计量经济学·多元线性回归模型

计量经济学·多元线性回归模型应用作业1985~2014年中国GDP与进口、出口贸易总额的关系一、概述在当今市场上，一国的GDP与多个因素存在着紧密的联系，例如进口总额和出口总额等都是影响一国GDP的重要因素。本次将以中国1985－2014年GDP和进口总额、出口总额两个因素因素的数据，通过建立计量经济模型来分析上述变量之间的关系，强调贸易对GDP的重要性，从而促进国内生产总值的发展。二、模型构建过程⒈变量的定义解释变量：X1进口贸易总额，X2出口贸易总额被解释变量：Y国内生产总值建立计量经济模型：解释原油产量与进口贸易总额、出口贸易总额之间的关系。⒉模型的数学形式设定GDP与两个解释变量相关关系模型，样本回归模型为：⒊数据的收集该模型的构建过程中共有两个变量,分别是中国从1990－2006年民用汽车拥有量、电力产量、国内生产总值以及能源消费总量，因此为时间序列数据，最后一个即2006年的数据作为预测对比数据，收集的数据如下所示时间国内生产总值(亿元)出口总额(人民币亿元)进口总额(人民币亿元)1985年9039.9808.91257.81986年10308.81082.11498.31987年12102.214701614.21988年15101.11766.72055.11989年17090.319562199.91990年18774.32985.82574.31991年21895.53827.13398.71992年27068.34676.34443.31993年35524.35284.85986.21994年48459.610421.89960.11995年61129.812451.811048.11996年71572.312576.411557.41997年79429.515160.711806.51998年84883.715223.611626.11999年90187.716159.813736.52000年99776.320634.418638.82001年110270.422024.420159.22002年12100226947.924430.32003年136564.636287.934195.62004年160714.449103.346435.82005年185895.862648.154273.72006年217656.677597.263376.862007年268019.493563.673300.12008年316751.7100394.9479526.532009年345629.282029.6968618.372010年408903107022.8494699.32011年484123.5123240.56113161.392012年534123129359.31148012013年588018.8137131.4121037.52014年636138.7143911.66120422.84数据来源：国家统计局三、模型的检验及结果的解释、评价(一）OLS法的检验相关系数：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.9975652794446187X20.9835242294506280.99756527944461871线性图：0100,000200,000300,000400,000500,000600,000700,000868890929496980002040608101214YX1X2估计参数：DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:14:47Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C3775.3193593260248769.92804671830.43048464471025450.6702600664360232X1-0.91272630855511891.938518631883585-0.47083700591944140.6415389475333828X25.522785592511612.2548570541426052.4492841275083020.021087030146243R-squared0.9675860494429319Meandependentvar173871.8233333334AdjustedR-squared0.9651850160683343S.D.dependentvar187698.4414104575S.E.ofregression35022.22758863741Akaikeinfocriterion23.8599929764685Sumsquaredresid33117023482.29852Schwarzcriterion24.00011271463471Loglikelihood-354.8998946470274Hannan-Quinncriter.23.90481848460881F-statistic402.9873385683694Durbin-Watsonstat0.5432849836158895Prob(F-statistic)7.850214650723685e-21统计检验：（1）拟合优度：从上表可以得到R2=0.9675860494429319，修正后的可决系数R2=0.9651850160683343，这说明模型对样本的拟合很好。（2）F检验：针对H0：（二）多重共线性的检验及修正相关系数矩阵：X1X2X110.9975652794446187X20.99756527944461871辅助回归的R2值DependentVariable:X1Method:LeastSquaresDate:12/14/15Time:15:13Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-236.1503079858336853.796869002943-0.27658839773166180.7841276813528842X21.1603536176166710.015330102952961675.691182321284056.205455045312624e-34R-squared0.9951364867534203Meandependentvar43924.96633333334AdjustedR-squared0.9949627898517566S.D.dependentvar48106.05415975261S.E.ofregression3414.245696799649Akaikeinfocriterion19.17364126464171Sumsquaredresid326398062.9872178Schwarzcriterion19.26705442341918Loglikelihood-285.6046189696256Hannan-Quinncriter.19.20352493673524F-statistic5729.155081193856Durbin-Watsonstat0.730903182658975Prob(F-statistic)6.205455045312711e-34因为方差扩大因子VIF大于等于10为204.081，所以存在严重的多重共线性。对多重共线性的处理：DependentVariable:LOG(Y)Method:LeastSquaresDate:12/14/15Time:15:35Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C3.2221181940.233348310913.8081916319.37848682999216855165604345750091e-14LOG(X1)0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared0.9877359836279073Meandependentvar11.38310574067848AdjustedR-squared0.9868275379707153S.D.dependentvar1.306196606830758S.E.ofregression0.1499139436548128Akaikeinfocriterion-0.8628711662239941Sumsquaredresid0.6068031435577368Schwarzcriterion-0.7227514280577785Loglikelihood15.94306749335991Hannan-Quinncriter.-0.8180456580836856F-statistic1087.28130935309Durbin-Watsonstat0.4125950217515378Prob(F-statistic)1.572322907613123e-26检验模型的异方差：（一）图形法.00.01.02.03.04.05.06.07.08020,00060,000100,000140,000X1E2.00.01.02.03.04.05.06.07.08020,00060,000100,000140,000X2E2（goldfeld-Quandt检验）DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:16:04Sample:111Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.C5479.8790806823941364.2892958688484.0166547500415090.003859098436432651X11.4331353437969051.7592030257396050.81465034042582160.4388484070935154X23.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared0.9848299439189845Meandependentvar25135.82727272728AdjustedR-squared0.9810374298987306S.D.dependentvar16782.16114325512S.E.ofregression2310.981594158292Akaikeinfocriterion18.55573317233263Sumsquaredresid42725087.42830722Schwarzcriterion18.664250064914Loglikelihood-99.05653244782944Hannan-Quinncriter.18.48732847210918F-statistic259.6773376866937Durbin-Watsonstat2.590461609402877Prob(F-statistic)5.296009374728331e-08DependentVariable:YMethod:LeastSquaresDat