# RECORD 53a228745dc9a32b1002f59f1be59cdca85e461e # TITLE: Variance analysis and linear regression: Exploring the impact of location factors on the average logarithmic price of pre-owned housing in Shenzhen # YEAR: 2024.0 VENUE: Theoretical and Natural Science DOI: 10.54254/2753-8818/39/20240598 # AUTHORS: Yunzhong Ding; Zehua Tang; Min-Jia Wang # PAGES: 10 CANDIDATE TABLE PAGES (1-based): [6, 7, 8] # ABSTRACT: The primary purpose of this report is to investigate the impact of locational factors on the average prices of second-hand homes in Shenzhen, providing a theoretical foundation for the pricing of such properties. To achieve this, the report first establishes indicators to describe the characteristics of second-hand homes. Then, it constructs an analysis of the variance model to explore the impact of multiple related factors on housing prices regarding the average logarithmic price of pre-owned housing in Shenzhen. The model results indicate significant correlations between administrative divisions, whether the property is in a school district, the orientation of the house, the age of the house, and the area with the logarithmic price per unit area of second-hand housing. At the end of the report, two inter-complimentary multivariate linear regression models are constructed, and simulated data produced through R studio are also provided, and the final model is used for practical application to accurately predict the price of second homes under the appropriate conditions. ===== PAGE 1 (score 10, numeric-paren 0, table-words 0, var-words 10) ===== Variance analysis and linear regression: Exploring the impact of location factors on the average logarithmic price of pre- owned housing in Shenzhen Yunzhong Ding1,4, Zehua Tang2, Minjia Wang3 1College of Arts and Sciences, University of North Carolina at Chapel Hill, NC, 27599-3140, USA 2School of Electrical Engineering, Suihua University, Suihua,152001, China 3Shenzhen College of International Education, Shenzhen, 518000, China 4dingding@ad.unc.edu Abstract. The primary purpose of this report is to investigate the impact of locational factors on the average prices of second-hand homes in Shenzhen, providing a theoretical foundation for the pricing of such properties. To achieve this, the report first establishes indicators to describe the characteristics of second-hand homes. Then, it constructs an analysis of the variance model to explore the impact of multiple related factors on housing prices regarding the average logarithmic price of pre-owned housing in Shenzhen. The model results indicate significant correlations between administrative divisions, whether the property is in a school district, the orientation of the house, the age of the house, and the area with the logarithmic price per unit area of second-hand housing. At the end of the report, two inter-complimentary multivariate linear regression models are constructed, and simulated data produced through R studio are also provided, and the final model is used for practical application to accurately predict the price of second homes under the appropriate conditions. Keywords: Average logarithmic price, multivariate linear regression, Shenzhen 1. Introduction There has never been any doubt that the real estate industry has long been a decisive factor in pivoting the direction of China’s economy. Indeed, it would be an understatement to delineate such a vital industry consisting of real estate firms resembling an extensive range of the economic spectrum as the pillar of China’s economy; many would instead refer to the industry as the heart and soul of China. Yue Geng, a researcher at Anhui Business College of Vocational Technology, depicted the trend of real estate value fluctuation in the Modern Business Trade Industry Journal through a bird’s eye view over the past decade. She stated that since China implemented the housing system reform in the country in 2003, the average sale price of commercial-based residential buildings has grown at an annual rate of about 8.6% from 2003 to 2020. Though the momentum for further price inflation was undoubtedly hindered by the devastating side effects of the COVID-19 pandemic on the economy and trade, housing costs have unexpectedly experienced an anomalous uptick in certain regions of China despite the economic and political sabotage toward private-owned real estate companies under the epidemic prevention policies, Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/39/20240598 © 2024 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/). 317 ===== PAGE 6 (score 23, numeric-paren 0, table-words 3, var-words 12) ===== prices across districts. Futian stands out with the highest logarithmic price of approximately 3.066, translating to an original price of around 21,500 CNY per square meter. Conversely, Longhua is the most economical district, with a logarithmic price near 0.173, equating to roughly 1,180 CNY per square meter. A comparative analysis of both mean and median values underscores that Futian and Nanshan are the priciest districts, while Dapeng and Pingshan are the most affordable, with other districts positioned at intermediate levels and exhibiting slight variations. Table 2. District Data. District N MU SD MIN MED MAX Bao’an 398 1.724 0.305 0.696 1.690 2.772 Dapeng 240 1.052 0.309 0.287 1.029 2.077 Futian 397 1.949 0.322 0.872 1.913 3.066 Guangming 240 1.528 0.252 0.627 1.561 2.098 Longgang 240 1.437 0.267 0.657 1.413 2.041 Longhua 300 1.720 0.358 0.173 1.749 2.591 Luohu 300 1.573 0.329 0.531 1.545 2.521 Nanshan 405 2.077 0.337 1.308 2.053 3.005 Pingshan 240 1.277 0.179 0.607 1.285 1.903 Yantian 240 1.520 0.248 1.049 1.464 2.534 Applying the same analysis method previously for district variation, the study examines how property values are influenced by age, location, and features. Older properties in central areas, south-facing homes in Shenzhen, and properties in school districts command higher prices. Sea views and proximity to subway stations significantly increase value. Elevators and renovations also boost prices, reflecting preferences for convenience and reduced renovation needs. These factors underscore the complex interplay of location, amenities, and property characteristics in determining real estate values. 