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19852014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19852014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。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：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19902006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.422024.420159.22002年26947.924430.32003年.636287.934195.62004年.449103.346435.82005年.862648.154273.72006年.677597.263376.862007年.493563.673300.12008年.7.9479526.532009年.282029.6968618.372010年.8494699.32011年.5.56.392012年.32013年.8.4.52014年.7.66.84数据来源：国家统计局3、 模型的检验及结果的解释、评价(一）OLS法的检验相关系数：YX1X2Y10.670260.0628X10.6702610.46187X20.06280.461871线性图：估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C3775.48769.0.025450.60232X1-0.511891.3585-0.944140.33828X25.1612.26052.83020.6243R-squared0.29319Mean dependent var.Adjusted R-squared0.83343S.D. dependent var.S.E. of regression35022.Akaike info criterion23.85Sum squared resid.29852Schwarz criterion24.471Log likelihood-354.74Hannan-Quinn criter.23.881F-statistic402.94Durbin-Watson stat0.58895Prob(F-statistic)7.3685e-21统计检验：（1） 拟合优度：从上表可以得到R2=0.29319，修正后的可决系数R2=0.83343，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：X1X2X110.46187X20.461871辅助回归的R2值Dependent Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-236.36853.3-0.166180.28842X21.66710.2961675.4056.2624e-34R-squared0.34203Mean dependent var43924.Adjusted R-squared0.17566S.D. dependent var48106.S.E. of regression3414.9Akaike info criterion19.171Sum squared resid.Schwarz criterion19.918Log likelihood-285.56Hannan-Quinn criter.19.524F-statistic5729.6Durbin-Watson stat0.8975Prob(F-statistic)6.2711e-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：Dependent Variable: LOG(Y)Method: Least SquaresDate: 12/14/15 Time: 15:35Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C3.92160.5516513.4349.0091e-14LOG(X1)0.469490.290661.43080.71318LOG(X2)0.756130.493982.8220.R-squared0.79073Mean dependent var11.848Adjusted R-squared0.07153S.D. dependent var1.0758S.E. of regression0.48128Akaike info criterion-0.39941Sum squared resid0.77368Schwarz criterion-0.77785Log likelihood15.991Hannan-Quinn criter.-0.36856F-statistic1087.Durbin-Watson stat0.15378Prob(F-statistic)1.3123e-26检验模型的异方差：（一） 图形法（goldfeld-Quandt检验）Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:04Sample: 1 11Included observations: 11VariableCoefficientStd. Errort-StatisticProb.C5479.41364.84.15090.X11.69051.96050.582160.35154X23.99731.50021.12250.75676R-squared0.89845Mean dependent var25135.Adjusted R-squared0.87306S.D. dependent var16782.S.E. of regression2310.2Akaike info criterion18.263Sum squared resid.Schwarz criterion18.4Log likelihood-99.944Hannan-Quinn criter.18.918F-statistic259.37Durbin-Watson stat2.2877Prob(F-statistic)5.8331e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficientStd. Errort-StatisticProb.C-.44951.-2.32220.X10.794812.08070.340770.60894X24.92332.30281.7920.23522R-squared0.85157Mean dependent var.Adjusted R-squared0.06446S.D. dependent var.S.E. of regression41690.Akaike info criterion24.962Sum squared resid.87124Schwarz criterion24.1Log likelihood-130.79Hannan-Quinn criter.24.618F-statistic74.82Durbin-Watson stat2.3539Prob(F-statistic)6.5899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic8.8028Prob. F(5,24)0.Obs*R-squared18.681Prob. Chi-Square(5)0.Scaled explained SS24.745Prob. Chi-Square(5)0.Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-.-0.370530.63495X1-.-1.07430.56973X12-14.04617.546-0.652770.64741X1*X241.75239.0281.86580.50328X2.1.64410.X22-28.10922.863-1.56840.92591R-squared0.75604Mean dependent var.Adjusted R-squared0.83021S.D. dependent var.S.E. of regression.Akaike info criterion45.074Sum squared resid4.0382e+19Schwarz criterion45.318Log likelihood-669.12Hannan-Quinn criter.45.136F-statistic8.8028Durbin-Watson stat1.833Prob(F-statistic)0.所以存在异方差 异方差修正：自相关的检验与修正：一 图示检验法DW检验DW 0. 对样本容量为30、两个解释变量的模型，5%的显著水平，查DW统计表可知， =1.567 =1.284 模型中DW ,显然模型中有自相关。BG检验Breusch-Godfrey Serial Correlation LM Test:F-statistic19.24107Prob. F(2,25)0.0000Obs*R-squared18.18566Prob. Chi-Square(2)0.0001Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/20/15 Time: 20:42Sample: 1985 2014Included observations: 30Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C-3494.4895807.583-0.0.5528X13.1.2.0.0408X2-3.1.-2.0.0477RESID(-1)0.0.4.0.0001RESID(-2)0.0.0.0.5883R-squared0