计量经济小论文.doc

成绩：20112012学年第一学期计量经济学综合作业1学院：理学院专业：统计学班级：09级1班姓名：雷文玉学号：091414753单方程作业：年份总指数建材类农副产品类纺织原料类yearyx1x2x3lnylnx1lnx2lnx31989126.4122.7128.9128.54.8394514.8097424.8590374.8559291990105.6115.2107.8107.44.6596584.746674.6802784.676561991109.1101.2106.8108.94.6922654.6170994.6709584.690431992111118.8103.4100.54.709534.7774414.6386054.6101581993135.1140.9112.2107.14.9060154.948054.7202834.6737631994118.2114.3148.3139.64.7723784.7388274.9992374.9387811995115.3102.6143.1123.64.7475374.6308384.9635444.8170511996103.9102.5114.794.54.6434294.6298634.742324.54861997101.399.710294.74.6180864.6021664.6249734.550714199895.898.694.594.34.5622634.5910714.54864.546481199996.798.889.896.84.5716134.5930984.4975854.5726472000105.1101.599.9102.44.6549124.6200594.604174.628887200199.898.6101.299.74.6031684.5910714.6170994.602166200297.798.295.797.14.5819024.5870064.5612184.5757412003104.899.7106.7101.44.6520544.6021664.6700214.6190732004111.4105.1114.2104.74.7131274.6549124.7379514.6510992005108.3103.1101.7102.44.6849054.6356994.6220274.6288872006106101.9104.3102.94.6634394.6239924.6472714.6337582007104.4103106.1101.44.648234.6347294.6643824.6190732008110.5109.5107.5103.14.7050164.6959254.6774914.635699200992.1101.19798.84.5228754.616114.5747114.593098表一915建材材料，农副产品和纺织类价格指数数据来源中中国统计年鉴20101对数据做回归处理： 1）原始数据的描述性统计量X1X2X3YMean106.5238108.8476105.2286107.5476Median102.5000106.1000102.4000105.6000Maximum140.9000148.3000139.6000135.1000Minimum98.2000089.8000094.3000092.10000Std. Dev.10.6030114.8222711.6500310.14853Skewness1.9100441.4804931.7469221.031591Kurtosis6.3186684.5710395.2898884.079687Jarque-Bera22.405809.83115415.269224.744637Probability0.0000140.0073310.0004830.093264Sum2237.0002285.8002209.8002258.500Sum Sq. Dev.2248.4784393.9922714.4632059.852Observations21212121表二由上至下分别是均值，中位数，最大值，最小值，标准差，偏度，峰度，正态性检验，P值等。同时由EVIEWS软件输出的回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/11 Time: 18:44Sample: 1989 2009Included observations: 21CoefficientStd. Errort-StatisticProb.C6.01998710.727650.5611650.5820X10.6741730.0976906.9011320.0000X20.2495650.1434401.7398540.1000X30.0242100.1875220.1291050.8988R-squared0.855602Mean dependent var107.5476Adjusted R-squared0.830121S.D. dependent var10.14853S.E. of regression4.182861Akaike info criterion5.869511Sum squared resid297.4376Schwarz criterion6.068468Log likelihood-57.62987Hannan-Quinn criter.5.912690F-statistic33.57685Durbin-Watson stat2.375577Prob(F-statistic)0.000000 表三（1）建立方程： Y = 6.01998690022 + 0.674172705671*X1 + 0.249565404554*X2 + 0.0242100329345*X3 2）为了消除异方差影响，对数据取对数，如第一个表。Dependent Variable: LNYMethod: Least SquaresDate: 12/06/11 Time: 16:42Sample: 1989 2009Included observations: 21CoefficientStd. Errort-StatisticProb.C0.1812390.4973110.3644380.7200LNX10.6483780.1074826.0324120.0000LNX20.2760520.1471681.8757570.0780LNX30.0378580.1862440.2032690.8413R-squared0.842677Mean dependent var4.673898Adjusted R-squared0.814915S.D. dependent var0.091020S.E. of regression0.039158Akaike info criterion-3.472766Sum squared resid0.026067Schwarz criterion-3.273809Log likelihood40.46404Hannan-Quinn criter.