非参数回归在房价预测上的应用

Application of Nonparametric Regression in House Price Forecast

摘要: 住房与人类生活息息相关，是居民总财富的重要组成部分，在一定程度上也影响着人们的幸福指数，因此国内外都很重视对房价定性和定量的研究。本文利用哈里森和鲁宾菲尔德的波士顿房价数据，使用R软件，探讨OLS回归和非参数回归在房价预测上的比较分析。实验结果表明：使用OLS回归模型预测房价违反了OLS回归统计假设，使用OLS回归是不符合理论依据的。基于非参数回归的特性，更适合采用非参数回归(Lasso回归和Ridge回归)对房价进行预测，并使用Bootstrap法和循环法对模型进行选择。在使用多元线性回归对数据进行分析时，不能忽略其多元线性回归成立时的前提假设，而现实中的数据往往是非理想化的，因此非参数回归的适用性更广。

Abstract: Housing is closely related to human life, which is an important part of the total wealth of residents and also affects people’s happiness index to a certain extent. Therefore, great importance is attached to the qualitative and quantitative research on housing prices both at home and abroad. Based on the Boston house price data of Harrison and Rubinfeld, this paper discusses the comparative analysis of OLS regression and nonparametric regression in house price prediction by using R software. The results show that the OLS regression model is against the OLS regression statistical hypothesis, and OLS regression is not in line with the theoretical basis. Based on the characteristics of nonparametric regression, it is more suitable to use nonparametric regression (Lasso regression and Ridge regression) to predict house prices, and Bootstrap method and circulation method are used to select the model. When using multiple linear regression to analyze the data, we can’t ignore the premise hypothesis when the multiple linear regression is established. However, the data in reality are often not ideal, so the applicability of nonparametric regression is wider.