中國房屋平均銷售價格的影響因素分析

1、計 模量 型經(jīng) 設(shè)濟 計中國房屋平均銷售價格影響因素分 二O一O年五月中國房屋平均銷售價格影響因素分析一、前言作為國家的支柱產(chǎn)業(yè),房地產(chǎn)業(yè)的穩(wěn)定與發(fā)展關(guān)乎國計民生。從1998年開始,我國房地產(chǎn)業(yè)進入了新一輪快速發(fā)展期,尤其是近幾年來房地產(chǎn)行業(yè)持續(xù)保持高速發(fā)展,房地產(chǎn)投資和房地產(chǎn)價格持續(xù)上漲。雖然從全國總體來看,房地產(chǎn)市場保持健康、快速發(fā)展態(tài)勢,供求基本平衡,但部分地區(qū)仍然存在房價上漲過快、住宅供給結(jié)構(gòu)不合理等問題。要解決這些問題,使中國房地產(chǎn)市場保持持續(xù)健康發(fā)展,國家的宏觀經(jīng)濟政策對房地產(chǎn)價格的調(diào)節(jié)作用顯得非常重要。而要進行有效調(diào)控,得首先識別在各種因素中,到底哪些因素能對房地產(chǎn)價格有影響,哪

2、些因素對房地產(chǎn)價格的影響力強,哪些對房地產(chǎn)價格的影響力稍弱等問題。在作此報告前，我查閱了一些資料，其中，在一本學術(shù)周刊新財經(jīng)上，看到了一篇影響中國房價的主要因素的文章，但該文章并沒有對這些影響因素進行具體數(shù)學上的分析。因此我想看看這些影響因素是怎樣影響房價的。所以做了此計量報告，來研究中國自改革開放以來房屋平均銷售價格和其影響因素之間具體的關(guān)系。二、理論背景20世紀90年代以后，各國學者就開始采用宏觀經(jīng)濟模型來研究房價的變化，他們得出宏觀經(jīng)濟變量在一定程度上可以解釋房價波動的結(jié)論，例如：Evans指出土地利用規(guī)劃以及其他方面的供給限制，會體現(xiàn)在地價的不斷上漲，從而推進房價的提高。喬志敏用實證分

3、析表明生產(chǎn)成本的波動對房地產(chǎn)價格的波動有較強作用；張紅、潘琦、鄭思奇對北京市商品住宅市場進行回歸分析，說明住宅實際建造成本和實際生產(chǎn)總值對住宅價格有著顯著的影響；謝敘祎發(fā)現(xiàn)在短期內(nèi)房價和地價相互影響，而長期內(nèi)房價決定地價，并證明依靠降低地價來控制房價上漲的做法是不可行的。歸納他們的研究，從供給和需求出發(fā)，影響住宅價格的因素有：房地產(chǎn)投資、成本、失業(yè)率、人均收入、住宅區(qū)綠化率等。 其中我認為，對房屋平均銷售價格影響較為顯著的因素有竣工房屋造價、建成區(qū)綠化覆蓋率、居民消費價格指數(shù)、職工年平均工資、登記失業(yè)率。而竣工房屋造價、建成區(qū)綠化覆蓋率、居民消費價格指數(shù)是影響房屋平均銷售價格的最主要因素。因此

4、，以下我對此展開了計量經(jīng)濟學模型分析。三、模型的選擇與建立本模型是通過對1978年到2007年的房地產(chǎn)平均價格及其影響因素的定量數(shù)據(jù)進行分析，來研究其之間的關(guān)系。1.模型包含的變量。被解釋變量為房屋平均銷售價格，解釋變量為竣工房屋造價、建成區(qū)綠化覆蓋率、職工平均工資、登記失業(yè)率和居民消費價格指數(shù)。2.模型的數(shù)學形式。初步確定被解釋變量與解釋變量之間的數(shù)學關(guān)系式為：Y=0+1X1+2X2+3X3+4X4+5X5+解釋變量有5個，0為常數(shù)項，為隨機誤差項，描述變量外的因素對模型的干擾。其中解釋變量分別為：Y：房屋平均銷售價格；X1：竣工房屋造價；X2：建成區(qū)綠化覆蓋率；X3：職工共平均工資；X4：

