房地产影响因素分析 （背景）2002年以来，我国商品房销售额大幅攀升带动了房地产开发和城市基础设施投资的新一轮高速增长。通过产业链的传递，进而又拉动钢材、有色金属、建材、石化等生产资料价格的快速上涨，刺激这些生产资料部门产能投资的成倍扩张，最后导致全社会固定资产投资规模过大、增速过快情况的出现。房价过快上涨在推动投资增长过快的同时，已经成为抑制消费的重要因素。 房地产价格本身呈自然上涨趋势，房价中长期趋势总是看涨。随着我国经济发展，居民可支配收入提高，民间资金雄厚，大量资金需要寻找投资渠道，而股票市场等投资渠道目前又处于低迷状态，这是房地产投资需求不断扩大的经济背景。强劲的CPI上涨说明当前的房价上涨并非孤立，是有其宏观经济背景的。宏观调控能否有效防止局部行业过热出现反弹，其中的关键就是要继续加强和完善对房地产业的调控。 （引言）国际上关于房地产有一种普遍的观点：人均收入超过1000美元，房地产市场呈现高速发展阶段。欧美等发达国家基本都经历了这样一个阶段。我们这篇论文，主要探讨房地产影响因素分析，主要从人均收入对房地产长期发展的影响阐述。 年份 X1 X2 X3 Y 1990 2551.736 1510.16 222 704.3319 1991 1111.236 1700.6 233.3 786.1935 1992 590.5998 2026.6 253.4 994.6555 1993 2897.019 2577.4 294.2 1291.456 1994 3532.471 3496.2 367.8 1408.639 1995 3983.081 4282.95 429.6 1590.863 1996 4071.181 4838.9 467.4 1806.399 1997 3527.536 5160.3 481.9 1997.161 1998 2966.057 5425.1 479 2062.569 1999 2818.805 5854 472.8 2052.6 2000 2674.264 6279.98 476.6 2111.617 2001 2830.688 6859.6 479.9 2169.719 2002 2906.16 7702.8 475.1 2250.177 2003 3011.424 8472.2 479.4 2359.499 2004 3441.62 9421.6 495.2 2713.878
X1=建材成本（元/平方米 ） X2=居民人均收入（元） X3=物价指数 Y=房地产价格（元/平方米） 初定模型：Y=c+a1*x1 +a2*x2 +a3*x3+et Dependent Variable: Y Method: Least Squares Date: 06/05/05 Time: 23:04 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X3 2.537578 0.590422 4.297908 0.0013 X2 0.146495 0.020968 6.986568 0.0000 X1 -0.018016 0.035019 -0.514447 0.6171 C 33.20929 118.2747 0.280781 0.7841 R-squared 0.983094 Mean dependent var 1753.317 Adjusted R-squared 0.978483 S.D. dependent var 600.9536 S.E. of regression 88.15143 Akaike info criterion 12.01917 Sum squared resid 85477.42 Schwarz criterion 12.20798 Log likelihood -86.14376 F-statistic 213.2186 Durbin-Watson stat 1.504263 Prob(F-statistic) 0.000000
一：多元线性回归 Dependent Variable: Y Method: Least Squares Date: 06/05/05 Time: 23:05 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X1 0.336010 0.151084 2.223999 0.0445 C 792.0169 453.4460 1.746662 0.1043 R-squared 0.275612 Mean dependent var 1753.317 Adjusted R-squared 0.219889 S.D. dependent var 600.9536 S.E. of regression 530.7855 Akaike info criterion 15.51016 Sum squared resid 3662533. Schwarz criterion 15.60457 Log likelihood -114.3262 F-statistic 4.946171 Durbin-Watson stat 0.275870 Prob(F-statistic) 0.044490
Dependent Variable: Y Method: Least Squares Date: 06/05/05 Time: 23:09 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X3 5.501779 0.525075 10.47809 0.0000 C -486.8605 220.1227 -2.211769 0.0455 R-squared 0.894128 Mean dependent var 1753.317 Adjusted R-squared 0.885984 S.D. dependent var 600.9536 S.E. of regression 202.9191 Akaike info criterion 13.58706 Sum squared resid 535290.2 Schwarz criterion 13.68146 Log likelihood -99.90293 F-statistic 109.7903 Durbin-Watson stat 0.440527 Prob(F-statistic) 0.000000
Dependent Variable: Y Method: Least Squares Date: 06/05/05 Time: 23:10 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X2 0.236347 0.015879 14.88417 0.0000 C 561.9975 88.56333 6.345713 0.0000 R-squared 0.944572 Mean dependent var 1753.317 Adjusted R-squared 0.940308 S.D. dependent var 600.9536 S.E. of regression 146.8243 Akaike info criterion 12.93992 Sum squared resid 280245.9 Schwarz criterion 13.03432 Log likelihood -95.04937 F-statistic 221.5384 Durbin-Watson stat 0.475648 Prob(F-statistic) 0.000000
