计量经济学书后复习资料

xx?i2inxynx2nx49216626.?0y?1x3.93751.40764.505yixi7xi回归系数1的经济意义：价格每上涨(或下跌)一个单位，企业销售额平均提高(降低)1.407个单位。(2)(?1)(?0)(1i2x22?x)2?x)1212?212?26而2?2n2i22yi2y221625)(?1)1?218.39681812(?0)(16)?2(116811626)8.3964.256681(3)以0.05的显著性水平检验00t?0t0?00s?0s11?s s0.20101(4)求1的置信度为95%的置信区间。1/19xxxx?t(n2(5)求拟合优度22SSR(y?iy)2?1(xiyinxy)160.398R0.577SST(yiy)2yny2277.936拟合优度57.7%不高，说明价格只能解释企业销售额总变差的58%左右，还有42%左右(6)回归直线未解释销售变差部分SSESSTSSR277.936160.398117.538(7)当价格xf7时，预测该企业的销售额f?0?1xf4.5051.40775.3442i2i→xixixixinx→22xi22所以当x0或者x(2)求2的无偏估计量与总体方差D(i)E()ff22xinxy2222ii2i2相对应的样本方差为i2f22i)2ii]2/193/19xxyxxy22=[2212ixi2yi)]i22=[2212xix2xi2x22=[2212]即E(22)(n1)222i)22=(n1)22222n2i1=(222x1x2i2(?)?(?)?2i22xii22xi0i02R解式xixixixiyiDxiyixixixixi22iiii22(iiiii4/19tts但这一等式成立的前提是i0和ixi0同时成立(见书第32页第8行)；而i0和ixi0是用最小二乘法推导0和1的估计量时得到的两个方程(见书第18页的前两行)。yiyixi得到一个方程即ixi0(见书第22ii22iii的情况下，用最小二乘法推导的估计量时只18页的倒数第2行)。因此，在此情况下2yi2y2i2i2成立。2yi2yyi2i2iiii)i2i2i)??i2i2?i)2ixiiyiy(1)临界值00tnt2.109821t临界值，说明122i222R2yi0?0? ?00s?00s??11??1110?0?t(n2)s?022ss0?0?1t?10t?0t0?04.839152.10984.8391510.209即(4.791,25.209)；边际劳动生产率为14.743，即工作人数每增加一个单位(千人)，该工业部门年产量平均增加14.743个单位(万吨)。5/19tt(1)?1=1.0598说明有价证券收益率每提高一个单位，相应地IBM股票的收益率则平均提高1.0598个单位。(2)R2=0.4710，拟合优度不高，说明有价证券收益率只能解释IBM股票收益率总变差的47.1%，还有52.9%得不到说明。这一事实表明，只用有价证券收益率一个因素不能充IBM收益率的总变差，还需考虑别的有关因素，建立多元回归模型。(3)建立假设： 1s?1sH0:111.645，则接受原假设H0:11RAdjustedRStdErrorofheEstimatea.Predictors:(Constant),VAR00003,VAR000021mofEANOVdf279E2FSig.a.Predictors:(Constant),VAR00003,VAR00002bDependentVariableVAR000016/19aaUnstandardizedCoefficie95%ConfidenceIntervalCoefficientsntsforBModelBStd.ErrorBetatSig.LowerBoundUpperBound1(Constant).836.5471.526.171-.4592.130VAR000025.627E-02.021.6482.671.032.006.106VAR00003-.816.378-.524-2.159.068-1.711.078a.DependentVariable:VAR000010?0??2降低D0.2990.0563个单位；当家庭收入不变时，耐用品价格指数每增加一00s?0.547t?00D0.0004D(?2)0.1431s?1ss s0.021t t2t?2t2.159当223646，.2t?2t零；而0、2未通过t检验。2(3)回归参数95%的置信区间：7/191RRSquare.795a.632AdjustedRStdErrorofheEstimatea.Predictors:(Constant),VAR00006,VAR00005ANOVSumofModelSquaresdfMeanSquare1Regression4.76122.381Residual2.76814.198Total7.52916a.Predictors:(Constant),VAR00006,VAR00005bDependentVariableVAR00004FaaaUnstandardizedCoefficie95%ConfidenceIntervalCoefficientsntsforBModelBStd.ErrorBetatSig.LowerBoundUpperBound1(Constant)51.9655.2239.949.00040.76363.167VAR000055.570E-02.084.113.662.519-.125.236VAR000063.120.706.7534.420.0011.6064.634a.DependentVariable:VAR000041RAdjustedRStdErrorofheEstimatea.Predictors:(Constant),VAR00007,VAR000058/19xx1mofANOVdf2E2FSig.a.Predictors:(Constant),VAR00007,VAR00005bDependentVariableVAR00004aaUnstandardizedCoefficie95%ConfidenceIntervalCoefficientsntsforBModelBStd.ErrorBetatSig.LowerBoundUpperBound1(Constant)81.065.642126.355.00079.68982.441VAR00005-8.96E-02.047-.182-1.888.080-.191.012VAR00007-.464.043-1.031-10.721.000-.557-.371a.DependentVariable:VAR00004(3)解：平均小时工资采用响，是实际工资；而(2)中的按当前价计算的平均小时工资，含有通货膨胀的影响，是名(2)中回归方程平均小时工资的系数为负，说明即使名义工资是上升的，实际工资也12x(112x0(2)两边求对数lnylne01x即lny0第三章作业9/19yyylnyy01x1e→ln(11)(011e→ln(11)(01xyy令ylny则y0→lny令ylny则y01y(4)(4)yx→y令yxey用数据(t,lnyt)求参数的1y1((01x)→1y1e01e010y1yy1y0x10x10tln(1B)tOLS估计量。