightly higher prices than smaller ones. It can be inferred that Beijing’s dwellers have larger demand on smaller housings. The coefficient for subway is positive and is relatively large (974.9528), which every small improvement in access to subway station is associated by a relatively large increase in price. This supports what is argued in other papers that the access to subway or other transportation including buses indeed is a contributing factor in determining the house’s price. Positive coefficient for communityAverage indicate that the overall reputation or price level of the community significantly affects the price of individual properties. This reflects a broader trend in Beijing, where buyers are willing to pay a premium for homes in well-established or prestigious communities, particularly those with better amenities or a higher social status. This trend ties into the broader socio-economic context of Beijing, where the rapid growth of wealth and urban development drives demand for properties in prestigious neighborhoods. Table 7: 2SLS Regression with Robust Standard Errors Price coefficient Robust SE z-statistics p-value [95% CI] square -52.27434 11.09248 -4.71 0.000 -74.0152 -30.53347 livingRoom 299.7442 408.9099 0.73 0.464 -501.7045 1101.193 drawingRoom 1812.467 407.2673 4.45 0.000 1014.238 2610.696 ladderRatio 2368.047 1112.697 2.13 0.033 187.2018 4548.892 elevator 663.3836 404.546 1.64 0.101 -129.512 1456.279 subway 974.9528 314.9833 3.10 0.002 357.597 1592.309 communityAverage 0.8450588 0.0079132 106.79 0.000 0.8295493 0.8605683 Constant -3711.986 822.7467 -4.51 0.000 -5324.539 -2099.432 Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 170 ===== PAGE 8 (score 33, numeric-paren 0, table-words 11, var-words 10) ===== As shown in Table 8, the Chi-square statistic of 14163.62 as well as the p-value smaller than any possible significance level indicate that the model has an overall statistically significance. In other words, the independent variables collectively are able to explain the variation in the dependent variable (price), since the null hypothesis (H0: None of the independent variables in the model explain the dependent variable) fails to be rejected. Also, the R-squared value of 0.8688 means that 86.88% of the change in 𝑦 (price) can be explained by the independent variables, suggesting the variables are suitable predictors. Table 8: Other Statistics Associated with the OLS Regression Statistics Value Chi-square statistic 14163.62 P-value 0.0000 R-squared 0.8688 Lastly, the endogeneity test (results shown in Table 9) yields p-values that fail to rejects the hull hypothesis (H0: Variables are exogenous). There is no convincing evidence that the variables are endogenous. Thus, endogeneity issue is effectively alleviated by using bathroom and followers as IVs for square. Table 9: The Results for Endogeneity Test Statistics Value p-value Robust score chi2 (1) 0.555293 0.4562 Robust regression F(1, 3130) 0.555014 0.4563 3.5. Discussion By VIF test, White test, residual test, and endogeneity test, the potential issues of the model is detected and addressed to persue a more accurate estimates. With this in mind, some implications can be drawn. Primarily, the negative coefficient between square and price can be analyzed. This can be due to the inability for people - especially the younger generation who do not need very large houses to afford the overly high housing prices in Beijing, but have demand to live in Beijing; preference for smaller, more centrally located properties or a saturation effect where bigger properties reduce marginal price per square meter can be seen. This trend significantly differs from Japan, which tend to have similar character as China (Tokyo as the main center with most population centered at, and both countries are large economic forces in Asia). According to Inoue et al., factors like geographic segmentation and local neighborhood characteristics is the determinant factor in Tokyo; also, in Tokyo, properties in Minato-city and Shibuya-city retain high per-square-meter prices especially for larger homes [10]. This can be attribute to people living in the expensive area in Tokyo is living there from economic booth period, so they already have wealth and holds families and thus prioritize larger living spaces in premium locations. By contrast, in Beijing, access to amenities such as subway stations dominate buyer preferences, possibly due to people living there is still workers and do not have sufficient funds to support families and larger housings, but only have the need to stick in the economic center, Beijing. When considering the fitness of IVs, the reason why variable bathroom is suitable as an IV for square can be because it decently satisfies the two conditions: relevance and exclusion. The number of bathrooms is usually determined when the house is designed based on the size of the house and the expected living needs, so it is related to the square footage of the house (relevance) and will not change due to other fluctuations - namely, will not change following error term (exclusion). On Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies DOI: 10.54254/2754-1169/148/2024.LD19187 171