1# RECORD 53a228745dc9a32b1002f59f1be59cdca85e461e2# TITLE: Variance analysis and linear regression: Exploring the impact of location factors on the average logarithmic price of pre-owned housing in Shenzhen3# YEAR: 2024.0 VENUE: Theoretical and Natural Science DOI: 10.54254/2753-8818/39/202405984# AUTHORS: Yunzhong Ding; Zehua Tang; Min-Jia Wang5# PAGES: 10 CANDIDATE TABLE PAGES (1-based): [6, 7, 8]6# 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.789===== PAGE 1 (score 10, numeric-paren 0, table-words 0, var-words 10) =====1011Variance analysis and linear regression: Exploring the impact 12of location factors on the average logarithmic price of pre-13owned housing in Shenzhen 14Yunzhong Ding1,4, Zehua Tang2, Minjia Wang3 151College of Arts and Sciences, University of North Carolina at Chapel Hill, NC, 1627599-3140, USA 172School of Electrical Engineering, Suihua University, Suihua,152001, China 183Shenzhen College of International Education, Shenzhen, 518000, China 19 204dingding@ad.unc.edu 21Abstract. The primary purpose of this report is to investigate the impact of locational factors on 22the average prices of second-hand homes in Shenzhen, providing a theoretical foundation for the 23pricing of such properties. To achieve this, the report first establishes indicators to describe the 24characteristics of second-hand homes. Then, it constructs an analysis of the variance model to 25explore the impact of multiple related factors on housing prices regarding the average 26logarithmic price of pre-owned housing in Shenzhen. The model results indicate significant 27correlations between administrative divisions, whether the property is in a school district, the 28orientation of the house, the age of the house, and the area with the logarithmic price per unit 29area of second-hand housing. At the end of the report, two inter-complimentary multivariate 30linear regression models are constructed, and simulated data produced through R studio are also 31provided, and the final model is used for practical application to accurately predict the price of 32second homes under the appropriate conditions. 33Keywords: Average logarithmic price, multivariate linear regression, Shenzhen 341. Introduction 35There has never been any doubt that the real estate industry has long been a decisive factor in pivoting 36the direction of China’s economy. Indeed, it would be an understatement to delineate such a vital 37industry consisting of real estate firms resembling an extensive range of the economic spectrum as the 38pillar of China’s economy; many would instead refer to the industry as the heart and soul of China. Yue 39Geng, a researcher at Anhui Business College of Vocational Technology, depicted the trend of real estate 40value fluctuation in the Modern Business Trade Industry Journal through a bird’s eye view over the past 41decade. She stated that since China implemented the housing system reform in the country in 2003, the 42average sale price of commercial-based residential buildings has grown at an annual rate of about 8.6% 43from 2003 to 2020. Though the momentum for further price inflation was undoubtedly hindered by the 44devastating side effects of the COVID-19 pandemic on the economy and trade, housing costs have 45unexpectedly experienced an anomalous uptick in certain regions of China despite the economic and 46political sabotage toward private-owned real estate companies under the epidemic prevention policies, 47Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation 48DOI: 10.54254/2753-8818/39/20240598 49© 2024 The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 50(https://creativecommons.org/licenses/by/4.0/). 51317 525354===== PAGE 6 (score 23, numeric-paren 0, table-words 3, var-words 12) =====5556prices across districts. Futian stands out with the highest logarithmic price of approximately 3.066, 57translating to an original price of around 21,500 CNY per square meter. Conversely, Longhua is the most 58economical district, with a logarithmic price near 0.173, equating to roughly 1,180 CNY per square 59meter. A comparative analysis of both mean and median values underscores that Futian and Nanshan are 60the priciest districts, while Dapeng and Pingshan are the most affordable, with other districts positioned 61at intermediate levels and exhibiting slight variations. 