2025年计量经济学实验报告

计量經济學综合试验汇报一元线性回归检查一种国家的货品周转量与货运量是密不可分的，為了考察货品周转量与货运量之间的关系，运用计量經济學的措施，進行回归分析。中国1990—货运量与货运周转量的数据如表1.1所示。表1.1中国的货运量与货运周转量年份货运量X（萬吨）货品周转量Y（亿吨公裏）19909706022620819919857932798719921045899292181993111590230647199411803963343519951234938359091996129842136590199712782183838519981267427380891999129300840568135868244321140178647710148344750686156449253859170641269445186206680258203706088840227582210141925859371103002825222122133.3数据来源：《中国交通年鉴》（）整顿建立模型根据表一数据，為對其進行线性回归分析，建立如下一元回归模型：Y=表1.2給出了采用Eviews软件對表1.1数据進行最小二乘线性回归分析的成果。表1.2中国货运周转量對货运量的回归分析（1990--）DependentVariable:YMethod:LeastSquaresSample:1990Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C-30611.522621.031-11.679190.0000X0.0558390.00161634.551220.0000R-squared0.985146Meandependentvar55300.37AdjustedR-squared0.984321S.D.dependentvar29604.40S.E.ofregression3706.977Akaikeinfocriterion19.36846Sumsquaredresid2.47E+08Schwarzcriterion19.46803Loglikelihood-191.6846F-statistic1193.787Durbin-Watsonstat0.705251Prob(F-statistic)0.000000根据表1.2写出如下回归分析成果：Y=（-11.68）（34.55），，其中括号内的数為對应参数的t检查值，為可决系数，F為方程整体线性明显性检查值，為模型序列有关性检查值模型检查從回归估计的成果看，模型拟合很好。可决系数，表明模型在整体上拟合的非常好。并且從常数项和解释变量系数的检查值看，比給定5%明显性水平下自由度為n-2=19的临界值2.093都大的多，阐明参数值是比较明显的。而從可以看出，遠遠不小于模型的整体的线性关系也是非常明显的。，在(0,d=1.2)之间，则应當存在一阶有关关系，运用拉格朗曰乘数法進行二阶有关关系检查得表2.1如下：表2.1Breusch-GodfreySerialCorrelationLMTest:F-statistic7.558370Probability0.004887Obs*R-squared9.716146Probability0.007765DependentVariable:RESIDVariableCoefficientStd.Errort-StatisticProb.C171.95132366.1900.0726700.9430X-0.0001410.001521-0.0927320.9273RESID(-1)0.8971660.2341263.8319750.0015RESID(-2)-0.4233190.285806-1.4811400.1580R-squared0.485807Meandependentvar-9.19E-12AdjustedR-squared0.389396S.D.dependentvar3608.106S.E.ofregression2819.415Akaikeinfocriterion18.90330Sumsquaredresid1.27E+08Schwarzcriterion19.10245Loglikelihood-185.0330F-statistic5.038913Durbin-Watsonstat2.077498Prob(F-statistic)0.01由表2.1可知，9.716，该值不小于明显性水平為5%，自由度為2的分布的临界值（2）=5.991，由此判断存在二阶序列有关性。再运用拉格朗曰乘数法進行三阶有关关系检查，得表2.2：表2.2Breusch-GodfreySerialCorrelationLMTest:F-statistic5.163250Probability0.011920Obs*R-squared10.16063Probability0.017249DependentVariable:RESIDVariableCoefficientStd.Errort-StatisticProb.C-219.01102437.122-0.0898650.9296X9.83E-050.0015630.0629010.9507RESID(-1)0.8239920.2526753.2610770.0053RESID(-2)-0.2122090.386183-0.5495030.5907RESID(-3)-0.2745290.333503-0.8231680.4233R-squared0.508031Meandependentvar-9.19E-12AdjustedR-squared0.376840S.D.dependentvar3608.106S.E.ofregression2848.257Akaikeinfocriterion18.95912Sumsquaredresid1.22E+08Schwarzcriterion19.20805Loglikelihood-184.5912F-statistic3.872437Durbin-Watsonstat2.051318Prob(F-statistic)0.023534由表2.2可知，虽然10.161，仍然比明显性水平為5%，自由度為3的分布的临界值（3）=7.815要大，但由于的参数不明显，且阐明不存在三阶序列有关。