5、登記失業(yè)率；X5：居民消費價格指數(shù)四、數(shù)據(jù)的來源與分析1、數(shù)據(jù)來源：國家統(tǒng)計局網(wǎng)站年度數(shù)據(jù) 天津財經(jīng)大學圖書館中國統(tǒng)計年鑒2、所需數(shù)據(jù)：變量YX1X2X3X4X5年份房屋平均銷售價格竣工房屋造價建成區(qū)綠化覆蓋率職工年平均工資登記失業(yè)率居民消費價格指數(shù)197816610414.26155.3100197918311314.86685.4101.91980201123157624.9109.5198121613915.37723.8112.2198224514715.57983.2114.4198327016515.98262.3116.7198429818716.29741.9119.91985

6、32420516.411481.8134.2198635523116.913292143.6198740827017.114592156.219885033011717472188.5198957336717.819352.6219.2199070341319.221402.5222199178643720.123402.3233.319929955122127112.3253.41993129163221.333712.6294.21994140979122.145382.8367.81995159191123.955002.9429.619961806111124.4362103467.4

7、19971997117525.5364703.1481.919982063121826.5674793.147819992053115227.5883463.1471.320002112113928.1593713.1473.220012170112828.38108703.6476.520022250118429.75124224472.720032359127331.15140404.3478.420042778140231.66160244.2497.120053168145133.9183644.250620063367156435.1210014.1513.6200738641657

8、35.3249324538.320083890179537.4292294.2570.1注：1、房屋平均銷售價格單位：元；竣工房屋造價單位：元；建成區(qū)綠化覆蓋率：%；職工年平均工資：元；登記失業(yè)率：%。2、由于改革開放初期國家實行單位分房制，并無房屋銷售價格，所以前幾期數(shù)據(jù)是由本人按規(guī)律推寫出來的；3、居民消費價格指數(shù)均是以1978年為基期計算的。3、變量間相關(guān)系數(shù)表1.000000 0.985728 0.990310 0.962989 0.310562 0.948192 0.985728 1.000000 0.983599 0.914539 0.273185 0.984957 0.99031

9、0 0.983599 1.000000 0.954206 0.289958 0.951884 0.962989 0.914539 0.954206 1.000000 0.396207 0.840497 0.310562 0.273185 0.289958 0.396207 1.000000 0.216094 0.948192 0.984957 0.951884 0.840497 0.216094 1.0000004、樣本數(shù)據(jù)的散點圖050010001500200001000200030004000YX1五、模型的估計與分析1、模型的回歸分析（1）五元回歸：t0.025 (24)=2.064 F

10、0.05 (5，24)=2.62VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C114.29990.3717970.7133959.34500.993984否X11.3389092.8933830.0080X2-3.578603-0.1682380.8678X30.0648064.0277820.0005X4-19.41561-1.0748440.2931X50.0347390.0304670.9759（2）四元回歸：t0.025 (25)=2.060 F0.05 (4，25)=2.76Var

11、iableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C113.38260.3782300.70851249.0990.994225否X11.3517867.3214870.0000X2-3.369396-0.1708110.8657X30.0644136.8282970.0000X4-19.36032-1.0994260.2821VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-28.20427-0.10

12、13710.92011191.4910.993947否X11.3557682.9224370.0073X22.7540790.1343310.8942X30.0589593.8816310.0007X5-0.088386-0.0776700.9387VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-112.9568-0.3339780.7412924.48770.992210否X2-0.059381-0.0024570.9981X30.0936666.5200750.0000X4-21.187

