计量经济学张晓峒第三版课后作业

7、已知我国粮食产量Q（万吨、农业机械总动力1x（万千瓦）、化肥施用量2x（万吨）、土地灌溉面积3x（千公顷）。（1）试估计一元线性回归模型011ˆˆ tttQXe10,00015,00020,00025,00030,00035,00040,00045,00050,00030,00035,00040,00045,00050,00055,000QX1DependentVariable:QMethod:LeastSquaresDate:10/09/12Time:21:20Sample:19781998Includedobservations:21CoefficientStd.Errort-StatisticProb.X10.6080260.03910215.549720.0000C25107.081085.94023.120120.0000R-squared0.927146Meandependentvar41000.89AdjustedR-squared0.923311S.D.dependentvar6069.284S.E.ofregression1680.753Akaikeinfocriterion17.78226Sumsquaredresid53673653Schwarzcriterion17.88174Loglikelihood-184.7138Hannan-Quinncriter.17.80385F-statistic241.7938Durbin-Watsonstat1.364650Prob(F-statistic)0.000000025107.0810.610t23.121t15.55则样本回归方程为1Q25107.080.61Xtt（23.12）（15.55）r2=0.93括号内的数字为回归系数对应的t统计量的值，以下同。0121ˆˆttQXe8001,2001,6002,0002,4002,8003,2003,6004,0004,40030,00035,00040,00045,00050,00055,000QX2DependentVariable:QMethod:LeastSquaresDate:10/09/12Time:21:21Sample:19781998Includedobservations:21CoefficientStd.Errort-StatisticProb.X25.9094730.35674716.564880.0000C26937.69916.697229.385590.0000R-squared0.935241Meandependentvar41000.89AdjustedR-squared0.931833S.D.dependentvar6069.284S.E.ofregression1584.623Akaikeinfocriterion17.66447Sumsquaredresid47709547Schwarzcriterion17.76395Loglikelihood-183.4770Hannan-Quinncriter.17.68606F-statistic274.3953Durbin-Watsonstat1.247710Prob(F-statistic)0.000000026937.6915.910t29.391t16.56则样本回归方程为2Q26937.695.91Xtt(29.39)(16.56)r2=0.94013ˆˆtttQXe42,00044,00046,00048,00050,00052,00054,00030,00035,00040,00045,00050,00055,000QX3DependentVariable:QMethod:LeastSquaresDate:10/09/12Time:21:23Sample:19781998Includedobservations:21CoefficientStd.Errort-StatisticProb.X31.9468770.2708957.1868270.0000C-49775.6212650.60-3.9346450.0009R-squared0.731070Meandependentvar41000.89AdjustedR-squared0.716916S.D.dependentvar6069.284S.E.ofregression3229.199Akaikeinfocriterion19.08825Sumsquaredresid1.98E+08Schwarzcriterion19.18773Loglikelihood-198.4266Hannan-Quinncriter.19.10984F-statistic51.65048Durbin-Watsonstat0.300947Prob(F-statistic)0.000001049774.6211.950t3.931t7.193Q49775.621.95Xtt(-3.93)(7.19)r2=0.73(2)对以上三个模型的估计结果进行结构分析和统计检验。3Q49775.621.95Xtt①对回归方程的结构分析：α1=0.61是样本回归方程的斜率，它表示我国粮食产量的边际消费倾向，说明农业机械总动力每消耗1万千瓦，将生产0.61万吨粮食。α0=25107.08，是样本回归方程的截距，它表示不受农业机械总动力的影响的粮食产量。他们的大小，均符合经济理论及目前的实际情况。②统计检验：r2=0.93,说明总离差平方和的93%被样本回归直线解释，仅有7%未被解释，因此，样本回归直线对样本的拟合优度是很高的。给出显著水平α=0.05，查自由度v=21-2=19的t分布，得临界值t0.025(19)=2.09,t0=23.12t0.025(19)=2.09,t1=15.55t0.025(19)=2.09,故回归系数均显著不为零，回归模型中应包含常数项，X1对Qt有显著影响。2Q26937.695.91Xtt①对回归方程的结构分析：β1=5.91是样本回归方程的斜率，它表示我国粮食产量的边际消费倾向，说明化肥施用量每消耗1万吨，将生产5.91万吨粮食。β0=2693.69，是样本回归方程的截距，它表示不受化肥施用量的影响的粮食产量。他们的大小，均符合经济理论及目前的实际情况。②统计检验：r2=0.94,说明总离差平方和的94%被样本回归直线解释，仅有6%未被解释，因此，样本回归直线对样本的拟合优度是很高的。给出显著水平α=0.05，查自由度v=21-2=19的t分布，得临界值t0.025(19)=2.09,t0=29.39t0.025(19)=2.09，t1=16.56t0.025（19）=2.09,故回归系数均显著不为零，回归模型中应包含常数项，X2t对Qt有显著影响。3Q49775.621.95Xtt①对回归方程的结构分析：γ1=1.95是样本回归方程的斜率，它表示我国粮食产量的边际消费倾向，说明土地灌溉面积每消耗1千公顷，将生产1.95万吨粮食。γ0=-49775.62，是样本回归方程的截距，它表示不受化肥施用量的影响的粮食产量。他们的大小，不符合经济理论及目前的实际情况。②统计检验：r2=73%,说明总离差平方和的73%被样本回归直线解释，有27%未被解释，因此，样本回归直线对样本的拟合优度不是很高的。给出显著水平α=0.05，查自由度v=21-2=19的t分布，得临界值t0.025(19)=2.09,T0=-3.93t0.025(19)=2.09,t1=7.17t0.025（19）=2.09,故回归系数均显著不为零，回归模型中应包含常数项，X2t对Qt有显著影响。（3）用其中最好的模型求预测值。由上述分析可知，X2t预测的最准确，假定1999年，2000年，2001年，2002年化肥施用量分别为4190.8万吨，4287.5万吨，4367.9万吨，4495.7万吨，预测值分别为65452.97万吨，66963.25万吨,68218.36万吨,70214.97万吨。25,00030,00035,00040,00045,00050,00055,00060,00078808284868890929496980002QF±2S.E.Forecast:QFActual:QForecastsample:19782002Includedobservations:21RootMeanSquaredError1507.277MeanAbsoluteError1129.227MeanAbs.PercentError2.903414TheilInequalityCoefficient0.018198BiasProportion0.000000VarianceProportion0.016736CovarianceProportion0.9832642000年的预测区间为：[66963.25-2.09×2657.32,66963.25+2.09×2657.32]计算得：[61409.45,72517.05]