UnstandardizedCoefficie95%ConfidenceIntervalCoefficientsntsforBModelBStd.ErrorBetatSig.LowerBoundUpperBound1(Constant)4.165.006696.506.0004.1524.178VAR000081.533E-02.001.98823.301.000.014.017a.DependentVariable:YLnA4.16510/19yy用数据(y1xix0,yi1x)求参数的OLS估计量。aaUnstandardizedCoefficie95%ConfidenceIntervalCoefficientsntsforBModelBStd.ErrorBetatSig.LowerBoundUpperBoundConstant2.236.18312.224.0001.8042.669K7.604.751.96810.131.0005.8299.379a.DependentVariable:VAR0001311xi则yi则yxi0iixii的异方差结构为iix12x22ixiiiU根据矩阵形式的参数估计量公式?(XX)1XY得：11/19xxxxxxxx1222x1ix2ix1iYx22222i22222i22(x1ix2i)22i2=221i2i(x1ix2i)221i2i0?02x1i2x2?2?221i2ixixi)221i2i3、解：原始数据见第123页表4-2ii的等级xi的等级等级差di2di2d91-82203306447548641768449525-1-3-158240.8256026di26d112/19srn2srn22rsr1222754.1604ttxix1234yiyii.1027.18542i2.1716.1228.1797.1514Lnxi0以Ln为因变量、Lnxi为自变量做OLS得：afficieCoefficientsntsModelBStd.ErrorBetatSig.(Constant)-5.661.423-13.393.000LX2.482.467.8385.315.000a.DependentVariable:LRLn=-5.661+2.482Lnxi5.315)2t788，说明原始数据中存在异方差。13/19xxxxxxxx则f(xi)yiyii1i01.241ixixiiiii10.8111.25390.6380.79750.957.51830.59280.65870.9221.79190.66970.55810.89292.07390.6750.48220.86792.36360.50770.42310.84622.66040.6390.37590.82692.96380.50610.33740.80983.43020.61220.29150.78713.90940.61390.25580.76744.40020.50.22730.754.73360.44360.21130.73945.24220.43870.19080.72495.58670.57280.1790.716原模型经异方差校正后的样本回归方程为：1BStd.ErrorXXXXtSig.a.DependentVariable:YYbLinearRegressionthroughtheOrigin(0.684)(12.074)3、解：做DW检验dldududl2.62dd14/19 (3)d(4)d1.40，1.38d1.72，不能确定有无自相关；2.502.28d2.62，不能确定有无自相关；3.97d2.62，则随机干扰项存在负的自相关。dntt2nt1t2t1t2ttt2t1t2t1t2t41.51afficieCoefficientsntsModelBStd.ErrorBetatSig.1(Constant)-.475.793-.599.559VAR00003.916.082.94811.166.000a.DependentVariable:VAR0000411.948a.Predictors:(Constant),VAR00003b.DependentVariable:VAR00004bStd.ErroroftheEstimatedd622dyt1xtt15/19xtxt0.46xt110.4600.540xtx1.542.082.623.163.74.244.785.325.866.46.947.488.028.569.1yty1.081.080.082.542.623.163.77.245.46.46.947.484.027.48.48afficieCoefficientsntsModelBStd.ErrorBetatSig.1(Constant)-.781.860-.908.380X.994.148.8816.713.000a.DependentVariable:Y1RRSquare.881a.776tantXYAdjustedRbStd.ErroroftheEstimatedd??1593. 16/19第六章作业(1)因为x1(2)在两个自变量中任取一个作为自变量，进行一元线性回归分析即可得到参数估计量。AdjustedRStd.ErrorofModelRRSquareSquaretheEstimate1.988a.975.972.7028a.Predictors:(Constant),VAR001ANOV1mofdf189Faa.Predictors:(Constant),VAR001bDependentVariableVAR00001CoefficientsafficieCoefficientsntsModelBStd.ErrorBetatSig.1(Constant)20.179.44645.226.000VAR001-.688.039-.988-17.780.000a.DependentVariable:VAR000011RaRSquareAdjustedRStdErroroftimate7028a.Predictors:(Constant),VAR00217/19ANOV1mofdf189Faa.Predictors:(Constant),VAR002bDependentVariableVAR00001CoefficientsafficieCoefficientsntsModelBStd.ErrorBetatSig.1(Constant)19.835.43046.180.000VAR002-.344.019-.988-17.780.000