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1、摘要：中国是一个农业大国，几千年传统的原始落后的农耕社会使得中国的农业发展滞后于全社会经济的发展。新世纪中国发展的关键在于解决九亿农民的发展问题，其实质就在于提高农民的实际收入。建立投资额模型，研究某地区实际投资额与国民生产总值 ( GNP ) 及物价指数 ( PI ) 的关系,根据对未来GNP及PI的估计，预测未来投资额 。以下是地区连续20年的统计数据，为了增加数据可比性，投资额和国民生产总值是以第一年为基期将数据换算后的。：关键词：投资额 国民生产总值 物价指数 1实验目的掌握运用eviews软件进行多元回归分析的基本操作方法和步骤，并能够对软件运行结果进行解释。2变量选择建立投资额模型
2、，研究某地区实际投资额与国民生产总值 ( GNP ) 及物价指数 ( PI ) 的关系,根据对未来GNP及PI的估计，预测未来投资额 。以下是地区连续20年的统计数据，为了增加数据可比性，投资额和国民生产总值是以第一年为基期将数据换算后的。：年份投资额国民生产总值物价指数Yx1x2199490.9596.70.7167199597.4637.70.72771996113.5691.10.74361997125.77560.76761998122.87990.79061999133.3873.40.82542000149.39440.86792001144.2992.70.91452002166
3、.41077.60.960120031951185.912004229.81326.41.05752005228.71434.21.15082006206.11549.21.25082007257.917181.32342008324.11918.31.40052009386.62163.91.504220104232417.81.63422011401.92631.71.78422012474.92954.71.95142013424.530732.0688下面是进行简单的多元回归：Dependent Variable: YMethod: Least SquaresDate: 11/05/1
4、5 Time: 20:32Sample: 1994 2013Included observations: 20VariableCoefficientStd. Errort-StatisticProb.X10.6361320.0685559.2791080.0000X2-892.3898127.2399-7.0134420.0000C334.707447.716337.0145250.0000R-squared0.991022Mean dependent var234.8000Adjusted R-squared0.989965S.D. dependent var125.7070S.E. of
5、regression12.59240Akaike info criterion8.041544Sum squared resid2695.663Schwarz criterion8.190904Log likelihood-77.41544Hannan-Quinn criter.8.070701F-statistic938.2299Durbin-Watson stat0.828098Prob(F-statistic)0.000000各个解释变量都都用过了t检验，总体也通过了F检验。第二次作业五、异方差的诊断与修正1）图形检验法首先，产生序列。e 2=resid2用残差的平方和X作图。X作为X轴
6、，残差的平方作为Y轴。这是得出的X1与e2的散点图从图中我们可以看到，随着X的增加，e2有着增加的趋势，但不是很明显，很难判断是否存在异方差。2）戈里瑟检验结论：由下图知F-statistic ，Obs*R-squared， P值大于0.05，所以不存在异方差。Heteroskedasticity Test: GlejserF-statistic0.389602Prob. F(2,17)0.6832Obs*R-squared0.876533Prob. Chi-Square(2)0.6452Scaled explained SS0.602108Prob. Chi-Square(2)0.7400T
7、est Equation:Dependent Variable: ARESIDMethod: Least SquaresDate: 11/08/15 Time: 19:10Sample: 1994 2013Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C9.41039925.284800.3721760.7144X10.0048520.0363270.1335520.8953X2-5.85997967.42423-0.0869120.9318R-squared0.043827Mean dependen
8、t var9.757171Adjusted R-squared-0.068664S.D. dependent var6.454763S.E. of regression6.672690Akaike info criterion6.771404Sum squared resid756.9214Schwarz criterion6.920764Log likelihood-64.71404Hannan-Quinn criter.6.800561F-statistic0.389602Durbin-Watson stat1.521978Prob(F-statistic)0.6832213）怀特检验打开
9、x与y的等式，从视图窗口导出怀特检验图，如下图Heteroskedasticity Test: WhiteF-statistic0.466019Prob. F(5,14)0.7953Obs*R-squared2.853746Prob. Chi-Square(5)0.7225Scaled explained SS1.058796Prob. Chi-Square(5)0.9577Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 11/05/15 Time: 20:37Sample: 1994 2013Include
10、d observations: 20VariableCoefficientStd. Errort-StatisticProb.C3452.8889317.5340.3705800.7165X16.33984826.299230.2410660.8130X120.0022610.0189700.1191730.9068X1*X2-10.5997270.23460-0.1509190.8822X2-13390.4149003.38-0.2732550.7886X2211944.6265113.090.1834440.8571R-squared0.142687Mean dependent var13
11、4.7832Adjusted R-squared-0.163496S.D. dependent var140.1420S.E. of regression151.1648Akaike info criterion13.11794Sum squared resid319911.3Schwarz criterion13.41666Log likelihood-125.1794Hannan-Quinn criter.13.17626F-statistic0.466019Durbin-Watson stat1.399326Prob(F-statistic)0.795252在 H 0 ： x1 x2 =
12、C=0 的原假设下， nR2 渐进地服从 X0.052(5)。 若 nR2X0.052(5)， 则拒绝H 0 ， 接受 H 1 ， 表明回归模型中参数至少有 一个显著地不为零， 即随机误差项存在异方差性。反之， 则认为不存在异方差性。在此结果中，nR2= Obs*R-squared =2.853746X0.052(5)=11.070。故接受原假设，认为不存在异方差性。六、多重共线性首先，先对解释变量进行相关系数检验，如图相关系数表X1X2X11.0000000.998582X20.9985821.00000其次，拿X1、x2分别跟y做回归，选出最优的解释变量，如下图1）X1与Y：Depende
13、nt Variable: YMethod: Least SquaresDate: 11/05/15 Time: 20:44Sample: 1994 2013Included observations: 20VariableCoefficientStd. Errort-StatisticProb.X10.1560050.00699822.291890.0000C2.81029511.724230.2397000.8133R-squared0.965044Mean dependent var234.8000Adjusted R-squared0.963102S.D. dependent var12
