基于PCA和灰色系统的住房价格建模

Housing Price Modeling with PCA and Gray System

摘要: 本文从房屋供给和需求两个方面科学的分析影响我国房价的因素，运用主成分分析法去除各影响因素间的线性相关性，同时减少了影响因素的个数；接下来利用最小二乘法确立房价与影响因素间的线性回归方程；最后引入灰色系统理论中的灰色预测方法，建立各影响因素的灰色预测模型，并对其进行量化分析、预测，将所得到的影响因素预测值代入到回归方程，以预测房价。

Abstract: In this paper, we analyze the factors which affect the house prices from two aspects: housing supply and demand. The approach of principal component analysis is taken to remove the linear correlation between the factors and to reduce the number of factors. Furthermore, we use the least squares method to set up the linear regression equation between prices and affecting factors. At last, we get gray forecasting model of factors by introducing gray prediction method of the gray system theory and substitute the predictive value of the factors into the regression equation to predict the house prices.