# RECORD 71977f92d0454f114374d8e7935fc5debd79713d # TITLE: Predicting Housing Price Using Regression Analysis: A Study Based on California Housing Price # YEAR: 2025.0 VENUE: Theoretical and Natural Science DOI: 10.54254/2753-8818/2025.23005 # AUTHORS: Yiting Gu # PAGES: 7 CANDIDATE TABLE PAGES (1-based): [4, 5] # 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. ===== PAGE 1 (score 7, numeric-paren 0, table-words 1, var-words 5) ===== Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/2025.23005 © 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/). 128 Predicting Housing Price Using Regression Analysis: A Study Based on California Housing Price Yiting Gu Shanghai International High School of BANZ, Shanghai, China gu.yiting@outlook.com 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. Keywords: Housing price, linear regression model, influencing factors. 1. Introduction In modern society, where a house usually acts as one of the most significant investments made by people, the housing market plays a pivotal role in shaping both individual wealth and indicating financial stability [1]. Therefore, it is important to examine the factors influencing housing prices for both buyers and policymakers. As the state whose GDP comprises the biggest proportion of the GDP in the United States, the housing price in California is influenced by a complex interplay of different factors [2]. Therefore, 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. Housing prices can be predicted using multiple methods according to different conditions. Lim et al. compared the accuracy of artificial neural networks (ANN), autoregressive integrated moving average (A, and multiple regression analysis (MRA) in predicting Singapore condominium prices and discovered that the ANN model can reach high precision in multiple ways [3]. Also, focusing on the differences between the ANN and the MRA models, Nguyen and Cripps concluded that the ANN performs better than the MRA when using a moderate to large sample size [4]. Truong et al. explored different models in machine learning for predicting house prices using the Beijing house price dataset and found out that the error occurs the least in the Random Forest method, in spite of overfitting problems [5]. The specific method of linear regression can be applied in multiple ways. Fedotova et al. described a study of the application of MRL in software development estimation and showed that the test using ===== PAGE 4 (score 12, numeric-paren 5, table-words 1, var-words 5) ===== Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/2025.23005 131 Figure 2: Scatter plot of x1 and y Similarly, x7 shows scattered data points with no visible patterns, suggesting that the number of households in California is not strongly predictive of housing prices in this dataset (Figure 3). Figure 3: Scatter plot of x7 and y 3.2. Correlation analysis To further quantify the correlation between the variables, an additional analysis is conducted using the Pearson correlation coefficients. The results are shown in Figure 4. The Pearson correlation analysis reveals several relationships between median house prices in blocks in California and the independent variables as stated. Among them, median income shows the strongest positive correlation with California house prices (0.69), suggesting a substantial association. Other variables, such as housing median age (0.11), total rooms (0.13), total bedrooms (0.05), and households (0.07), also show positive correlations with the dependent variable, though weaker in magnitude. ===== PAGE 5 (score 16, numeric-paren 0, table-words 4, var-words 2) ===== Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/2025.23005 132 Figure 4: Relevance between independent and dependent variables Conversely, latitude (-0.14), longitude (-0.05), and population (-0.025) demonstrate significant negative correlations with California house prices, indicating inverse relationships. Despite their statistical significance, the correlation strengths remain relatively weak, except for median income, which stands out as the most influential factor. These findings highlight the need for further analysis and perhaps transformation of these variables before incorporating them into a regression model. 