1# RECORD 0b9eefecd90b818651be4c57fe476bab879583592# TITLE: Determining Factors on Housing Price in Beijing Using Regression Analysis3# YEAR: 2025.0 VENUE: Advances in Economics, Management and Political Sciences DOI: 10.54254/2754-1169/2024.ld191874# AUTHORS: Yoshiki Hayashi5# PAGES: 10 CANDIDATE TABLE PAGES (1-based): [4, 6, 7]6# 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.789===== PAGE 1 (score 11, numeric-paren 0, table-words 1, var-words 9) =====1011 12 13Determining Factors on Housing Price in Beijing Using 14Regression Analysis 15Yoshiki Hayashi1,a,* 161Guangdong Experimental High School, Guangzhou, Guangdong, China 17a. yoshiki.hys10@gmail.com 18*corresponding author 19Abstract: This paper investigates the correlation between the characteristics of the houses and 20their prices using Multiple Linear Regressions. Using datasets from Lianjia, this study reveals 21factors including total housing area, proximity to subways, number of drawing rooms, and 22community average price, with robust standard errors confirming the reliability of these 23results. In the initial Ordinary Least Square (OLS) Regression, multicollinearity was not 24detected by the VIF test, while heteroskedasticity was detected by the White test so robust 25standard error is used. To address potential endogeneity issue, Two-Stage Least Squares 26(2SLS) regression with appropriate instrumental variables is further applied. Notably, the 27results show a negative relationship between housing size and its price, indicating a demand 28for smaller, centrally located properties, driven by high housing prices and preferences of 29younger buyer. As a persuit for accuracy, variables bathroom and followers are used in 30combination as IVs for the potentially endogenous variable square. The conclusion that socio-31economic factors, urban development, and access to subway station play significant roles in 32determining housing prices in Beijing is drawn from the regressions. 33Keywords: Beijing housing prices, OLS regression, 2SLS regression, endogeneity, urban 34development. 351. 36Introduction 37This paper analyzed the factors that affect housing prices in Beijing. Nowadays, mainly attributing to 38increasing modernization and economic breakthrough, the housing prices surges in especially large 39cities in China. Although current researches have revealed significant insight toward the factors that 40affect the property values in Beijing or other China’s large cities, there are few that only used 41quantitative data, and also that most of them are using relatively old data, which limits their 42predictability of constantly changing housing prices. This paper aimed to study the factors that affect 43Beijing’s housing prices solely using quantitative data from an econometric scope, allowing for more 44subjective and data-based statistical analysis. The research is significant on its usage of regression 45analysis and quantitative data, as well as the dataset obtained from the period in which Beijing’s 46undulation and movements in housing prices are relatively large. The large data size also contribute 47to a relatively accurate estimate. 48Fang et al. conducted a large-scale investigation based on dataset from China Commercial Bank 49about mortgage loan from 2003 to 2013, using hedonic price regressions [1]. The research reveals the 50price surge was especially significant in first-tier cities (Beijing, Shanghai, Shenzhen, and Guangzhou) 51Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 52DOI: 10.54254/2754-1169/148/2024.LD19187 53© 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 54(https://creativecommons.org/licenses/by/4.0/). 55164 565758===== PAGE 4 (score 35, numeric-paren 0, table-words 14, var-words 3) =====5960 61 62𝑦= 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽4𝑥4 + 𝛽5𝑥5 + 𝛽6𝑥6 + 𝛽7𝑥7 + 𝜀 (1) 63However, to address potential possibility of endogeneity issue, Two-Stage Least Squares (2SLS) 64Regression Analysis is applied. 65𝑦= 𝛽0 + 𝛽1･ 𝐸(𝑥1) + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽4𝑥4 + 𝛽5𝑥5 + 𝛽6𝑥6 + 𝛽7𝑥7 + 𝜀 (2) 663. 67Results and Discussion 683.1. Results of the OLS Regression 69Table 2 shows the results of the OLS Regression. The p-values for all of the coefficients are less than 700.05, and none of the 95% confidence interval contains 0; both facts indicate that all of the listed 71independent variable have statistically significant correlation with the independent variable - price. 72The coefficient of square is negative meaning that as the total housing area of a typical home increases, 73the price will decrease, which is apparent regardless of other factors. Other variables’ coefficients are 74all positive. The coefficient for ladderRatio is especially large (as ladderRatio increase by one unit, 75price will increase 2716.725), followed by drawingRoom and subway. 