13、14-1.0313450.3123X53.0479155.7687540.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C64.949410.7201340.47811247.6680.994218否X11.3344582.9463150.0069X30.0629335.5246830.0000X4-18.57386-1.0915370.2854X5-0.027187-0.0256970.9797VariableCoefficientt-StatisticProb. F-statist

14、icAdjusted R-squared是否通過T-F檢驗C-584.9202-1.8175040.0811742.81180.990321否X12.4944015.4160370.0000X355.685202.8579070.0085X45.1818840.2403100.8120X5-3.644913-4.2117390.0003（2）三元回歸：t0.025 (26)=2.056 F0.05 (3，26)=2.98VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-26.88977-0.0

15、987320.92211651.8010.994178否X11.3227967.2097890.0000X22.2627150.1183090.9067X30.0599267.0181800.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-1557.951-5.4235890.0000598.91960.984090否X10.7731512.8397110.0087X299.631324.7224270.0001X432.664941.2396420.2262VariableCoef

16、ficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-560.9879-1.8672660.07321027.6390.990672是X12.5207345.7400080.0000X255.388102.9014590.0075X5-3.707847-4.5789620.0001VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-1754.699-6.4132580.0000544.97770.982540否X2128.

17、54309.2056820.0000X30.0327142.2449360.0335X4-0.947246-0.0312580.9753VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-271.7684-0.9013950.37571229.2850.992191否X26.9074720.2973470.7686X30.0876766.6646740.0000X52.9548515.6690690.0000VariableCoefficientt-StatisticProb. F-statis

18、ticAdjusted R-squared是否通過T-F檢驗C-2214.883-13.437740.0000469.26130.979774否X2146.199310.095730.0000X432.969201.0889280.2862X50.5142420.8914830.3808VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-113.7658-1.4975440.14631281.9560.992510否X30.09363417.873230.0000X4-21.17303-1.09

19、47100.2837X53.04671815.236840.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C63.230211.0660940.29621730.0540.994440否X11.32298117.938600.0000X30.06318110.593550.0000X4-18.57917-1.1135390.2757VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C7.7

20、817980.1055930.91671651.0030.994176否X11.3600882.9959370.0059X30.0603085.3964880.0000X5-0.041218-0.0388190.9693VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C284.77342.4076500.0234774.24950.987653否X13.62335313.548350.0000X41.2716230.0523180.9587X5-4.969380-6.0199280.0000（2

21、）二元回歸：t0.025 (27)=2.052 F0.05 (2，27)=3.35VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-1508.463-5.2508360.0000880.11590.983774是X10.7496542.7330740.0109X2102.83504.8631670.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C5.1501730.1815970.85

22、732571.6060.994391是X11.34269718.671630.0000X30.06068310.932730.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-263.2276-2.2957420.0297495.95280.971538否X12.03620629.893700.0000X447.907961.3696440.1821VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過

23、T-F檢驗C289.52683.8958220.00061205.9140.988109是X13.62835714.803980.0000X5-4.983145-6.4897400.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-1759.704-8.0826680.0000848.87510.983186是X2128.68309.9150240.0000X30.0325242.5029250.0187VariableCoefficientt-StatisticProb. F-sta

24、tisticAdjusted R-squared是否通過T-F檢驗C-2315.565-19.361720.0000708.88360.979928否X2158.484735.755020.0000X427.455500.9298940.3607VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-2169.529-13.557510.0000698.49330.979635否X2150.640010.804020.0000X50.3859280.6811120.5016VariableCoeff

25、icientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C626.51113.4693120.0018188.97130.928385否X30.16084918.408870.0000X4-90.43376-1.5556840.1314VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-183.0323-4.3375690.00021908.3130.992455是X30.09130718.998630.0000X53.09816

26、315.882370.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-903.9548-4.0906990.0003137.80960.904170否X4119.04731.8826020.0706X56.05614115.698150.0000（2）二元回歸：t0.025 (28)=2.048 F0.05 (1，28)=4.20VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-12