14、5.7070S.E. of regression24.14699Akaike info criterion9.300836Sum squared resid10495.38Schwarz criterion9.400409Log likelihood-91.00836Hannan-Quinn criter.9.320273F-statistic496.9285Durbin-Watson stat1.274525Prob(F-statistic)0.000000回归的不错2）x2与y：Dependent Variable: YMethod: Least SquaresDate: 11/05/15
15、 Time: 20:45Sample: 1994 2013Included observations: 20VariableCoefficientStd. Errort-StatisticProb.X2286.609016.2112617.679620.0000C-101.104320.15924-5.0152860.0001R-squared0.945548Mean dependent var234.8000Adjusted R-squared0.942523S.D. dependent var125.7070S.E. of regression30.13737Akaike info cri
16、terion9.744048Sum squared resid16348.70Schwarz criterion9.843621Log likelihood-95.44048Hannan-Quinn criter.9.763486F-statistic312.5690Durbin-Watson stat1.254911Prob(F-statistic)0.000000下面进行二元回归：X1与x2与Y的回归：Dependent Variable: YMethod: Least SquaresDate: 11/05/15 Time: 20:32Sample: 1994 2013Included o
17、bservations: 20VariableCoefficientStd. Errort-StatisticProb.X10.6361320.0685559.2791080.0000X2-892.3898127.2399-7.0134420.0000C334.707447.716337.0145250.0000R-squared0.991022Mean dependent var234.8000Adjusted R-squared0.989965S.D. dependent var125.7070S.E. of regression12.59240Akaike info criterion8
18、.041544Sum squared resid2695.663Schwarz criterion8.190904Log likelihood-77.41544Hannan-Quinn criter.8.070701F-statistic938.2299Durbin-Watson stat0.828098Prob(F-statistic)0.000000所以最优的回归方程是Y = 0.636131593744*X1 - 892.389823974*X2 + 334.707383297七、序列自相关性1）散点图 X1与y的散点图X2与y散点图2）残差的诊断X1与y的残差图：X2与y的残差图：可以
19、看出，逆转的次数很少。这是一种正相关的征兆。作残差 etet-1 散点图大部分的点在一三象限，所以存在正的自相关。3）D-W检验 Dependent Variable: YMethod: Least SquaresDate: 11/05/15 Time: 20:32Sample: 1994 2013Included observations: 20VariableCoefficientStd. Errort-StatisticProb.X10.6361320.0685559.2791080.0000X2-892.3898127.2399-7.0134420.0000C334.707447.71
20、6337.0145250.0000R-squared0.991022Mean dependent var234.8000Adjusted R-squared0.989965S.D. dependent var125.7070S.E. of regression12.59240Akaike info criterion8.041544Sum squared resid2695.663Schwarz criterion8.190904Log likelihood-77.41544Hannan-Quinn criter.8.070701F-statistic938.2299Durbin-Watson
21、 stat0.828098Prob(F-statistic)0.000000其中DW=0.828098，小于1，明显小于 ，所以认为有正的自相关。4）LM检验判断在估计窗口选择拉格朗日检验，首先设定滞后一期lag=1，得到LM检验结果.Breusch-Godfrey Serial Correlation LM Test:F-statistic5.961967Prob. F(1,16)0.0266Obs*R-squared5.429356Prob. Chi-Square(1)0.0198Test Equation:Dependent Variable: RESIDMethod: Least Sq
22、uaresDate: 11/08/15 Time: 19:55Sample: 1994 2013Included observations: 20Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.X1-0.0056340.060360-0.0933470.9268X27.152890111.98530.0638730.9499C-0.54763841.98190-0.0130450.9898RESID(-1)0.5759510.2358802.441
23、7140.0266R-squared0.271468Mean dependent var2.04E-13Adjusted R-squared0.134868S.D. dependent var11.91121S.E. of regression11.07891Akaike info criterion7.824821Sum squared resid1963.877Schwarz criterion8.023967Log likelihood-74.24821Hannan-Quinn criter.7.863696F-statistic1.987322Durbin-Watson stat1.8
24、48134Prob(F-statistic)0.156528结论：此时，LM=nR2= Obs*R-squared=5.429356 该值大于显著性水平为5%，自由度为1的卡方值为3.841.可以拒绝原假设，表明存在自相关。修正Dependent Variable: YMethod: Least SquaresDate: 11/08/15 Time: 20:02Sample (adjusted): 1995 2013Included observations: 19 after adjustmentsConvergence achieved after 11 iterationsVariabl
25、eCoefficientStd. Errort-StatisticProb.X10.7251500.06376611.372090.0000X2-1054.849115.5821-9.1264070.0000C388.776243.359138.9664200.0000AR(1)0.5997880.1952433.0720130.0077R-squared0.994600Mean dependent var242.3737Adjusted R-squared0.993520S.D. dependent var124.3753S.E. of regression10.01163Akaike info criterion7.630036Sum squared resid1503.492Schwarz criterion7.828866Log likelihood-68.48535Hannan-Quinn criter.7.663686F-statistic920.9971Durbin-Watson stat1.678210Prob(F-statistic)0.000000Inverted AR Roots.60