62Table 2. District Data. 63District 64N 65MU 66SD 67MIN 68MED 69MAX 70Bao’an 71398 721.724 730.305 740.696 751.690 762.772 77Dapeng 78240 791.052 800.309 810.287 821.029 832.077 84Futian 85397 861.949 870.322 880.872 891.913 903.066 91Guangming 92240 931.528 940.252 950.627 961.561 972.098 98Longgang 99240 1001.437 1010.267 1020.657 1031.413 1042.041 105Longhua 106300 1071.720 1080.358 1090.173 1101.749 1112.591 112Luohu 113300 1141.573 1150.329 1160.531 1171.545 1182.521 119Nanshan 120405 1212.077 1220.337 1231.308 1242.053 1253.005 126Pingshan 127240 1281.277 1290.179 1300.607 1311.285 1321.903 133Yantian 134240 1351.520 1360.248 1371.049 1381.464 1392.534 140Applying the same analysis method previously for district variation, the study examines how property 141values are influenced by age, location, and features. Older properties in central areas, south-facing 142homes in Shenzhen, and properties in school districts command higher prices. Sea views and proximity 143to subway stations significantly increase value. Elevators and renovations also boost prices, reflecting 144preferences for convenience and reduced renovation needs. These factors underscore the complex 145interplay of location, amenities, and property characteristics in determining real estate values. 1463.2. Model construction 147Building on the descriptive analysis, this report leverages R language to delve deeper into the 148relationship between the logarithmic prices of second-hand houses and various explanatory variables. 149In order to build the model, we need to define the parameters first. 150Table 3. Parameters Definition 151Parameters 152Definition 153Logarithmic Price 154Y 155Administrative Division 156X1 157School 158X2 159Subway 160X3 161Sea 162X4 163Elevator 164X5 165Renovation 166X6 167Age 168X7 169Orientation 170X8 171Area 172X9 173Random Disturbance 174ε 175From this we can build model A: 176Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9 + ε 177(1) 178The implementation is carried out in R, with parameter estimation and testing results shown in Table 1794. The model’s overall F-test is highly significant (P-<0.001), indicating that at least one of the 180Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation 181DOI: 10.54254/2753-8818/39/20240598 182322 183184185===== PAGE 7 (score 29, numeric-paren 0, table-words 8, var-words 8) =====186187considered factors significantly impacts the logarithmic price. The adjusted R-squared value, R2=0.637, 188reflects the proportion of variance explained by the model. A closer examination of the t-test results for 189each explanatory variable reveals the following insights: 190Prices per unit area vary significantly across districts, with Dapeng being the lowest and Nanshan 191the highest, 20.6% higher than Bao’an. Properties with sea views are, on average, 45.2% more expensive 192than those without. School district properties are 27.3% more expensive than non-school district ones. 193There’s a slight decline in price with increasing property age. Additionally, there’s a positive relationship 194between price and area; larger properties command higher prices. In summary, the value attributed to 195school district properties varies by region. 196Table 4. Model A results. 197Variable 198Estimate 199Std.Error 200P 201Note 202Intercept 2031.566 2040.045 205<0.001 206Reference group: 207district Bao’an 208district Dapeng 209-0.794 2100.027 211<0.001 212district Futian 2130.172 2140.019 215<0.001 216district Guangming 217-0.332 2180.026 219<0.001 220district Longgang 221-0.448 2220.021 223<0.001 224district Longhua 225-0.115 2260.020 227<0.001 228district Luohu 229-0.139 2300.020 231<0.001 232district Nanshan 2330.206 2340.019 235<0.001 236district Pingshan 237-0.546 2380.025 239<0.001 240district Yangtian 241-0.462 2420.027 243<0.001 244school 2450.273 2460.011 247<0.001 248 249subway 250-0.014 2510.018 252 253 254sea 2550.452 2560.032 257<0.001 258 259elevator 2600.052 2610.029 262 263 264renovation 2650.033 2660.022 267 268 269age New house 2700.069 2710.023 272 273Reference group: 274middle-aged houses 275age Old house 276-0.177 2770.015 278<0.001 279age relatively new house 280-0.004 2810.014 282 283age as older house 284-0.024 2850.015 286 287orientation 2880.009 2890.010 290 291 292area 