Research on the mathematics model and its application on housing price problem

摘要

The housing price is closely linked to national economy and people's livelihood, it also has a significant impact on the national economic development and social stability. As the housing price is increasing constantly, this problem has become a focus issue that draws public attention. This article will predict the house price and its rationality in the next few years. The question we are discussing can boil down to a binary linear regression problem. Per capita disposable income and building costs are two main factors that affect the housing price. Here we take Beijing, Anhui and Ningxia as research objects. By using data from China Statistical Yearbook which are attested to be normally distributed, we get the linear regression equations. In equations, local average house price is used as dependent variable, and the household disposable income and costs of construction are independent variables. Equation of average house price in Beijing: y1 = -8114.517 + 1.004x11. Equation of average house price in Anhui: y2 = 265.941 - 0.025x12 + 0.001x22. Equation of average house price in Ningxia: y3 = -2826.025 - 0.203x13 + 0.013x23. To predict house price in the next few years, we need to firstly identify per capita disposable income and building costs. Per capita disposable income has strict linear relationship with year. While linear relationship between building costs and year is unconspicuous with little data. In order to improve the accuracy of the prediction, we can use grey forecasting to predict building costs in the futur. We can make a judgment at the rationality of house price based on the Housing Price-to-Income Ratio of the 3 areas. It shows that house price in Beijing is quite unreasonable as it is beyond local people’s burden level. As for Anhui and Ningxia, house price is also too high to be reasonable.