27、7.5502-2.1753350.0382959.99810.970648是X12.06169230.983840.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-2254.319-22.637500.00001423.7820.980025是X2159.679837.733040.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C369.87574.9114710.00003

28、57.39540.924753是X30.15546318.904900.0000VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C278.29580.4286700.67142.9888350.064179否X4333.55941.7288250.0949VariableCoefficientt-StatisticProb. F-statisticAdjusted R-squared是否通過T-F檢驗C-569.9175-4.1428110.0003249.41230.895462是X56.21

29、308615.792790.00002、選取較優(yōu)的解釋變量并擬定模型通過以上對模型回歸分析的T-F檢驗我們可以看到，對于由被解釋變量Y（房屋平均銷售價格）、解釋變量X1（竣工房屋造價）、X2（建成區(qū)綠化覆蓋率）、X5（居民消費價格指數(shù)）建立的模型進行檢驗可以看到，模型總體具有較顯著的線性關(guān)系；并且由t簡言之可以看出，每個解釋變量與被解釋變量之間有較強的線性關(guān)系?？偵戏治?，選取Y、X1、X2、X5作為分析模型的解釋變量。建立模型：Y=560.9879+2.520734X1+55.38810X23.707847X5+ei (1.867266)(5.740008) (2.901459) (4.578

30、962)R2= 0.9916 = 0.9906 D.W.=1.2203 F=1027.639解釋變量的統(tǒng)計意義：當X2、X5保持不變時，X1每增加1個單位，Y平均增加2.520743個單位；當X1、X5保持不變時，X2每增加1個單位，Y平均增加55.38810個單位；當X1、X2保持不變時，X5每增加1個單位，Y平均減少3.707847個單位；解釋變量的經(jīng)濟意義：在建成區(qū)綠化覆蓋率和居民消費價格指數(shù)不變的情況下，竣工房屋造價每增加1元，房屋平均銷售價格增加2.520743元；在竣工房屋造價和居民消費價格指數(shù)不變的情況下，建成區(qū)綠化覆蓋率每增加1%，房屋平均銷售價格增加0.553881元；在竣工

31、房屋造價和建成區(qū)綠化覆蓋率不變的情況下，居民消費價格指數(shù)每增加1%，房屋平均銷售價格減少0.037078元。3、異方差性檢驗（1）采用E-Q方法對X1進行異方差檢驗1)按照X1排序由于N=30，C=N/4=7.5，所以刪除位于中間的8個數(shù)據(jù)，得到兩個容量為11的子樣本。對兩個子樣本分別作OLS回歸，求各自的殘差平方和RSS1和RSS2：子樣本1（Sample: 1978 1988）：VariableCoefficientStd. Errort-StatisticProb. C-217.4636251.2783-0.8654290.4155X10.7851790.5142221.5269260.

32、1706X29.79539416.262260.6023390.5659X51.6428200.7909272.0770820.0764R-squared0.993115 Mean dependent var288.0909Adjusted R-squared0.990165 S.D. dependent var103.6074S.E. of regression10.27494 Akaike info criterion7.772581Sum squared resid739.0209 Schwarz criterion7.917270Log likelihood-38.74919 F-st

33、atistic336.5900Durbin-Watson stat1.324676 Prob(F-statistic)0.000000由上圖知Y= -217.4636+ 0.785179X1 -9.795394X2+1.642820X5+ei(-0.865429)(1.526926) (-0.602339)(2.077082)R2= 0.993115 RSS1= 739.0209子樣本2（Sample: 1997 2007）：VariableCoefficientStd. Errort-StatisticProb. C-9479.519889.9965-10.651190.0000X1-0.3

34、464540.377740-0.9171750.3896X286.327009.5005479.0865290.0000X520.173162.4811808.1304730.0001R-squared0.997387 Mean dependent var2561.909Adjusted R-squared0.996268 S.D. dependent var638.6818S.E. of regression39.01794 Akaike info criterion10.44121Sum squared resid10656.80 Schwarz criterion10.58590Log