用科克伦—奥科特迭代法對原模型進行修正，并用拉格朗曰乘数法進行检查，得表2.3如下：表2.3Breusch-GodfreySerialCorrelationLMTest:F-statistic0.981613Probability0.415681Obs*R-squared3.152755Probability0.206723DependentVariable:RESIDMethod:LeastSquaresVariableCoefficientStd.Errort-StatisticProb.C-418.679711658.54-0.0359120.9722X0.0038150.0332670.1146770.9115X(-1)0.0117680.0366230.3213150.7562X(-2)-0.0163020.039801-0.4095980.6928AR(1)1.7270241.2970731.3314770.2197AR(2)-0.6954500.687141-1.0120910.3411RESID(-1)-1.9575451.397689-1.4005580.1989RESID(-2)-0.9676880.935849-1.0340210.3314R-squared0.197047Meandependentvar-3.90E-07AdjustedR-squared-0.505537S.D.dependentvar2756.964S.E.ofregression3382.804Akaikeinfocriterion19.39765Sumsquaredresid91546893Schwarzcriterion19.78394Loglikelihood-147.1812F-statistic0.280461Durbin-Watsonstat1.947722Prob(F-statistic)0.944432由表2.3可看出，修正後的3.153，该值不不小于明显性水平為5%，自由度為2的分布的临界值（2）=5.991，由此可以判断模型不再存在有关关系。检查模型与否存在异方差在表1.2的基础上，运用white检查對模型与否存在异方差進行检查，得表2.4如下：表2.4WhiteHeteroskedasticityTest:F-statistic4.972142Probability0.019946Obs*R-squared7.381368Probability0.024955DependentVariable:RESID^2Method:LeastSquaresSample:1990Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C-4607806229706420-1.5511150.1393X58.8903935.148641.6754670.1121X^2-1.22E-059.47E-06-1.2908430.2140R-squared0.369068Meandependentvar12367509AdjustedR-squared0.294841S.D.dependentvar13246720S.E.ofregression11123765Akaikeinfocriterion35.42455Sumsquaredresid2.10E+15Schwarzcriterion35.57391Loglikelihood-351.2455F-statistic4.972142Durbin-Watsonstat1.196673Prob(F-statistic)0.019946由表2.4可知，7.381，该值不小于明显性水平為5%，自由度為2的分布的临界值（2）=5.991，因此拒绝同方差的原假设。下面采用加权最小對原模型進行回归，即采用為权重進行加权最小二乘估计，得表2.5（未加权项略）如下：表2.5DependentVariable:YSample:1990Includedobservations:20Weightingseries:1/ZVariableCoefficientStd.Errort-StatisticProb.C-30343.752120.160-14.312010.0000X0.0556740.00151336.787590.0000R-squared0.999979Meandependentvar47286.79AdjustedR-squared0.999977S.D.dependentvar148089.5S.E.ofregression702.6228Akaikeinfocriterion16.04216Sumsquaredresid8886217.Schwarzcriterion16.14173Loglikelihood-158.4216F-statistic1353.326Durbin-Watsonstat0.781900Prob(F-statistic)0.000000由表2.5与表1.2對照可清晰的看到，無论是拟合优度，還是参数的明显性，加权後最小二乘估计比加权前均有了改善，并且對加权後的回归模型進行检查，也可验证，模型不再存在异方差（如表2.6所示）。表2.6WhiteHeteroskedasticityTest:F-statistic0.009460Probability0.990590Obs*R-squared0.022234Pro