Comparative Analysis of Linear and Polynomial Regression Models in Predicting Shanghai Housing Prices

Abstract

This study presents a comparative analysis of linear and polynomial regression models for predicting housing prices in Shanghai's dynamic real estate market. Utilizing a dataset of 100 second-hand housing listings sourced from Lianjia between 2020 and 2023, with living area as the primary predictive feature, we rigorously train and evaluate both models. Our findings demonstrate that a second-degree polynomial regression model (MSE = 0. 58, R² = 0. 89)significantly outperforms a simple linear regression model (MSE = 0. 97, R² = 0. 78)in predictive accuracy and explanatory power. Residual analysis further reveals that the linear model suffers from heteroscedasticity, indicating its inadequacy in capturing the market's complexity, particularly for high-value properties. The results underscore the importance of selecting appropriately complex models for economic forecasting. We conclude that polynomial regression offers a superior fit for the non- linear trends prevalent in Shanghai's housing market. This study provides practical insights for stakeholders in real estate investment, policy formulation, and urban economics, while also acknowledging limitations related to dataset size and feature selection, suggesting directions for future research involving multivariate approaches and regularization techniques.