35、likelihood-53.42664 F-statistic890.8060Durbin-Watson stat2.518796 Prob(F-statistic)0.000000由上圖知Y= -9479.519-0.346454X1-86.32700X2+ 20.17316X5+ei(-10.65119)(- 0.917175)(9.086529)( 8.130473)R2= 0.997387 RSS1= 10656.80計算F統(tǒng)計量：F= RSS2/RSS1= 10656.80/739.0209=14.4201605 在5%的顯著性水平下，自由度為（7，7）的F分布的臨界值為F0.05

36、(7，7) =3.79，據(jù)此拒絕兩組字樣方差相同的假設(shè)，表明該總體隨機干擾項存在單調(diào)遞減型異方差。2)采用加權(quán)最小二乘法對原模型進行回歸:VariableCoefficientStd. Errort-StatisticProb. CE-530.713551.16165-10.373270.0000X1E2.5166740.07044635.724890.0000X2E52.870384.56597211.579220.0000X5E-3.6199700.278083-13.017590.0000R-squared0.999956 Mean dependent var61.43356Adjust

37、ed R-squared0.999951 S.D. dependent var146.6126S.E. of regression1.022769 Akaike info criterion3.006471Sum squared resid27.19748 Schwarz criterion3.193297Log likelihood-41.09706 Durbin-Watson stat1.474623Y=-530.7135CE+2.516674X1E+52.87038X2E-3.619970X5E+ei(-10.37327) (35.72489) (11.57922) (-13.01759

38、)Adjusted R-squared=0.999951 Durbin-Watson stat=1.474623（2）對加權(quán)后的模型進行異方差檢驗：1）按照X1E排序：由于N=30，C=N/4=7.5，所以刪除位于中間的8個數(shù)據(jù)，得到兩個容量為11的子樣本。對兩個子樣本分別作OLS回歸，求各自的殘差平方和RSS1和RSS2：子樣本1（Sample: 1978 1988）：VariableCoefficientStd. Errort-StatisticProb. CE1372.867587.52852.3366820.0521X1E4.5272040.8869025.1045170.0014X2

39、E-88.1393139.72235-2.2188850.0620X5E-3.9058561.554246-2.5130230.0402R-squared0.956472 Mean dependent var7.292641Adjusted R-squared0.937817 S.D. dependent var2.779201S.E. of regression0.693038 Akaike info criterion2.379822Sum squared resid3.362107 Schwarz criterion2.524512Log likelihood-9.089023 Durb

40、in-Watson stat1.802052Y= 1372.867+ 4.527204X1 -88.13931X2-3.905856X5 (2.336682) (5.104517) (-2.218885) (-2.513023)R2=0.956472 RSS1=3.362107子樣本2（Sample: 1997 2007）：VariableCoefficientStd. Errort-StatisticProb. CE-571.327056.24636-10.157580.0000X1E2.5683740.07687733.408950.0000X2E57.177565.11093811.18

41、7290.0000X5E-3.9150880.316096-12.385740.0000R-squared0.999984 Mean dependent var147.3203Adjusted R-squared0.999977 S.D. dependent var222.3401S.E. of regression1.065446 Akaike info criterion3.239951Sum squared resid7.946220 Schwarz criterion3.384640Log likelihood-13.81973 Durbin-Watson stat1.007639Y=

42、 -571.3270+2.568374X1+57.17756X2-3.915088X5 (-10.15758)( 33.40895) (11.18729) (-12.38574)R2= 0.999984 RSS1= 7.946220由上有F= RSS2/RSS1= 7.946220/3.362107=2.363464 F0.05 (7，7) =3.79, 據(jù)此我們可以認為加權(quán)后的模型已經(jīng)消除了異方差。2）按照X2E排序：由于N=30，C=N/4=7.5，所以刪除位于中間的8個數(shù)據(jù)，得到兩個容量為11的子樣本。對兩個子樣本分別作OLS回歸，求各自的殘差平方和RSS1和RSS2：子樣本1（Samp