-3.429587F-statistic30.35273Durbin-Watson stat2.257620Prob(F-statistic)0.000000表四1.建立方程：LNY = C(1) + C(2)*LNX1 + C(3)*LNX2 + C(4)*LNX3LNY = 0.181238993815 + 0.648378343687*LNX1 + 0.27605201835*LNX2 + 0.0378576549048*LNX3 拟合优度检验：由上数据可知拟合程度较高.。对变量进行T检验:在10%的置信水平下1.740，显然lnx1,lnx2通过了T检验对方程进行F检验:3.20所以通过了F检验2.异方差性检验：（1）怀特检验：Heteroskedasticity Test: WhiteF-statistic0.266757Prob. F(9,11)0.9715Obs*R-squared3.762235Prob. Chi-Square(9)0.9264Scaled explained SS2.727734Prob. Chi-Square(9)0.9741Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/08/11 Time: 11:28Sample: 1989 2009Included observations: 21CoefficientStd. Errort-StatisticProb.C-2.2392342.259356-0.9910940.3429LNX10.7367410.7537260.9774650.3493LNX120.0094750.0905870.1045960.9186LNX1*LNX2-0.1443410.404810-0.3565650.7282LNX1*LNX3-0.0314430.343677-0.0914900.9287LNX21.0392381.9896180.5223310.6118LNX220.0229500.1092830.2100010.8375LNX2*LNX3-0.1301510.247499-0.5258640.6094LNX3-0.8249712.063398-0.3998120.6969LNX320.1726440.2295740.7520200.4678R-squared0.179154Mean dependent var0.001241Adjusted R-squared-0.492447S.D. dependent var0.001892S.E. of regression0.002311Akaike info criterion-8.996128Sum squared resid5.88E-05Schwarz criterion-8.498737Log likelihood104.4593Hannan-Quinn criter.-8.888181F-statistic0.266757Durbin-Watson stat1.522903Prob(F-statistic)0.971467表五怀特统计量=21*0.179154=3.762234,该值小于在1%显著性水平下，自由度为9的分布的相应临界值=21.66599，因此在1%的置信水平下接受同方差的假设。（2）G-Q检验：将原始数据按X2排成升序，去掉中间5个数据，得两个容量为8的子样本。对两个子样本分别作最小二乘回归，求各自的残差平方和RSS1和RSS2。子样本1回归结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/08/11 Time: 21:14Sample: 1989 1996Included observations: 8CoefficientStd. Errort-StatisticProb.C0.2297861.2055530.1906060.8581LNX10.6551950.1971013.3241660.0293LNX20.2056550.3011740.6828440.5322LNX30.0907070.3142720.2886270.7872R-squared0.795096Mean dependent var4.746283Adjusted R-squared0.641418S.D. dependent var0.090419S.E. of regression0.054144Akaike info criterion-2.687477Sum squared resid0.011726Schwarz criterion-2.647756Log likelihood14.74991Hannan-Quinn criter.-2.955377F-statistic5.173781Durbin-Watson stat3.574743Prob(F-statistic)0.073121表六子样本一：LNY = 0.2297859988 + 0.655195068173*LNX1 + 0.205654847593*LNX2 + 0.0907073254034*LNX30.795096 0.641418RSS1=0.011726子样本2回归结果如下：Dependent Variable: SER01Method: Least SquaresDate: 12/08/11 Time: 21:38Sample: 2002 2009Included observations: 8CoefficientStd. Errort-StatisticProb.C-5.0630584.026459-1.2574470.2770SER020.1308860.6276030.2085490.8450SER030.2180240.5712460.3816640.7221SER041.7514121.5173171.1542820.3127R-squared0.792146Mean dependent var4.646443Adjusted R-squared0.636255S.D. dependent var0.064493S.E. of regression0.038896Akaike info criterion-3.348983Sum squared resid0.006052Schwarz criterion-3.309262Log likelihood17.39593Hannan-Quinn criter.-3.616884F-statistic5.081426Durbin-Watson stat1.617656Prob(F-statistic)0.075155表七子样本二：SER01 = -5.06305769616 + 0.130885629473*SER02 + 0.218023842813*SER03 + 1.75141205662*SER040.792146 0.636255RSS2=0.006052计算F的统计量：0.516118在5%的显著性水平下，6.388233，由此可见接受原假设，即不存在异方差性。