Dependent Variable: Y Method: Least Squares Date: 06/07/05 Time: 21:42 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X3 2.355833 0.458340 5.139923 0.0002 X2 0.150086 0.019157 7.834714 0.0000 C 37.56794 114.2991 0.328681 0.7481 R-squared 0.982687 Mean dependent var 1753.317 Adjusted R-squared 0.979802 S.D. dependent var 600.9536 S.E. of regression 85.40783 Akaike info criterion 11.90961 Sum squared resid 87533.98 Schwarz criterion 12.05122 Log likelihood -86.32207 F-statistic 340.5649 Durbin-Watson stat 1.408298 Prob(F-statistic) 0.000000
得到结果发现，ｘ１的系数小，然后对ｙ与ｘ１回归可决系数小，相关性差，剔出这个因素。因为价格更多取决于供需关系。 修正之后为：Y＝c+a2*x2+a3*x3＋et 二：多重线性分析：三个表如上： X2 与X3 存在多重共线性， 1.000000 0.876073 0.876073 1.000000
Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. X2 0.236347 0.015879 14.88417 0.0000 C 561.9975 88.56333 6.345713 0.0000 R-squared 0.944572 Mean dependent var 1753.317 Adjusted R-squared 0.940308 S.D. dependent var 600.9536 S.E. of regression 146.8243 Akaike info criterion 12.93992 Sum squared resid 280245.9 Schwarz criterion 13.03432 Log likelihood -95.04937 F-statistic 221.5384 Durbin-Watson stat 0.475648 Prob(F-statistic) 0.000000
由于引入物价指数改善小，所以模型仅一步改进为：Y＝c+a2*x2＋et
三：异方差检验： ARCH Test: F-statistic 1.315031 Probability 0.335173 Obs*R-squared 3.963227 Probability 0.265462 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 06/05/05 Time: 23:46 Sample(adjusted): 1993 2004 Included observations: 12 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. C 22737.94 10296.61 2.208295 0.0582 RESID^2(-1) 0.241952 0.383144 0.631493 0.5453 RESID^2(-2) -0.327769 0.404787 -0.809734 0.4415 RESID^2(-3) -0.273720 0.378355 -0.723449 0.4900 R-squared 0.330269 Mean dependent var 16705.23 Adjusted R-squared 0.079120 S.D. dependent var 18205.33 S.E. of regression 17470.29 Akaike info criterion 22.63559 Sum squared resid 2.44E+09 Schwarz criterion 22.79723 Log likelihood -131.8136 F-statistic 1.315031 Durbin-Watson stat 1.842435 Prob(F-statistic) 0.335173
ＡＲＣＨ＝３．９６３＜临界值７．８１４７３ 所以无异方差 White Heteroskedasticity Test: F-statistic 0.159291 Probability 0.854522 Obs*R-squared 0.387928 Probability 0.823687 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 06/05/05 Time: 23:46 Sample: 1990 2004 Included observations: 15 Variable Coefficient Std. Error t-Statistic Prob. C 31063.28 22612.20 1.373740 0.1946 X2 -5.055754 9.640127 -0.524449 0.6095 X2^2 0.000421 0.000907 0.464605 0.6505 R-squared 0.025862 Mean dependent var 18683.06 Adjusted R-squared -0.136494 S.D. dependent var 18673.13 S.E. of regression 19906.77 Akaike info criterion 22.81236 Sum squared resid 4.76E+09 Schwarz criterion 22.95397 Log likelihood -168.0927 F-statistic 0.159291 Durbin-Watson stat 1.357657 Prob(F-statistic) 0.854522
ＷＨＩＴＥ＝０．３８７９＜临界值７．８１４７３ 无异方差。
