计量经济学·多元线性回归模型

1、.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

2、，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21895.538

3、27.13398.71992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1365

4、64.636287.934195.62004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4.8494699.32011年484123.5123240.56113161.392012年534123129359.31148012013年588018.8137131.4121037.52014年636138.7

5、143911.66120422.84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：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.9975652794446187X20.9835242294506280.99756527944461871线性图：估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included observations: 30Va

6、riableCoefficientStd. Errort-StatisticProb.C3775.3193593260248769.92804671830.435450.67232X1-0.91272630855511891.9385-0.474140.64828X25.522785592511612.2548570541426052.4492841275083020.6243R-squared0.9675860494429319Mean dependent var173871.8233333334Adjusted R-squared0.9651850160683343S.D. depende

7、nt var187698.4414104575S.E. of regression35022.22758863741Akaike info criterion23.8599929764685Sum squared resid33117023482.29852Schwarz criterion24.471Log likelihood-354.8998946470274Hannan-Quinn criter.23.981F-statistic402.9873385683694Durbin-Watson stat0.5432849836158895Prob(F-statistic)7.8585e-2

8、1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Dependent Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30VariableCoef

9、ficientStd. Errort-StatisticProb.C-236.36853.796869002943-0.27658839773166180.7841276813528842X21.16710.961675.6916.2624e-34R-squared0.99503Mean dependent var43924.96633333334Adjusted R-squared0.9949627898517566S.D. dependent var48106.S.E. of regression3414.245696799649Akaike info criterion19.173641

10、26464171Sum squared resid326398062.9872178Schwarz criterion19.267Log likelihood-285.66Hannan-Quinn criter.19.224F-statistic5729.6Durbin-Watson stat0.7375Prob(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

11、:35Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C3.2221181949992160.233348310985516513.8349.378486825750091e-14LOG(X1)0.299690.231661.2964839209043080.21318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.174436R-squared0.9877359836279073Mean dep

12、endent var11.38310574067848Adjusted R-squared0.9868275379707153S.D. dependent var1.3758S.E. of regression0.14998Akaike info criterion-0.8628711662239941Sum squared resid0.67368Schwarz criterion-0.7227514280577785Log likelihood15.943Hannan-Quinn criter.-0.86856F-statistic1087.28130935309Durbin-Watson

13、 stat0.4125950217515378Prob(F-statistic)1.572322907613123e-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.C5479.87964.2892958688484.15090.6432651X11.43351.75920

14、.814650.4388484070935154X23.2482294959499731.98356.6375741114312250.1476R-squared0.9848299439189845Mean dependent var25135.82727272728Adjusted R-squared0.98106S.D. dependent var16782.16114325512S.E. of regression2310.981594158292Akaike info criterion18.55573317233263Sum squared resid42725087.4283072

15、2Schwarz criterion18.664250064914Log likelihood-99.944Hannan-Quinn criter.18.48732847210918F-statistic259.6773376866937Durbin-Watson stat2.5977Prob(F-statistic)5.2961e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficientStd.

16、Errort-StatisticProb.C-131209.4951.25277685769-2.92220.265213X10.994812.58070.36122230001340770.7272868120760894X24.82832.80281.7920.12522R-squared0.9492597452885157Mean dependent var376906.7363636364Adjusted R-squared0.9365746816106446S.D. dependent var165542.7249904584S.E. of regression41690.91509

17、980208Akaike info criterion24.342Sum squared resid.87124Schwarz criterion24.449471814801Log likelihood-130.8752520722079Hannan-Quinn criter.24.27255022199618F-statistic74.8328719030782Durbin-Watson stat2.3539Prob(F-statistic)6.628428440105899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic8.8

18、028Prob. F(5,24)0.47031907Obs*R-squared18.881Prob. Chi-Square(5)0.3307292Scaled explained SS24.48540340808745Prob. Chi-Square(5)0.44911128Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-Statist

19、icProb.C-172076058.12474.8325652-0.390530.6998968080763495X1-434816.18595.0535233542-1.6428923279307430.16973X12-14.04617.43640515048546-0.804470.42941X1*X241.03239.8281.86580.31298X2532589.06551.76908160161.7373542669164410.116304X22-28.6178784222710922.88697651710863-1.25840.22321R-squared0.62694M

20、ean dependent var1103900782.743284Adjusted R-squared0.54921S.D. dependent var2013044843.410424S.E. of regression1351611130.658886Akaike info criterion45.074Sum squared resid4.384446356450382e+19Schwarz criterion45.344Log likelihood-669.9578971647112Hannan-Quinn criter.45.136F-statistic8.8028Durbin-W

21、atson stat1.623Prob(F-statistic)0.47031907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 0.54328498 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 Variab