43、le: 1978 1988）：RSS2= 7.997950子樣本2（Sample: 2006:1 2008:4）：RSS1= 8.157957計算F統(tǒng)計量：F= RSS2/RSS1=8.157957/ 7.997950=1.02在5%的顯著性水平下，自由度為（7,7）的F分布的臨界值為F0.05 ( 7,7) =3.79，據(jù)此我們可以認為加權(quán)后的模型已經(jīng)消除了異方差。3）按照X5E排序：由于N=30，C=N/4=7.5，所以刪除位于中間的8個數(shù)據(jù)，得到兩個容量為11的子樣本。對兩個子樣本分別作OLS回歸，求各自的殘差平方和RSS1和RSS2：子樣本1（Sample:1978 1988）：RSS

44、2=8.056220子樣本2（Sample: 1997 2007）：RSS1=7.946220計算F統(tǒng)計量：F= RSS2/RSS1=7.946220/8.056220=0.986345在5%的顯著性水平下，自由度為（7,7）的F分布的臨界值為F0.05 (7,7) =3.79，據(jù)此我們可以認為加權(quán)后的模型已經(jīng)消除了異方差。4、自相關(guān)性檢驗現(xiàn)在我們采用杜賓-瓦森檢驗法檢驗是否存在序列自相關(guān)：VariableCoefficientStd. Errort-StatisticProb. CE-530.713551.16165-10.373270.0000X1E2.5166740.07044635.7

45、24890.0000X2E52.870384.56597211.579220.0000X5E-3.6199700.278083-13.017590.0000R-squared0.999956 Mean dependent var61.43356Adjusted R-squared0.999951 S.D. dependent var146.6126S.E. of regression1.022769 Akaike info criterion3.006471Sum squared resid27.19748 Schwarz criterion3.193297Log likelihood-41.

46、09706 Durbin-Watson stat1.474623DW = =1.474623由課本378頁D.W.檢驗上下表可知，D.W.（30,4）的上界du=1.65,下界dl=1.21。當D.W.在（0,1.21）之間時，存在正自相關(guān)；在（1.21,1.65）之間時，不能確定是否存在自相關(guān)；在（1.65，2.35）之間時，無自相關(guān)；在（2.35,2.79）之間時，不能確定是否存在自相關(guān)；在（2.79，4）之間時，存在負自相關(guān)。而此模型中D.W.為1.474623，在（1.21,1.65）之間，可知，不能確定是否存在自相關(guān)。下面采用1階廣義差分法后E-views軟件的輸出結(jié)果：Variab

47、leCoefficientStd. Errort-StatisticProb. CE-513.110056.78305-9.0363220.0000X1E2.5156000.07628932.974530.0000X2E51.383145.2353059.8147380.0000X5E-3.5658850.325969-10.939350.0000AR(1)0.2870720.2083541.3778050.1810R-squared0.999960 Mean dependent var63.43539Adjusted R-squared0.999954 S.D. dependent var1

48、48.7899S.E. of regression1.012359 Akaike info criterion3.018029Sum squared resid24.59689 Schwarz criterion3.253769Log likelihood-38.76142 Durbin-Watson stat1.923739由上結(jié)果可知，采用1階廣義差分法后的模型為：Y=513.1100+2.515600X1+51.38314X23.565885X5+0.287072AR(1)+ei (-9.036322)（32.97453）(9.814738) (-10.93935) (1.377805) =0.999954 D.W.= 1.923739經(jīng)檢驗，D.W.（29,4）的上界du=1.65,下界dl=1.20。當D.W.在（0,1.20）之間時，存在正自相關(guān)；在（1.20,