3.序列相关性检验：（1）回归检验法：Dependent Variable: EMethod: Least SquaresDate: 12/08/11 Time: 22:15Sample (adjusted): 1990 2009Included observations: 20 after adjustmentsCoefficientStd. Errort-StatisticProb.E1-0.4062180.266395-1.5248730.1447C0.0010640.0080600.1320510.8964R-squared0.114402Mean dependent var-0.000725Adjusted R-squared0.065202S.D. dependent var0.036883S.E. of regression0.035660Akaike info criterion-3.734923Sum squared resid0.022890Schwarz criterion-3.635350Log likelihood39.34923Hannan-Quinn criter.-3.715485F-statistic2.325239Durbin-Watson stat1.236495Prob(F-statistic)0.144669表八由以上回归结果得到方程：，由D.W=1.236495，dl=1.13,du=1.54,所以正好落入盲区，不能确定。（2）D.W检验法：D.W.= 2.257620在2的附近，dl=1.13,du=1.54，4-du=2.46, 所以不存在自相关性。（3）LM检验法：Breusch-Godfrey Serial Correlation LM Test:F-statistic2.129001Prob. F(1,16)0.1639Obs*R-squared2.466160Prob. Chi-Square(1)0.1163Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/08/11 Time: 22:17Sample: 1989 2009Included observations: 21Presample missing value lagged residuals set to zero.CoefficientStd. Errort-StatisticProb.C-0.0080880.481608-0.0167930.9868LNX10.0178130.1047950.1699830.8672LNX20.0020320.1425190.0142560.9888LNX3-0.0177940.180764-0.0984410.9228RESID(-1)-0.4168970.285720-1.4591100.1639R-squared0.117436Mean dependent var-6.75E-16Adjusted R-squared-0.103205S.D. dependent var0.036102S.E. of regression0.037919Akaike info criterion-3.502452Sum squared resid0.023006Schwarz criterion-3.253756Log likelihood41.77574Hannan-Quinn criter.-3.448478F-statistic0.532250Durbin-Watson stat1.465473Prob(F-statistic)0.713931表九接受原假设，所以不存在一阶序列相关性。4.多重共线性的检验：对于多个解释变量的模型，采用综合统计检验法。【在普通最小二乘法下，模型的，F值为30.35273均较大，但各参数估计值的t检验值较小，说明各解释变量对Y的联合线性作用显著，但各解释变量间存在共线性而使得他们对Y的独立作用不能分辨，固t检验不显著。】（1） 判定系数检验法由于在OLS下，较大为0.842677，而且F=30.35273=3.20,故认为材料总指数与上述解释变量间总体关系线性关系显著，符号的经济意义也合理，但X3没通过t检验，故认为解释变量间存在多重共线性。检验简单相关系数：X1，X2，X3的相关系数如下：LNX1LNX2LNX3LNX110.41801339480188510.4655594460191656LNX20.418013394801885110.8817193507144089LNX30.46555944601916560.88171935071440891表十由表中数据发现X2与X3间存在高度相关性讨论：第一步，在初始模型中引入X2，模型拟合优度有所提高，且参数符号合理，变量也通过了t检验，（2）D.W检验也表明不存在一阶序列相关性。原始模型利用逐步回归继续检验逐步回归：Dependent Variable: LNYMethod: Least SquaresDate: 12/06/11 Time: 17:39Sample: 1989 2009Included observations: 21CoefficientStd. Errort-StatisticProb.C0.8210520.5813521.4123150.1740LNX10.8260610.1246206.6286220.0000R-squared0.698119Mean dependent var4.673898Adjusted R-squared0.682230S.D. dependent var0.091020S.E. of regression0.051309Akaike info criterion-3.011506Sum squared resid0.050020Schwarz criterion-2.912028Log likelihood33.62082Hannan-Quinn criter.-2.989917F-statistic43.93862Durbin-Watson stat1.871486Prob(F-statistic)0.000002表十一他的拟合优度为0.698119，可见材料总指数受建材类的影响最大，与经验向符合，因此选它作为初始的回归模型。下面引入lnx2Dependent Variable: LNYMethod: Least SquaresDate: 12/06/11 Time: 17:41Sample: 1989 2009Included observations: 21CoefficientStd. Errort-StatisticProb.C0.2145500.4568590.4696200.6443LNX10.6533230.1018686.4134320.0000LNX20.3016180.0743534.0565840.0007R-squared0.842295Mean dependent var4.673898Adjuste