2930.001 2940 295<0.001 296 297Model Global Tests 298P-value<0.001 299 300Adjusted R2 3010.63 302The advantage of Model A is that because it is a multi-factor model, it integrates multiple single 303factors under the same model framework for comparison, and it can be simple and fast to analyze the 304discrete variables under the regression analysis framework, but the disadvantage is also too simple, the 305interaction between different factors is not taken into account, and the expansion is too poor, so a new 306model is established with the interaction of the two factors of administrative districts and the school and 307Model B is established: 308Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β5X5 + β6X6 + β7X7 + β8X8 + β9X9 + γX1 ∗X2 + ε (2) 309The results for Model B, as displayed in Table 5, emphasize the interaction between administrative 310division and school district availability. Initially, this model is compared with the model from Table 4, 311which lacks the interaction term “Administrative Division * School District Availability,” using variance 312analysis. The highly significant F-test (Table 6) indicates the presence of this interaction effect. This 313finding suggests that the impact of being in a school district varies across different administrative 314divisions. For instance, in the Bao’an district, being in a school district can raise the property price by 315about 55.3% compared to properties not in a school district, which is a substantial increase. Given that 316Bao’an has few school district properties, the interaction between “Administrative Division” and 317Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation 318DOI: 10.54254/2753-8818/39/20240598 319323 320321322===== PAGE 8 (score 24, numeric-paren 0, table-words 4, var-words 7) =====323324“School District Availability” significantly influences property prices. Even in districts like Futian and 325Nanshan, where there are more school district properties, the presence of a school still offers a positive 326price uplift. It’s important to note that the negative interaction coefficients for Futian and Nanshan do 327not imply a negative effect on school district properties in these areas but rather indicate that the effect 328is not as pronounced as in Bao’an. 329Table 5. Model B results. 330Variable 331Estimate 332Std.Error 333P 334Note 335Intercept 3361.586 3370.045 338<0.001 339Reference group: 340district Bao’an 341district Dapeng 342-0.789 3430.027 344<0.001 345district Futian 3460.184 3470.021 348<0.001 349district Guangming 350-0.293 3510.027 352<0.001 353district Longgang 354-0.493 3550.025 356<0.001 357district Longhua 358-0.156 3590.021 360<0.001 361district Luohu 362-0.156 3630.021 364<0.001 365district Nanshan 3660.234 3670.021 368<0.001 369district Pingshan 370-0.537 3710.025 372<0.001 373district Yantian 374-0.292 3750.037 376<0.001 377school 3780.553 3790.125 380<0.001 381 382subway 383-0.003 3840.017 3850.859 386 387sea 3880.449 3890.032 390<0.001 391 392elevator 3930.029 3940.029 3950.318 396 397renovation 3980.020 3990.021 4000.349 401 402age New house 4030.065 4040.023 4050.005 406Reference group: 407age middle-aged 408houses 409age Old house 410-0.161 4110.015 412<0.001 413age relatively new house 4140.008 4150.014 4160.538 417age as older house 418-0.009 4190.015 4200.531 421orientation 4220.010 4230.010 4240.302 425 426area 4270.001 4280 429<0.001 430 431district Dapeng*school 432-0.139 4330.148 4340.345 435Reference group: 436district 437Bao’an*school 438 439district Futian*school 440-0.309 4410.128 4420.016 443district Guangming*school 444-0.483 4450.134 446<0.001 447district Longgang*school 448-0.167 4490.130 4500.198 451district Longhua*school 452-0.079 4530.130 4540.545 455district Longhu*school 456-0.192 4570.131 4580.143 459district Nanshan*school 460-0.346 4610.128 4620.007 463district Pingshan*school 464-0.243 4650.137 4660.075 467district Yantian*school 468-0.498 4690.131 470<0.001 471Model Global Tests 472P-value<0.001 473 474Adjusted R2 4750.643 476Table 6. Model Comparison. 