限购政策与自贸区成立对海南省商品住宅价格影响分析

Analysis of the Influence of the Purchase Restriction Policy and the Establishment of Free Trade Zone on the Price of Commodity Housing in Hainan Province

摘要: 我们根据搜集到的海南省商品住宅相关数据建立数学模型，并分别研究限购政策下以及海南自贸区(港)的成立后海南商品住宅价格走向。本文先对海南省商品住宅价格的影响因素进行定性分析，并搜集海南省人均生产总值、居民人均可支配收入等数据，对各因素与房价及因素之间进行插值、拟合和相关性分析，可知竣工面积与商品住宅价格R5 = −0.758，R1 = 0.909，R2 = 0.938，R3 = 0.930，R4 = 0.971，R6 = 0.880。然后通过主成分分析法对各因素进行因子分析，由得分建立主成分与各因素间关系，再进行线性回归分析主成分与房价之间的关系，最后通过EXCEL随机抽取的数据进行模型检验。以三亚市的商品住宅价格为例，首先对房价做序列值的标签，对处理后的数据进行拟合，得到房价的趋势及拟合后的数据，通过对拟合曲线的R方和平稳的R方值可知，拟合后残差序列是存在自相关的，通过整体的拟合图对应的R方和调整后的R方都趋于1。用SPSS中的AMRIMA模型进行不平稳时间序列的预测，得到未来一年的房价的走势图和未来一年的房价具体预测值以及预测值所处的氛围。

Abstract: We built a mathematical model based on the collected data on commercial housing in Hainan Province, and studied the price trend of Hainan commercial housing after the establishment of the purchase restriction policy and the Hainan Free Trade Zone (Hong Kong). For the first problem, this paper firstly analyzes the influencing factors of the commodity housing price in Hainan Province, and collects data such as the per capita GDP and the per capita disposable income of Hainan Province, and quantitatively analyzes the impact of various factors on the price of commercial housing. Using MATLAB and SPSS software to interpolate, fit and correlate various factors with house prices and various factors, the results obtained: the area of completion is negatively correlated with the price of commercial housing, R5 = −0.758. Other factors were positively correlated with house prices, R1 = 0.909, R2 = 0.938, R3 = 0.930, R4 = 0.971, R6 = 0.880. On the basis of the problem 1, the data is standardized by SPSS, and the factors are analyzed by principal component analysis. The relationship between the principal component and each factor is established by the score. Then the SPSS was used to analyze the relationship between the main component and the house price by linear regression. Finally, the model was tested by EXCEL randomly extracted data. For Question three, taking the price of commercial housing in Sanya as an example, first, the serial value label of the house price is used, and the processed data is fitted with SPSS to obtain the trend of the house price and the related data after fitting. By fitting the R square of the curve and the stationary R square value, it is known that after fitting the residual sequence is autocorrelation, and the R-square and the adjusted R-square corresponding to the overall fit map tend to be 1. The AMRIMA model in SPSS is used to predict the unsteady time series, and the trend chart of the house price in the coming year and the specific forecast value of the house price in the next year and the atmosphere of the predicted value are obtained.