76Table 2: OLS Regression Results 77Price 78SE 79t-statistics 80p-value 81[95% CI] 82square 834.82445 84-12.38 850.000 86-69.20572 87-50.28691 88livingRoom 89251.5072 902.16 910.031 9249.4778 931035.749 94drawingRoom 95327.9339 966.08 970.000 981350.025 992636 100ladderRatio 101838.3254 1023.24 1030.001 1041073.002 1054360.448 106elevator 107333.727 1082.53 1090.012 110189.0831 1111497.775 112subway 113326.3123 1142.97 1150.003 116328.9668 1171608.582 118communityAverage 1190.0063315 120133.34 1210.000 1220.8318034 1230.8566321 124Constant 125637.0295 126-6.15 1270.000 128-5165.927 129-2667.852 130 131As shown in Table 3, the p-value associated with F-statistic is 0.00, suggesting that there is 132convincing evidence against the null hypothesis that all coefficients are zero. In other words, overall 133F-test for the model is highly significant and the model is significant. Table 3 also shows that the R-134squared value is 0.8689. This means that 86.89% of the variation in price (dependent variable) can be 135explained by variation in the independent variables, validating the fitness of the regression. 136Table 3: Other Statistics Associated with the OLS Regression 137Statistics 138Value 139F-statistic 1402964.85 141P-value 1420.0000 143R-squared 1440.8689 145Adjusted R-squared 1460.8686 147 148Subsequently, to test whether the independent variables have high correlation with one another, 149VIF test is applicated. The results (Table 4) show that all of the VIF are less than 5. This means that 150there is multicollinearity issue but it is not serious. Additionally, since the mean VIF is close to 1, it 151can be concluded that multicollinearity is very mild. 152Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 153DOI: 10.54254/2754-1169/148/2024.LD19187 154167 155156157===== PAGE 5 (score 15, numeric-paren 0, table-words 6, var-words 1) =====158159 160 161Table 4: Results for the VIF Test 162Constant 163VIF 1641/VIF 165𝑥1 1663.35 1670.298482 168𝑥2 1692.69 1700.371829 171𝑥3 1721.86 1730.537082 174𝑥4 1751.33 1760.750873 177𝑥5 1781.20 1790.835150 180𝑥6 1811.16 1820.863709 183𝑥7 1841.12 1850.892681 186Mean 1871.82 188- 189 190Next, to test if the linear regression model fits in the correlation between variables, residual plot is 191made. As shown in Figure 1, the plot showed mild pattern. 192 193Figure 1: Residual Plot 194Therefore, residual test (one sample t-test) with “the mean of the residuals is zero” as the null 195hypothesis is conducted. The p-value of 1.00 foretells that there is no convincing evidence that the 196residual mean is different from zero. Since the errors are centered around zero, the regression model 197is fit on average in terms of residual behaviors. 1983.2. Robust Regression Results 199To test heteroskedasticity and avoid unreliable estimates, the White test was conducted. The Chi-200square test statistic value is 422.70, degree of freedom is 33, and the p-value is 0.0000, confirming 201the presence of heteroskedasticity. To address heteroskedasticity issue and better promote accuracy 202of the estimate, the subsequent regressions will use robust standard errors. 203Adjusted to the robust standard errors, p-value for the livingRoom coefficient increased to 0.063 204(0.063<0.05). Yet, it is lower than the significance level of 0.1, so the effect of number of living 205rooms on the house’s price still can be said significant (Table 5). 206Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 207DOI: 10.54254/2754-1169/148/2024.LD19187 208168 209210211===== PAGE 6 (score 23, numeric-paren 0, table-words 4, var-words 11) =====212213 214 215Table 5: OLS Regression with Robust Standard Errors 216Price 217coefficient 218Robust SE 219t-statistics 220p-value 221[95% CI] 222square 223-59.74631 2245.937107 225-10.06 2260.000 227-71.38733 228-48.1053 229livingRoom 230542.6135 231291.935 2321.86 2330.063 234-29.78979 2351115.017 236drawingRoom 2371993.013 238351.7496 2395.67 2400.000 2411303.329 2422682.696 243ladderRatio 2442716.725 245932.9369 2462.91 2470.004 248887.4948 2494545.954 250elevator 251843.4289 252327.006 2532.58 2540.010 255202.2612 2561484.597 257subway 258968.7746 259315.3396 2603.07 2610.002 262350.4814 2631587.068 264communityAverage 2650.8442177 2660.0078306 267107.81 2680.000 2690.8288642 0.8595713 270Constant 271term 272-3916.89 273769.663 274-5.09 2750.000 276-5425.985 277-2407.795 2783.3. Endogeneity Issue 279Although the regression has overall high fitness on the estimate, there is another concern: endogeneity. 