1# RECORD 71977f92d0454f114374d8e7935fc5debd79713d2# TITLE: Predicting Housing Price Using Regression Analysis: A Study Based on California Housing Price3# YEAR: 2025.0 VENUE: Theoretical and Natural Science DOI: 10.54254/2753-8818/2025.230054# AUTHORS: Yiting Gu5# PAGES: 7 CANDIDATE TABLE PAGES (1-based): [4, 5]6# ABSTRACT: The purpose of the essay is to examine the factors influencing housing prices in California, which can help people to obtain a perspective to observe the US economy. This paper uses the California House Price dataset to analyze the factors influencing house prices of blocks of California by performing correlation analysis and multiple linear regression. From the analyses, it is discovered that median income has the strongest correlation with median house price of blocks in California. A model predicting California house prices is also shown. It is observed that median income has the most significant correlation with median housing price in California from the correlation analysis. Additionally, the linear regression model is obtained to estimate the housing prices, with a good fit of the R2 value at 0.637. Though the issue of multicollinearity occurs, this model still provides an insight into explaining housing prices in California. For a more advanced housing price predicting model, this variable and other factors of blocks in California may be included.789===== PAGE 1 (score 7, numeric-paren 0, table-words 1, var-words 5) =====1011Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation12DOI: 10.54254/2753-8818/2025.2300513© 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.014(https://creativecommons.org/licenses/by/4.0/).1512816 17 18Predicting Housing Price Using Regression Analysis: A 19Study Based on California Housing Price 20Yiting Gu 21Shanghai International High School of BANZ, Shanghai, China 22gu.yiting@outlook.com 23Abstract: The purpose of the essay is to examine the factors influencing housing prices in 24California, which can help people to obtain a perspective to observe the US economy. This 25paper uses the California House Price dataset to analyze the factors influencing house prices 26of blocks of California by performing correlation analysis and multiple linear regression. 27From the analyses, it is discovered that median income has the strongest correlation with 28median house price of blocks in California. A model predicting California house prices is 29also shown. It is observed that median income has the most significant correlation with 30median housing price in California from the correlation analysis. Additionally, the linear 31regression model is obtained to estimate the housing prices, with a good fit of the R2 value at 320.637. Though the issue of multicollinearity occurs, this model still provides an insight into 33explaining housing prices in California. For a more advanced housing price predicting model, 34this variable and other factors of blocks in California may be included. 35Keywords: Housing price, linear regression model, influencing factors. 361. 37Introduction 38In modern society, where a house usually acts as one of the most significant investments made by 39people, the housing market plays a pivotal role in shaping both individual wealth and indicating 40financial stability [1]. Therefore, it is important to examine the factors influencing housing prices for 41both buyers and policymakers. As the state whose GDP comprises the biggest proportion of the GDP 42in the United States, the housing price in California is influenced by a complex interplay of different 43factors [2]. Therefore, the purpose of the essay is to examine the factors influencing housing prices 44in California, which can help people to obtain a perspective to observe the US economy. 45Housing prices can be predicted using multiple methods according to different conditions. Lim et 46al. compared the accuracy of artificial neural networks (ANN), autoregressive integrated moving 47average (A, and multiple regression analysis (MRA) in predicting Singapore condominium prices and 48discovered that the ANN model can reach high precision in multiple ways [3]. Also, focusing on the 49differences between the ANN and the MRA models, Nguyen and Cripps concluded that the ANN 50performs better than the MRA when using a moderate to large sample size [4]. Truong et al. explored 51different models in machine learning for predicting house prices using the Beijing house price dataset 52and found out that the error occurs the least in the Random Forest method, in spite of overfitting 53problems [5]. 54The specific method of linear regression can be applied in multiple ways. Fedotova et al. described 55a study of the application of MRL in software development estimation and showed that the test using 565758===== PAGE 4 (score 12, numeric-paren 5, table-words 1, var-words 5) =====5960Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation61DOI: 10.54254/2753-8818/2025.230056213163 64 65 66Figure 2: Scatter plot of x1 and y 67Similarly, x7 shows scattered data points with no visible patterns, suggesting that the number of 68households in California is not strongly predictive of housing prices in this dataset (Figure 3). 69 70Figure 3: Scatter plot of x7 and y 713.2. Correlation analysis 72To further quantify the correlation between the variables, an additional analysis is conducted using 73the Pearson correlation coefficients. The results are shown in Figure 4. The Pearson correlation 74analysis reveals several relationships between median house prices in blocks in California and the 75independent variables as stated. Among them, median income shows the strongest positive correlation 76with California house prices (0.69), suggesting a substantial association. Other variables, such as 77housing median age (0.11), total rooms (0.13), total bedrooms (0.05), and households (0.07), also 78show positive correlations with the dependent variable, though weaker in magnitude. 