3.3. Multiple Linear Regression (MLR) analysis The results of multiple linear regression analysis are shown in Table 2: Table 2: MLR results (n=20433) B S.E. Beta T P VIF tolerance Constant -3585395.747 62900.543 - -57.001 0.000 - - x1 -42730.120 717.087 -0.742 -59.588 0.000 8.714 0.115 x2 -42509.737 676.952 -0.787 -62.796 0.000 8.829 0.113 x3 1157.900 43.389 0.126 26.687 0.000 1.260 0.794 x4 -8.250 0.794 -0.156 -10.387 0.000 12.717 0.079 x5 113.821 6.931 0.415 16.423 0.000 36.004 0.028 x6 -38.386 1.084 -0.377 -35.407 0.000 6.371 0.157 x7 47.701 7.547 0.158 6.321 0.000 35.136 0.028 x8 40297.522 337.207 0.663 119.504 0.000 1.732 0.578 R2 0.637 From Table 2, the formula of the model can be obtained: 𝑦 = 3585395.747 − 42730.120𝑥1 −⋯ + 40297.522𝑥8 (2) ===== PAGE 6 (score 20, numeric-paren 0, table-words 5, var-words 9) ===== Proceedings of the 3rd International Conference on Mathematical Physics and Computational Simulation DOI: 10.54254/2753-8818/2025.23005 133 The value of R2 is 0.637, suggesting a good fit of the model and that the independent variables explain 63.7% of the changes in California house prices. The results show that x3, x5, x7, and x8 have a significant positive impact on y, while x1, x2, x4, and x6 have a significant negative impact on y. The multicollinearity test for the model reveals that the VIF values for x4, x5 and x7 exceed 10, indicating the presence of collinearity issues, which could be resolved by applying stepwise regression or ridge regression further. In addition, P values, which explain the significance of the results, are all 0.000. This indicates that the independent variables have significant impacts on housing prices in California. The multiple linear regression analysis was performed on a substantial sample of 20,433 observations, yielding an R² of 0.637 and indicating that approximately 63.7% of the variance in the dependent variable is explained by the predictors. The intercept was estimated at -3585395.747, which, given the measurement scales involved, requires cautious interpretation. All predictor variables (x1 through x8) exhibited statistically significant effects (p < 0.001). The standardized beta coefficients reveal that x2 (β = -0.787) and x1 (β = -0.742) exerted strong negative influences, whereas x8 (β = 0.663) had a robust positive effect on the outcome variable. Additionally, despite the high statistical significance of these coefficients, several predictors (notably x4, x5, and x7) displayed high variance inflation factors (VIFs of 12.717, 36.004, and 35.136, respectively), accompanied by very low tolerance values, signaling a potential issue of multicollinearity that may undermine the stability and interpretability of the coefficient estimates. 4. Conclusion This study is based on the California House Price dataset, with 20433 usable data entries for analysis. Correlation analysis and multiple linear regression are performed to investigate factors influencing house prices in California. 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. During the MLR analysis in this study, the issue of multicollinearity has been found among total rooms, total bedrooms, and households. This implies that there is a strong correlation among these variables, which means they share a lot of information and influence each other, leading to the instability of the estimated regression coefficients, hence causing the model to be unreliable. Therefore, further analysis, for instance, ridge regression, can be conducted to enhance this model by eliminating highly correlated independent variables. This study excludes an independent variable of ocean proximity, which is included in the original dataset. Hence, for a more advanced housing price predicting model, this variable and other factors of blocks in California (transportation convenience, infrastructure, etc.) may be included. References [1] Tsatsaronis, K. and Zhu, H. (2004) What drives housing price dynamics: cross-country evidence. BIS Quarterly Review, March. [2] Bohn, S. and Duan, J., (2025) California’s Economy, Public Institute of California. International Journal of Information Engineering & Electronic Business. [3] Park, B. and Bae, J.K. (2015) Using machine learning algorithms for housing price prediction: The case of Fairfax County, Virginia housing data. Expert systems with applications, 42(6), 2928-2934. [4] Nguyen, N. and Cripps, A. (2001) Predicting housing value: A comparison of multiple regression analysis and artificial neural networks. Journal of real estate research, 22(3), 313-336. [5] Truong, Q., Nguyen, M., Dang, H. and Mei, B. (2020) Housing price prediction via improved machine learning techniques. Procedia Computer Science, 174, 433-442. [6] Fedotova, O., Teixeira, L. and Alvelos, H. (2013) Software Effort Estimation with Multiple Linear Regression: Review and Practical Application. J. Inf. Sci. Eng., 29(5), 925-945.