280The conventional one-step OLS regression may render endogeneity issue considering theoretical 281contexts. It can be alleviated by using a 2SLS; when Ou et al. is studying about how PM2.5 levels 282play a role on urban cities’ housing prices, suggesting its usefulness in analyzing housing prices 283determining factors [9]. The variable square may be correlated with error term, resulting in such an 284issue. Firstly, simultaneity may exist. The size of the house may influence the price, and vice versa - 285higher prices may be a incentives for developers to build larger houses, seeking for the expected 286higher selling prices. Such an mutual influence can make the variable square and error term correlated, 287inducing endogeneity issue. Secondly, there may be omitted variable bias. Square could be correlated 288with unobserved factors such as neighborhood quality or demand fluctuations, proximity to amenities, 289or school districts. The study by Shi et al. have pointed out that the choice of the size of the house to 290live in should vary largely, depending on the buyer’s income level and social background [5]. Putting 291this into mind, the size of the house that a family wants to live in is definitely larger than that of a 292young person living alone (square is larger). Economic conditions of people with families are 293definitely better than those of freshmen, fore instance. Thus, they can afford higher price. This 294mutually effecting relationship, in other words, reverse causation, precludes us from drawing causal 295relationship between price and the variables, especially square. The housing prices-to-income ratios 296are calculated by Fang et al. [1]. In the sampled Chinese cities, price-to-income ratio is in the range 297of 6 to 10. In 2016, the price of a house with 90 square meters in Shanghai or Beijing is 25 times the 298average income of households [2]. 299Based on the viewpoint of this ratio, since people living in larger houses tend to hold families and 300thus a higher disposable income than freshmen. This makes the payment for buying houses occupy a 301smaller portion of the disposable funds for those holding families than the young; thus, their demand 302for buying the house is more elastic. When taking into account the economic conditions of the people 303who have demand for this house and the elasticities for their demand, it is possible that those omitted 304variables positively influencing housing prices, rather than square directly causing the price increase. 305The study also reveals that most Chinese buyer of houses are middle-aged people or above, largely 306attributing to their more stable savings than youngers. The motivations for them to purchase houses 307includes to use real estate as an investment or saving for retirement, or for their children’s marriage. 308The few chances of investment and expected relatively low returns of investment on finance products 309are driving people with abundant income or saving to devote their money into buying houses (Table 3106). 311Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 312DOI: 10.54254/2754-1169/148/2024.LD19187 313169 314315316===== PAGE 7 (score 34, numeric-paren 1, table-words 10, var-words 8) =====317318 319 320Table 6. Possible Choices for Instrumental Variable 321Variable 322Meaning 323Cid 324community ID 325kitchen 326the number of kitchen 327bathroom 328the number of bathroom 329DOM 330active days on market. 331followers 332the number of people follow the transaction 333 334Yet, 2SLS using Cid as an instrument variable (IV) yields multicollinearity issue, so it is not 335suitable as an IV. This may be because the ID number in some way is correlated with other variables. 336Also, when kitchen is used as an IV for square, the p-values for all regressors are larger than any 337possible significance level. This makes the correlation not statistically significant, so using kitchen 338as an IV for square is not suitable. Other variables alone were not suitable as well, either because it 339disqualifies the correlation between independent variables and dependent variable or because the 340endogeneity test had a small p-value. Thus, several variables need to be combined as IVs for square. 3413.4. Results of the 2SLS Regression 342The results of the 2SLS regression using bathroom and follower as IVs is shown in Table 7. The p-343values for square, drawingRoom, ladderRatio, subway, communityAverage are less than 0.05, 344suggesting there is statistically significant correlation between these variables and price. Coefficient 345of square is -52.274343. This indicates that for each additional one unit of square meter of the house, 346the price will decrease by 52 units; in other words, larger houses tend to have slightly higher prices 347than smaller ones. It can be inferred that Beijing’s dwellers have larger demand on smaller housings. 348The coefficient for subway is positive and is relatively large (974.9528), which every small 349improvement in access to subway station is associated by a relatively large increase in price. This 350supports what is argued in other papers that the access to subway or other transportation including 351buses indeed is a contributing factor in determining the house’s price. Positive coefficient for 352communityAverage indicate that the overall reputation or price level of the community significantly 353affects the price of individual properties. This reflects a broader trend in Beijing, where buyers are 354willing to pay a premium for homes in well-established or prestigious communities, particularly those 355with better amenities or a higher social status. This trend ties into the broader socio-economic context 356of Beijing, where the rapid growth of wealth and urban development drives demand for properties in 357prestigious neighborhoods. 