798081===== PAGE 5 (score 16, numeric-paren 0, table-words 4, var-words 2) =====8283Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation84DOI: 10.54254/2753-8818/2025.230058513286 87 88 89Figure 4: Relevance between independent and dependent variables 90Conversely, latitude (-0.14), longitude (-0.05), and population (-0.025) demonstrate significant 91negative correlations with California house prices, indicating inverse relationships. Despite their 92statistical significance, the correlation strengths remain relatively weak, except for median income, 93which stands out as the most influential factor. These findings highlight the need for further analysis 94and perhaps transformation of these variables before incorporating them into a regression model. 953.3. Multiple Linear Regression (MLR) analysis 96The results of multiple linear regression analysis are shown in Table 2: 97Table 2: MLR results (n=20433) 98 99B 100S.E. 101Beta 102T 103P 104VIF 105tolerance 106Constant 107-3585395.747 10862900.543 109- 110-57.001 1110.000 112- 113- 114x1 115-42730.120 116717.087 117-0.742 118-59.588 1190.000 1208.714 1210.115 122x2 123-42509.737 124676.952 125-0.787 126-62.796 1270.000 1288.829 1290.113 130x3 1311157.900 13243.389 1330.126 13426.687 1350.000 1361.260 1370.794 138x4 139-8.250 1400.794 141-0.156 142-10.387 1430.000 14412.717 1450.079 146x5 147113.821 1486.931 1490.415 15016.423 1510.000 15236.004 1530.028 154x6 155-38.386 1561.084 157-0.377 158-35.407 1590.000 1606.371 1610.157 162x7 16347.701 1647.547 1650.158 1666.321 1670.000 16835.136 1690.028 170x8 17140297.522 172337.207 1730.663 174119.504 1750.000 1761.732 1770.578 178R2 1790.637 180 181From Table 2, the formula of the model can be obtained: 182 183𝑦 = 3585395.747 − 42730.120𝑥1 −⋯ + 40297.522𝑥8 184(2) 185186187===== PAGE 6 (score 20, numeric-paren 0, table-words 5, var-words 9) =====188189Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation190DOI: 10.54254/2753-8818/2025.23005191133192 193 194The value of R2 is 0.637, suggesting a good fit of the model and that the independent variables 195explain 63.7% of the changes in California house prices. The results show that x3, x5, x7, and x8 196have a significant positive impact on y, while x1, x2, x4, and x6 have a significant negative impact 197on y. The multicollinearity test for the model reveals that the VIF values for x4, x5 and x7 exceed 10, 198indicating the presence of collinearity issues, which could be resolved by applying stepwise 199regression or ridge regression further. In addition, P values, which explain the significance of the 200results, are all 0.000. This indicates that the independent variables have significant impacts on housing 201prices in California. 202The multiple linear regression analysis was performed on a substantial sample of 20,433 203observations, yielding an R² of 0.637 and indicating that approximately 63.7% of the variance in the 204dependent variable is explained by the predictors. The intercept was estimated at -3585395.747, 205which, given the measurement scales involved, requires cautious interpretation. All predictor 206variables (x1 through x8) exhibited statistically significant effects (p < 0.001). The standardized beta 207coefficients reveal that x2 (β = -0.787) and x1 (β = -0.742) exerted strong negative influences, whereas 208x8 (β = 0.663) had a robust positive effect on the outcome variable. Additionally, despite the high 209statistical significance of these coefficients, several predictors (notably x4, x5, and x7) displayed high 210variance inflation factors (VIFs of 12.717, 36.004, and 35.136, respectively), accompanied by very 211low tolerance values, signaling a potential issue of multicollinearity that may undermine the stability 212and interpretability of the coefficient estimates. 2134. 214Conclusion 215This study is based on the California House Price dataset, with 20433 usable data entries for analysis. 216Correlation analysis and multiple linear regression are performed to investigate factors influencing 217house prices in California. It is observed that median income has the most significant correlation with 218median housing price in California from the correlation analysis. Additionally, the linear regression 219model is obtained to estimate the housing prices, with a good fit of the R2 value at 0.637. 220During the MLR analysis in this study, the issue of multicollinearity has been found among total 221rooms, total bedrooms, and households. This implies that there is a strong correlation among these 222variables, which means they share a lot of information and influence each other, leading to the 223instability of the estimated regression coefficients, hence causing the model to be unreliable. 224Therefore, further analysis, for instance, ridge regression, can be conducted to enhance this model by 225eliminating highly correlated independent variables. This study excludes an independent variable of 226ocean proximity, which is included in the original dataset. Hence, for a more advanced housing price 227predicting model, this variable and other factors of blocks in California (transportation convenience, 228infrastructure, etc.) may be included. 229References 230[1] Tsatsaronis, K. and Zhu, H. (2004) What drives housing price dynamics: cross-country evidence. BIS Quarterly 231Review, March. 232[2] Bohn, S. and Duan, J., (2025) California’s Economy, Public Institute of California. International Journal of 233Information Engineering & Electronic Business. 234[3] Park, B. and Bae, J.K. (2015) Using machine learning algorithms for housing price prediction: The case of Fairfax 235County, Virginia housing data. Expert systems with applications, 42(6), 2928-2934. 236[4] Nguyen, N. and Cripps, A. (2001) Predicting housing value: A comparison of multiple regression analysis and 237artificial neural networks. Journal of real estate research, 22(3), 313-336. 238[5] Truong, Q., Nguyen, M., Dang, H. and Mei, B. (2020) Housing price prediction via improved machine learning 239techniques. Procedia Computer Science, 174, 433-442. 240[6] Fedotova, O., Teixeira, L. and Alvelos, H. (2013) Software Effort Estimation with Multiple Linear Regression: 241Review and Practical Application. J. Inf. Sci. Eng., 29(5), 925-945. 242