3.2. Model construction Building on the descriptive analysis, this report leverages R language to delve deeper into the relationship between the logarithmic prices of second-hand houses and various explanatory variables. In order to build the model, we need to define the parameters first. Table 3. Parameters Definition Parameters Definition Logarithmic Price Y Administrative Division X1 School X2 Subway X3 Sea X4 Elevator X5 Renovation X6 Age X7 Orientation X8 Area X9 Random Disturbance ε From this we can build model A: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9 + ε (1) The implementation is carried out in R, with parameter estimation and testing results shown in Table 4. The model’s overall F-test is highly significant (P-<0.001), indicating that at least one of the Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/39/20240598 322 ===== PAGE 7 (score 29, numeric-paren 0, table-words 8, var-words 8) ===== considered factors significantly impacts the logarithmic price. The adjusted R-squared value, R2=0.637, reflects the proportion of variance explained by the model. A closer examination of the t-test results for each explanatory variable reveals the following insights: Prices per unit area vary significantly across districts, with Dapeng being the lowest and Nanshan the highest, 20.6% higher than Bao’an. Properties with sea views are, on average, 45.2% more expensive than those without. School district properties are 27.3% more expensive than non-school district ones. There’s a slight decline in price with increasing property age. Additionally, there’s a positive relationship between price and area; larger properties command higher prices. In summary, the value attributed to school district properties varies by region. Table 4. Model A results. Variable Estimate Std.Error P Note Intercept 1.566 0.045 <0.001 Reference group: district Bao’an district Dapeng -0.794 0.027 <0.001 district Futian 0.172 0.019 <0.001 district Guangming -0.332 0.026 <0.001 district Longgang -0.448 0.021 <0.001 district Longhua -0.115 0.020 <0.001 district Luohu -0.139 0.020 <0.001 district Nanshan 0.206 0.019 <0.001 district Pingshan -0.546 0.025 <0.001 district Yangtian -0.462 0.027 <0.001 school 0.273 0.011 <0.001 subway -0.014 0.018 sea 0.452 0.032 <0.001 elevator 0.052 0.029 renovation 0.033 0.022 age New house 0.069 0.023 Reference group: middle-aged houses age Old house -0.177 0.015 <0.001 age relatively new house -0.004 0.014 age as older house -0.024 0.015 orientation 0.009 0.010 area 0.001 0 <0.001 Model Global Tests P-value<0.001 Adjusted R2 0.63 The advantage of Model A is that because it is a multi-factor model, it integrates multiple single factors under the same model framework for comparison, and it can be simple and fast to analyze the discrete variables under the regression analysis framework, but the disadvantage is also too simple, the interaction between different factors is not taken into account, and the expansion is too poor, so a new model is established with the interaction of the two factors of administrative districts and the school and Model B is established: Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9 + γX1 ∗X2 + ε (2) The results for Model B, as displayed in Table 5, emphasize the interaction between administrative division and school district availability. Initially, this model is compared with the model from Table 4, which lacks the interaction term “Administrative Division * School District Availability,” using variance analysis. The highly significant F-test (Table 6) indicates the presence of this interaction effect. This finding suggests that the impact of being in a school district varies across different administrative divisions. For instance, in the Bao’an district, being in a school district can raise the property price by about 55.3% compared to properties not in a school district, which is a substantial increase. Given that Bao’an has few school district properties, the interaction between “Administrative Division” and Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/39/20240598 323 ===== PAGE 8 (score 24, numeric-paren 0, table-words 4, var-words 7) ===== “School District Availability” significantly influences property prices. Even in districts like Futian and Nanshan, where there are more school district properties, the presence of a school still offers a positive price uplift. It’s important to note that the negative interaction coefficients for Futian and Nanshan do not imply a negative effect on school district properties in these areas but rather indicate that the effect is not as pronounced as in Bao’an. Table 5. Model B results. Variable Estimate Std.Error P Note Intercept 1.586 0.045 <0.001 Reference group: district Bao’an district Dapeng -0.789 0.027 <0.001 district Futian 0.184 0.021 <0.001 district Guangming -0.293 0.027 <0.001 district Longgang -0.493 0.025 <0.001 district Longhua -0.156 0.021 <0.001 district Luohu -0.156 0.021 <0.001 district Nanshan 0.234 0.021 <0.001 