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：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.997

6、5652794446187X20.9835242294506280.99756527944461871线性图：估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C3775.3193593260248769.92804671830.43048464471025450.6702600664360232X1-0

7、.91272630855511891.938518631883585-0.47083700591944140.6415389475333828X25.522785592511612.2548570541426052.4492841275083020.021087030146243R-squared0.9675860494429319    Mean dependent var173871.8233333334Adjusted R-squared0.9651850160683343    S.D. dependent

8、 var187698.4414104575S.E. of regression35022.22758863741    Akaike info criterion23.8599929764685Sum squared resid33117023482.29852    Schwarz criterion24.00011271463471Log likelihood-354.8998946470274    Hannan-Quinn criter.23.904818484608

9、81F-statistic402.9873385683694    Durbin-Watson stat0.5432849836158895Prob(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

10、的R2值Dependent Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-236.1503079858336853.796869002943-0.27658839773166180.7841276813528842X21.1603536176166710.015330102952961675.691182321284056.

11、205455045312624e-34R-squared0.9951364867534203    Mean dependent var43924.96633333334Adjusted R-squared0.9949627898517566    S.D. dependent var48106.05415975261S.E. of regression3414.245696799649    Akaike info criterion19.17364126464171Sum

12、 squared resid326398062.9872178    Schwarz criterion19.26705442341918Log likelihood-285.6046189696256    Hannan-Quinn criter.19.20352493673524F-statistic5729.155081193856    Durbin-Watson stat0.730903182658975Prob(F-statistic)6.205455045312

13、711e-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.  C3.2221181949992160.233348310985516513.808191631604349.378486825750091e

14、-14LOG(X1)0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared0.9877359836279073    Mean dependent var11.38310574067848Adjusted R-squared0.9868275379707153   &

15、#160;S.D. dependent var1.306196606830758S.E. of regression0.1499139436548128    Akaike info criterion-0.8628711662239941Sum squared resid0.6068031435577368    Schwarz criterion-0.7227514280577785Log likelihood15.94306749335991    Hannan-Qui

16、nn criter.-0.8180456580836856F-statistic1087.28130935309    Durbin-Watson 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: 11Variab

17、leCoefficientStd. Errort-StatisticProb.  C5479.8790806823941364.2892958688484.0166547500415090.003859098436432651X11.4331353437969051.7592030257396050.81465034042582160.4388484070935154X23.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared0.9848299439189845 &

18、#160;  Mean dependent var25135.82727272728Adjusted R-squared0.9810374298987306    S.D. dependent var16782.16114325512S.E. of regression2310.981594158292    Akaike info criterion18.55573317233263Sum squared resid42725087.42830722   

19、0;Schwarz criterion18.664250064914Log likelihood-99.05653244782944    Hannan-Quinn criter.18.48732847210918F-statistic259.6773376866937    Durbin-Watson stat2.590461609402877Prob(F-statistic)5.296009374728331e-08Dependent Variable: YMethod: Least SquaresDate:

20、12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficientStd. Errort-StatisticProb.  C-131209.061546085344951.25277685769-2.9189189052732220.01932324601265213X10.90801015214794812.5137156596208070.36122230001340770.7272868120760894X24.8280901698092332.8182139453930281.7

21、13173755917920.1250330211123522R-squared0.9492597452885157    Mean dependent var376906.7363636364Adjusted R-squared0.9365746816106446    S.D. dependent var165542.7249904584S.E. of regression41690.91509980208    Akaike info criterion24.34095

22、492221962Sum squared resi87124    Schwarz criterion24.449471814801Log likelihood-130.8752520722079    Hannan-Quinn criter.24.27255022199618F-statistic74.8328719030782    Durbin-Watson stat2.016741299693539Prob(F-statistic)6.628

23、428440105899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic8.065639360788028    Prob. F(5,24)0.0001401031747031907Obs*R-squared18.80739651082681    Prob. Chi-Square(5)0.002087524503307292Scaled explained SS24.48540340808745    Prob.

24、 Chi-Square(5)0.0001751046944911128Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-172076058.1206036441097474.8325652-0.39010891682370530.6998968080763495X1-434816.1

25、859048981264665.0535233542-1.6428923279307430.1134443283056973X12-14.0260807141404617.43640515048546-0.80441355847652770.4290549805564741X1*X241.0314734815675239.804889285300281.0308149128986580.3129044598250328X2532589.0240447041306551.76908160161.7373542669164410.09514332316116304X22-28.6178784222

26、710922.88697651710863-1.2504001304356840.2232078922692591R-squared0.6269132170275604    Mean dependent var1103900782.743284Adjusted R-squared0.5491868039083021    S.D. dependent var2013044843.410424S.E. of regression1351611130.658886    Aka

27、ike info criterion45.06385981098074Sum squared resid4.384446356450382e+19    Schwarz criterion45.34409928731318Log likelihood-669.9578971647112    Hannan-Quinn criter.45.15351082726136F-statistic8.065639360788028    Durbin-Watson stat1.62042765626833Prob(F-statistic)0.0001401031747031907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-squared18.18