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

2、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

3、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

4、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.

5、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：YX1X2Y10.983524229450628X110.9975652794446187X20.9835242294506280.99

6、756527944461871线性图：估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C8769.92804671830.43048464471025450.6702600664360232X1-0.4708370059194414X25.522785592511612.2548570541426052

7、.449284127508302R-squared0.9675860494429319    Mean dependent var173871.8233333334Adjusted R-squared    S.D. dependent var187698.4414104575S.E. of regression35022.22758863741    Akaike info criterion23.8599929764685Sum squared resid33117023

8、482.29852    Schwarz criterionLog likelihood-354.8998946470274    Hannan-Quinn criter.23.90481848460881F-statistic402.9873385683694    Durbin-Watson stat0.5432849836158895Prob(F-statistic)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R

9、2=，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: 30VariableCoefficientStd. Errort-StatisticProb.  C853.796869002943-0.276588

10、3977316618X26.205455045312624e-34R-squared    Mean dependent var43924.96633333334Adjusted R-squared0.9949627898517566    S.D. dependent var48106.05415975261S.E. of regression3414.245696799649    Akaike info criterionSum squared resid3263980

11、62.9872178    Schwarz criterion19.26705442341918Log likelihood-285.6046189696256    Hannan-Quinn criter.19.20352493673524F-statistic    Durbin-Watson stat0.730903182658975Prob(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

12、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.  C0.23334831098551659.378486825750091e-14LOG(X1)1.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.

13、2485547972749398R-squared0.9877359836279073    Mean dependent varAdjusted R-squared0.9868275379707153    S.D. dependent varS.E. of regression    Akaike info criterionSum squared resid0.6068031435577368    Schwarz criteri

14、onLog likelihood15.94306749335991    Hannan-Quinn criter.F-statistic1087.28130935309    Durbin-Watson statProb(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 11I

15、ncluded observations: 11VariableCoefficientStd. Errort-StatisticProb.  C5479.8790806823941364.2892958688480.003859098436432651X11.7592030257396050.4388484070935154X23.2482294959499731.9835618267750021.637574111431225R-squared0.9848299439189845    Mean dependent var25135

16、.82727272728Adjusted R-squared    S.D. dependent varS.E. of regression2310.981594158292    Akaike info criterion18.55573317233263Sum squared resid42725087.42830722    Schwarz criterion18.664250064914Log likelihood-99.05653244782944 

17、60;  Hannan-Quinn criter.18.48732847210918F-statistic259.6773376866937    Durbin-Watson stat2.590461609402877Prob(F-statistic)5.296009374728331e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficie

18、ntStd. Errort-StatisticProb.  C-131209.061546085344951.25277685769X10.7272868120760894X24.828090169809233R-squared0.9492597452885157    Mean dependent var376906.7363636364Adjusted R-squared0.9365746816106446    S.D. dependent var165542.7249904584S.E.

19、 of regression41690.91509980208    Akaike info criterion24.34095492221962Sum squared resid    Schwarz criterion24.449471814801Log likelihood-130.8752520722079    Hannan-Quinn criter.24.27255022199618F-statistic74.8328719030782  &#

20、160; Durbin-Watson statProb(F-statistic)6.628428440105899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic8.065639360788028    Prob. F(5,24)Obs*R-squared18.80739651082681    Prob. Chi-Square(5)0.002087524503307292Scaled explained SS24.48540340808745

21、    Prob. Chi-Square(5)Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-172076058.1206036441097474.83256520.6998968080763495X1-434816.185904898126

22、4665.0535233542-1.642892327930743X12-14.0260807141404617.436405150485460.4290549805564741X1*X239.80488928530028X2532589.0240447041306551.76908160161.737354266916441X2222.88697651710863-1.2504001304356840.2232078922692591R-squared    Mean dependent var1103900782.743284Adjusted R-s

23、quared    S.D. dependent var2013044843.410424S.E. of regression1351611130.658886    Akaike info criterion45.06385981098074Sum squared resid4.384446356450382e+19    Schwarz criterion45.34409928731318Log likelihood-669.9578971647112 

24、0;  Hannan-Quinn criter.F-statistic8.065639360788028    Durbin-Watson stat1.62042765626833Prob(F-statistic)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-statistic19.24107    Prob. F(2,25)0.0000Obs*R-squared18.18566    Prob. Chi-Square(2)0.0001Test Equation:Dependent Variable: RESIDMethod: Least Square