房地產影響因素分析
（背景）2002年以來，我國商品房銷售額大幅攀升?帶動了房地產開發和城市基礎設施投資的新一輪高速增長。透過產業鏈的傳遞，進而又拉動鋼材、有色金屬、建材、石化等生產資料價格的快速上漲，刺激這些生產資料部門產能投資的成倍擴張，最後導致全社會固定資產投資規模過大、增速過快情況的.出現。房價過快上漲在推動投資增長過快的同時，已經成爲抑制消費的重要因素。
房地產價格本身呈自然上漲趨勢，房價中長期趨勢總是看漲。隨着我國經濟發展，居民可支配收入提高，民間資金雄厚，大量資金需要尋找投資渠道，而股票市場等投資渠道目前又處於低迷狀態，這是房地產投資需求不斷擴大的經濟背景。強勁的CPI上漲說明當前的房價上漲並非孤立，是有其宏觀經濟背景的。宏觀調控能否有效防止局部行業過熱出現反彈，其中的關鍵就是要繼續加強和完善對房地產業的調控。 （引言）國際上關於房地產有一種普遍的觀點：人均收入超過1000美元，房地產市場呈現高速發展階段。歐美等發達國家基本都經歷了這樣一個階段。我們這篇論文，主要探討房地產影響因素分析，主要從人均收入對房地產長期發展的影響闡述。
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=物價指數 Y=房地產價格（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：多元線性迴歸
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
得到結果發現，ｘ１的係數小，然後對ｙ與ｘ１迴歸可決係數小，相關性差，剔出這個因素。因爲價格更多取決於供需關係。
修正之後爲：Y＝c+a2*x2+a3*x3＋et
二：多重線性分析：三個表如上：
X2 與X3 存在多重共線性，
1.000000 0.876073
0.876073 1.000000
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
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
由於引入物價指數改善小，所以模型僅一步改進爲：Y＝c+a2*x2＋et
三：異方差檢驗：
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＜臨界值７．８１４７３
所以無異方差
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＜臨界值７．８１４７３
無異方差。
四：自相關分析：
ＤＷ＝０．４７５６
查表的ｄｌ＝１．０７７ ｄｕ＝１．３６１
存在自相關
廣義差分法修正：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：迴歸後可決係數降低，考慮其他方法。
1．迭代法：表：
發現可決係數提高，Ｆ統計量提高，ＤＷ＝１．５５４７〉１．３６１
已經無自相關。
結論：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．改進模型方程（對數法，然後用迭代法）：Lｙ－ｂLｙ（－１）＝ ｃ＊（１－ｂ）＋ａ２＊（Lｘ２－ｂ＊Lｘ２（－１）
可決係數很高，F統計量相對1中也有提高，DW=1.81>1.361
無自相關。
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1，2兩種修正，兩種效果都很好，都消除了自相關，相比較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
以上就是透過分析和檢驗得到的迴歸方程。所以，人均收入水平的高低在一定程度上影響房地產價格。當前的房地產價格增長背後收入是不可忽略的因素。
資料來源：中經網，國家統計局網站，