477Model 478Res.Df 479RSS 480Df 481Pr(>F) 482A 4832979 484193.16 485 486 487B 4882970 489185.86 4909 491<0.001 4923.3. Discussion 493As can be seen from the results of Model B, its advantage lies in its additivity, which allows it to interact 494with multiple factors to improve the accuracy of the model prediction, but this is also its disadvantage 495because it is too additive, which will greatly increase the complexity of the model if it analyzes the 496interaction of too many factors at the same time. Moreover, for the degree of influence of the interaction, 497Proceedings of the 2nd International Conference on Mathematical Physics and Computational Simulation 498DOI: 10.54254/2753-8818/39/20240598 499324 500501502===== PAGE 9 (score 17, numeric-paren 0, table-words 1, var-words 15) =====503504a rigorous statistical model is needed to test it, which also requires more workload. But overall, Model 505B is still the basic direction of the optimal model. 506This model has a wide range of applications. It can assist decision-makers in understanding the 507mechanisms behind property pricing and enable investors to identify potential investment opportunities. 508Primarily, the model serves as a valuable tool for facilitating second-hand housing transactions. For 509illustrative purposes, let’s use R language and Model B for a simple simulation. 510Consider a worker looking to purchase a relatively older home in the Nanshan district. The desired 511property faces south, aligning with future educational needs. Thus, being in a school district near a 512subway station is essential. The property should have an elevator, and be fully renovated to save on time 513and costs. A sea view is not a requirement for this buyer. 514Based on these parameters, this paper estimates the property’s price per square meter to be 515approximately 91,300 CNY, making the total price around 8,216,000 CNY. This example showcases 516how the model can be applied in real-world scenarios to predict property prices based on a set of defined 517factors, providing valuable insights for potential buyers and investors. 5184. Conclusion 519This report utilizes the logarithmic price per unit area of second-hand houses as the dependent variable, 520crafting an array of indicators to characterize second-hand housing features. These variables include 521administrative division, school district availability, sea view availability, house orientation, housing area, 522house age, proximity to the subway, elevator availability, and renovation status, totaling 9 independent 523variables. In addition, Model A and Model B were established to analyze the relationship between 524factors and house prices, to summarize the advantages and disadvantages of each of the two models, and 525to draw conclusions. The key conclusions of the report are summarized as follows: 526Administrative division, school district availability, sea view availability, house age, and the housing 527area, show a significant correlation with the logarithmic price per unit area. In contrast, proximity to the 528subway, renovation status, elevator availability, and house orientation are not as significant. In the 529Bao’an district, properties within school districts command higher prices, highlighting the potential for 530personalized property price assessment products. Given the complexity of factors influencing property 531prices, future research could incorporate additional elements, such as the proximity to top-tier hospitals 532or supermarkets. Expanding the study to include all districts in Shenzhen could also yield different 533insights. This analysis not only aids in understanding the current market dynamics but also paves the 534way for more nuanced and tailored approaches to property valuation in the realm of second-hand 535housing. 536Authors Contribution 537All the authors contributed equally and their names were listed in alphabetical order. 538References 539[1] 540Geng Y and Xu X L 2022 Research on the economic impact mechanism of COVID-19 on real 541estate prices. Modern Commerce and Trade Industry, 43(17), 13-14. 542[2] 543Xie L 2023 Research and thinking on the Impact of “Transfer of ownership with mortgage” on 544Real estate Market. Real Estate World, 19-22. 545[3] 546Zhang D 2024 The second-hand housing market in key cities achieved a “red start” in the Spring 547Festival holiday of the Year of the Dragon. The securities times. 548[4] 549Mi W 2018 Exploring the influencing factors of second-hand housing price. 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