358Table 7: 2SLS Regression with Robust Standard Errors 359Price 360coefficient 361Robust SE 362z-statistics 363p-value 364[95% CI] 365square 366-52.27434 36711.09248 368-4.71 3690.000 370-74.0152 371-30.53347 372livingRoom 373299.7442 374408.9099 3750.73 3760.464 377-501.7045 3781101.193 379drawingRoom 3801812.467 381407.2673 3824.45 3830.000 3841014.238 3852610.696 386ladderRatio 3872368.047 3881112.697 3892.13 3900.033 391187.2018 3924548.892 393elevator 394663.3836 395404.546 3961.64 3970.101 398-129.512 3991456.279 400subway 401974.9528 402314.9833 4033.10 4040.002 405357.597 4061592.309 407communityAverage 0.8450588 4080.0079132 409106.79 4100.000 4110.8295493 0.8605683 412Constant 413-3711.986 414822.7467 415-4.51 4160.000 417-5324.539 418-2099.432 419Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 420DOI: 10.54254/2754-1169/148/2024.LD19187 421170 422423424===== PAGE 8 (score 33, numeric-paren 0, table-words 11, var-words 10) =====425426 427 428As shown in Table 8, the Chi-square statistic of 14163.62 as well as the p-value smaller than any 429possible significance level indicate that the model has an overall statistically significance. In other 430words, the independent variables collectively are able to explain the variation in the dependent 431variable (price), since the null hypothesis (H0: None of the independent variables in the model explain 432the dependent variable) fails to be rejected. Also, the R-squared value of 0.8688 means that 86.88% 433of the change in 𝑦 (price) can be explained by the independent variables, suggesting the variables are 434suitable predictors. 435Table 8: Other Statistics Associated with the OLS Regression 436Statistics 437Value 438Chi-square statistic 43914163.62 440P-value 4410.0000 442R-squared 4430.8688 444 445Lastly, the endogeneity test (results shown in Table 9) yields p-values that fail to rejects the hull 446hypothesis (H0: Variables are exogenous). There is no convincing evidence that the variables are 447endogenous. Thus, endogeneity issue is effectively alleviated by using bathroom and followers as IVs 448for square. 449Table 9: The Results for Endogeneity Test 450Statistics 451Value 452p-value 453Robust score chi2 (1) 4540.555293 4550.4562 456Robust regression F(1, 3130) 4570.555014 4580.4563 4593.5. Discussion 460By VIF test, White test, residual test, and endogeneity test, the potential issues of the model is detected 461and addressed to persue a more accurate estimates. With this in mind, some implications can be drawn. 462Primarily, the negative coefficient between square and price can be analyzed. This can be due to 463the inability for people - especially the younger generation who do not need very large houses to 464afford the overly high housing prices in Beijing, but have demand to live in Beijing; preference for 465smaller, more centrally located properties or a saturation effect where bigger properties reduce 466marginal price per square meter can be seen. This trend significantly differs from Japan, which tend 467to have similar character as China (Tokyo as the main center with most population centered at, and 468both countries are large economic forces in Asia). According to Inoue et al., factors like geographic 469segmentation and local neighborhood characteristics is the determinant factor in Tokyo; also, in 470Tokyo, properties in Minato-city and Shibuya-city retain high per-square-meter prices especially for 471larger homes [10]. This can be attribute to people living in the expensive area in Tokyo is living there 472from economic booth period, so they already have wealth and holds families and thus prioritize larger 473living spaces in premium locations. By contrast, in Beijing, access to amenities such as subway 474stations dominate buyer preferences, possibly due to people living there is still workers and do not 475have sufficient funds to support families and larger housings, but only have the need to stick in the 476economic center, Beijing. 477When considering the fitness of IVs, the reason why variable bathroom is suitable as an IV for 478square can be because it decently satisfies the two conditions: relevance and exclusion. The number 479of bathrooms is usually determined when the house is designed based on the size of the house and the 480expected living needs, so it is related to the square footage of the house (relevance) and will not 481change due to other fluctuations - namely, will not change following error term (exclusion). On 482Proceedings of ICFTBA 2024 Workshop: Human Capital Management in a Post-Covid World: Emerging Trends and Workplace Strategies 483DOI: 10.54254/2754-1169/148/2024.LD19187 484171 485