district Pingshan -0.537 0.025 <0.001 district Yantian -0.292 0.037 <0.001 school 0.553 0.125 <0.001 subway -0.003 0.017 0.859 sea 0.449 0.032 <0.001 elevator 0.029 0.029 0.318 renovation 0.020 0.021 0.349 age New house 0.065 0.023 0.005 Reference group: age middle-aged houses age Old house -0.161 0.015 <0.001 age relatively new house 0.008 0.014 0.538 age as older house -0.009 0.015 0.531 orientation 0.010 0.010 0.302 area 0.001 0 <0.001 district Dapeng*school -0.139 0.148 0.345 Reference group: district Bao’an*school district Futian*school -0.309 0.128 0.016 district Guangming*school -0.483 0.134 <0.001 district Longgang*school -0.167 0.130 0.198 district Longhua*school -0.079 0.130 0.545 district Longhu*school -0.192 0.131 0.143 district Nanshan*school -0.346 0.128 0.007 district Pingshan*school -0.243 0.137 0.075 district Yantian*school -0.498 0.131 <0.001 Model Global Tests P-value<0.001 Adjusted R2 0.643 Table 6. Model Comparison. Model Res.Df RSS Df Pr(>F) A 2979 193.16 B 2970 185.86 9 <0.001 3.3. Discussion As can be seen from the results of Model B, its advantage lies in its additivity, which allows it to interact with multiple factors to improve the accuracy of the model prediction, but this is also its disadvantage because it is too additive, which will greatly increase the complexity of the model if it analyzes the interaction of too many factors at the same time. Moreover, for the degree of influence of the interaction, Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/39/20240598 324 ===== PAGE 9 (score 17, numeric-paren 0, table-words 1, var-words 15) ===== a rigorous statistical model is needed to test it, which also requires more workload. But overall, Model B is still the basic direction of the optimal model. This model has a wide range of applications. It can assist decision-makers in understanding the mechanisms behind property pricing and enable investors to identify potential investment opportunities. Primarily, the model serves as a valuable tool for facilitating second-hand housing transactions. For illustrative purposes, let’s use R language and Model B for a simple simulation. Consider a worker looking to purchase a relatively older home in the Nanshan district. The desired property faces south, aligning with future educational needs. Thus, being in a school district near a subway station is essential. The property should have an elevator, and be fully renovated to save on time and costs. A sea view is not a requirement for this buyer. Based on these parameters, this paper estimates the property’s price per square meter to be approximately 91,300 CNY, making the total price around 8,216,000 CNY. This example showcases how the model can be applied in real-world scenarios to predict property prices based on a set of defined factors, providing valuable insights for potential buyers and investors. 4. Conclusion This report utilizes the logarithmic price per unit area of second-hand houses as the dependent variable, crafting an array of indicators to characterize second-hand housing features. These variables include administrative division, school district availability, sea view availability, house orientation, housing area, house age, proximity to the subway, elevator availability, and renovation status, totaling 9 independent variables. In addition, Model A and Model B were established to analyze the relationship between factors and house prices, to summarize the advantages and disadvantages of each of the two models, and to draw conclusions. The key conclusions of the report are summarized as follows: Administrative division, school district availability, sea view availability, house age, and the housing area, show a significant correlation with the logarithmic price per unit area. In contrast, proximity to the subway, renovation status, elevator availability, and house orientation are not as significant. In the Bao’an district, properties within school districts command higher prices, highlighting the potential for personalized property price assessment products. Given the complexity of factors influencing property prices, future research could incorporate additional elements, such as the proximity to top-tier hospitals or supermarkets. Expanding the study to include all districts in Shenzhen could also yield different insights. This analysis not only aids in understanding the current market dynamics but also paves the way for more nuanced and tailored approaches to property valuation in the realm of second-hand housing. Authors Contribution All the authors contributed equally and their names were listed in alphabetical order. References [1] Geng Y and Xu X L 2022 Research on the economic impact mechanism of COVID-19 on real estate prices. Modern Commerce and Trade Industry, 43(17), 13-14. [2] Xie L 2023 Research and thinking on the Impact of “Transfer of ownership with mortgage” on Real estate Market. Real Estate World, 19-22. [3] Zhang D 2024 The second-hand housing market in key cities achieved a “red start” in the Spring Festival holiday of the Year of the Dragon. The securities times. [4] Mi W 2018 Exploring the influencing factors of second-hand housing price. Central China Normal University. [5] Guo Y, Yu H S and Ke J W 2021 Study on the influencing factors of second-hand house price in Yantai City based on covariance regression. Journal of Ludong University (Natural Science Edition), 38(3): 232-240. [6] Ke Y C 2022 Beijing Haidian district, second-hand housing prices influence factors analysis. Beijing university of posts and telecommunications. Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/39/20240598 325