四：自相关分析： ＤＷ＝０．４７５６ 查表的ｄｌ＝１．０７７ ｄｕ＝１．３６１ 存在自相关 广义差分法修正：ρ＝１－０．４７５６／２＝０．７６２２ Dependent Variable: DY Method: Least Squares Date: 06/06/05 Time: 00:18 Sample(adjusted): 1991 2004 Included observations: 14 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. DX2 0.182086 0.034918 5.214655 0.0002 C 236.5589 63.27388 3.738650 0.0028 R-squared 0.693820 Mean dependent var 544.1620 Adjusted R-squared 0.668305 S.D. dependent var 148.7133 S.E. of regression 85.64840 Akaike info criterion 11.86994 Sum squared resid 88027.77 Schwarz criterion 11.96124 Log likelihood -81.08959 F-statistic 27.19263 Durbin-Watson stat 1.584278 Prob(F-statistic) 0.000217
得出：回归后可决系数降低，考虑其他方法。 1．迭代法：表： 发现可决系数提高，Ｆ统计量提高，ＤＷ＝１．５５４７〉１．３６１ 已经无自相关。 结论：Y－bY（－１）＝ｃ*（１－ｂ）＋a2*（x2－b*x2（－１））+et
由下表的b=0.681 C=561.9975 a2=0.236347 179.2772 Y*= Y－0.681Y（－１） X*= x2－0.681*x2（－１） Y*=179.2272 +0.2363X*+et
Method: Least Squares Date: 06/07/05 Time: 20:57 Sample(adjusted): 1991 2004 Included observations: 14 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. E2 0.680509 0.177696 3.829624 0.0024 C 11.68773 24.88825 0.469608 0.6471 R-squared 0.549989 Mean dependent var 15.32764 Adjusted R-squared 0.512488 S.D. dependent var 133.2751 S.E. of regression 93.05539 Akaike info criterion 12.03583 Sum squared resid 103911.7 Schwarz criterion 12.12712 Log likelihood -82.25081 F-statistic 14.66602 Durbin-Watson stat 1.313042 Prob(F-statistic) 0.002397
2．改进模型方程（对数法，然后用迭代法）：Lｙ－ｂLｙ（－１）＝ ｃ＊（１－ｂ）＋ａ２＊（Lｘ２－ｂ＊Lｘ２（－１） 可决系数很高，F统计量相对1中也有提高，DW=1.81>1.361 无自相关。 Dependent Variable: LY Method: Least Squares Date: 06/06/05 Time: 10:24 Sample(adjusted): 1991 2004 Included observations: 14 after adjusting endpoints Convergence achieved after 7 iterations Variable Coefficient Std. Error t-Statistic Prob. LX2 0.586203 0.100243 5.847799 0.0001 C 2.525810 0.882350 2.862594 0.0154 AR(1) 0.567144 0.220457 2.572589 0.0259 R-squared 0.980054 Mean dependent var 7.460096 Adjusted R-squared 0.976428 S.D. dependent var 0.351331 S.E. of regression 0.053941 Akaike info criterion -2.814442 Sum squared resid 0.032006 Schwarz criterion -2.677501 Log likelihood 22.70109 F-statistic 270.2458 Durbin-Watson stat 1.810100 Prob(F-statistic) 0.000000 Inverted AR Roots .57
Dependent Variable: E1 Method: Least Squares Date: 06/07/05 Time: 21:00 Sample(adjusted): 1991 2004 Included observations: 14 after adjusting endpoints Variable Coefficient Std. Error t-Statistic Prob. E2 0.501784 0.219561 2.285394 0.0413 C 0.006639 0.015069 0.440600 0.6673 R-squared 0.303258 Mean dependent var 0.007495 Adjusted R-squared 0.245197 S.D. dependent var 0.064877 S.E. of regression 0.056365 Akaike info criterion -2.782368 Sum squared resid 0.038124 Schwarz criterion -2.691074 Log likelihood 21.47658 F-statistic 5.223026 Durbin-Watson stat 1.517853 Prob(F-statistic) 0.041274
用1，2两种修正，两种效果都很好，都消除了自相关，相比较2更好。 所以，方程：b=0.502 Y*= Lｙ－o.502*Lｙ（－１） X*= Lx2－0.502*Lx2（－１） Y*=1.2579+0.5862X*+et
以上就是通过分析和检验得到的回归方程。所以，人均收入水平的高低在一定程度上影响房地产价格。当前的房地产价格增长背后收入是不可忽略的因素。
资料来源：中经网，国家统计局网站，
