房屋空置率的分析研究

房屋空置率的分析研究

西南交通大学宿美丽、黄文瀚、顾泰发

目录

摘要 (1)

Abstract (2)

一、相关知识解析 (3)

二、研究房屋空置率的意义 (3)

三、问题提出 (4)

四、问题分析 (4)

五、符号说明 (5)

六、问题假设 (5)

七、模型的建立与求解 (5)

7.1 模型的准备 (5)

7.1.1定性分析： (5)

7.1.2 定量分析： (6)

7.2 模型的建立 (16)

7.3 模型检验 (17)

八、参考文献 (17)

九、附录 (18)

摘要

随着经济的发展，美国城市化水平不断上升，城市建筑不断在城市中屹立起来。在美国，空置是指房屋没有投入使用，处在待出租或出售的状态。空置率多以全部房屋存量为分母，以全部空置房屋为分子，计算出总空置率；

国外有学者使用过空置率这一指标来描述房地产领域的资源配置状况，研究影响空置率的回归模型具有很大的现实意义。所以我们决定建立空置率的线性回归模型。

本文我们先对各个因素进行定性分析；然后再利用相关软件对各因素进行了进一步的定量分析。在定量分析中，我们利用spss 软件，用多元线性回归得到描述的有美国房屋空置率和美元指数, 房指数，CPI ，S&P500，美国GDP 的回归方程，建立了估计美国房屋空置率的模型。

首先，绘散点图分析从网上收集到的相关数据，将对房屋空置率影响不大的因素去除。

其次，结合散点图，用一元线性回归分析分别得到各个因素和房屋空置率的近似的关系，并从拟合优度及线性相关性是否显著两方面进行检验。

然后，我们建立了综合所有因素和房屋空置率的多元线性回归方程：

1

2

3

5

3.6773465882470.008206134855443*0.02814136185459*

0.005905910596052*

0.0001809350435868*

y x

x

x x

=++--；

同时用该方程对04年到07年的空置率进行估计，参照网上查阅的对应实际空置率对回归效果进行检测。

最后，检验的结果为下表（单位：%）： 单位：% 时间 估计价格 实际价格 偏差率

2004 10.057331 10.2 0.01399 2005 10.913503 9.9 0.102374 2006 11.6397815 10.6 0.098093 2007

11.8311333

11.2

0.056351

由表可知，回归方程对实际价空置率合总体效果还是好的，但由于收集数据有限，所以难免存在一定误差。这说明：该模型具有一定的实际意义，但还有待于更进一步改进。

关键词： 散点图 一元线性回归 多元线性回归 拟合优度 线性相关性

Abstract

With the economic development, the urbanization level of American cities is rising, urban structures have stood up in the city . In the United States, Housing vacancy is defined as that a house is not put into use for rent or sale in the state. To calculate the overall Housing V acancy rate, we use the stock of all houses as the molecular, and use the vacant houses as the denominator.

Some foreign scholars value the vacancy rate as a indicator which is used to describe the allocation of resources in real estate conditions, the regression models of vacancy rate is of great practical significance. So we decided to create the the linear regression model of vacancy rate.

This paper, we first do the qualitative analysis of the various factors; then use related software on various factors, what is related to further quantitative analysis.

In quantitative analysis, we used SPSS to build the multiple linear regression, which is aimed to described the effect of the dollar index, house index, CPI, S & P500 and the U.S. GDP on the future Housing V acancy rate .

At the first beginning, we draw scatters of the data collected from the Internet, then we eliminated the factors that has little effect on oil futures prices;

Secondly, we, combining the plots, used linear regression analysis of various factors respectively and Housing V acancy rate to get the approximate relationship between Housing V acancy rate and each of the factors. To be more scientific, we also conduct Goodness-of-fit testing and the linear correlation inspection

Last but not least, we established a comprehensive multivariate linear regression equation involved all factors:

1

2

3

5

3.6773465882470.008206134855443*0.02814136185459*

0.005905910596052*

0.0001809350435868*

y x

x

x x

=++--.

Naturally , the next thing we had done was to use the equation to estimate the Housing V acancy rate varied from 2004 to 2007. Then we referred to the corresponding Housing V acancy rate, which was published online, to test the effect of regression. Finally, the results of the inspection are in the next table (%):

price fitting is good, but due to the limit of collecting enough data, it is not surprised to find there are some errors. To some degree, this model has practical significance, but on the other hand , it needs to be improved.