计量经济学多元线性回归模型教学提纲.docx

1、计量经济学多元线性回归模型教学提纲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

2、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1877

3、4.32985.82574.31991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

4、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534123129359.311480120

5、13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：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.9975652794446187X20.9835242294506280.99756527944461871线性图：估计参数：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sampl

6、e: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C3775.3193593260248769.92804671830.43048464471025450.6702600664360232X1-0.91272630855511891.938518631883585-0.47083700591944140.6415389475333828X25.522785592511612.2548570541426052.449284127508302.021*R-squared0.967586

7、0494429319Mean dependent var173871.8233333334Adjusted R-squared0.9651850160683343S.D. dependent var187698.4414104575S.E. of regression35022.22758863741Akaike info criterion23.8599929764685Sum squared resid33117023482.29852Schwarz criterion24.00011271463471Log likelihood-354.8998946470274Hannan-Quinn

8、 criter.23.90481848460881F-statistic402.9873385683694Durbin-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辅助回归的

9、R2值Dependent Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-236.150*36853.796869002943-0.27658839773166180.7841276813528842X21.1603536176166710.015330102952961675.691182321284056.205455045312624e-34R

10、-squared0.9951364867534203Mean dependent var43924.96633333334Adjusted R-squared0.9949627898517566S.D. dependent var48106.05415975261S.E. of regression3414.245696799649Akaike info criterion19.173*171Sum squared resid326398062.9872178Schwarz criterion19.26705442341918Log likelihood-285.6046189696256Ha

11、nnan-Quinn criter.19.20352493673524F-statistic5729.155*6Durbin-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: 30Variab

12、leCoefficientStd. Errort-StatisticProb.C3.2221181949992160.233348310985516513.808191631604349.378486825750091e-14LOG(X1)0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared0.9877359836279073Mean

13、 dependent var11.38310574067848Adjusted R-squared0.9868275379707153S.D. dependent var1.306196606830758S.E. of regression0.1499139436548128Akaike info criterion-0.8628711662239941Sum squared resid0.6068031435577368Schwarz criterion-0.7227514280577785Log likelihood15.94306749335991Hannan-Quinn criter.

14、-0.8180456580836856F-statistic1087.28130935309Durbin-Watson stat0.4125950217515378Prob(F-statistic)1.572322907613123e-26检验模型的异方差：（一） 图形法（二） （goldfeld-Quandt检验）Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:04Sample: 1 11Included observations: 11VariableCoefficientStd. Errort-Stati

15、sticProb.C5479.8790806823941364.2892958688484.0166547500415090.003859098436432651X11.4331353437969051.7592030257396050.814650*60.4388484070935154X23.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared0.9848299439189845Mean dependent var25135.82727272728Adjusted R-squared0.98

16、10374298987306S.D. dependent var16782.16114325512S.E. of regression2310.981594158292Akaike info criterion18.55573317233263Sum squared resid42725087.42830722Schwarz criterion18.664250064914Log likelihood.0565*Hannan-Quinn criter.18.48732847210918F-statistic259.6773376866937Durbin-Watson stat2.5904616

17、09402877Prob(F-statistic)5.296009374728331e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficientStd. Errort-StatisticProb.C-131209.061546085344951.25277685769-2.9189189052732220.01932324601265213X10.90801015214794812.51371565

18、96208070.36122230001340770.7272868120760894X24.8280901698092332.8182139453930281.713173755917920.125033*2R-squared0.9492597452885157Mean dependent var376906.7363636364Adjusted R-squared0.9365746816106446S.D. dependent var165542.7249904584S.E. of regression41690.91509980208Akaike info criterion24.340

19、95492221962Sum squared resid139*.87124Schwarz criterion24.449471814801Log likelihood-130.8752520722079Hannan-Quinn criter.24.27255022199618F-statistic74.8328719030782Durbin-Watson stat2.016741299693539Prob(F-statistic)6.628428440105899e-06（三）WHITE检验Heteroskedasticity Test: WhiteF-statistic8.06563936

20、0788028Prob. F(5,24)0.0001401031747031907Obs*R-squared18.80739651082681Prob. Chi-Square(5)0.002087524503307292Scaled explained SS24.48540340808745Prob. Chi-Square(5)0.0001751046944911128Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 12/14/15 Time: 16:18Sample: 1 30Included observ

21、ations: 30VariableCoefficientStd. Errort-StatisticProb.C-172076058.1206036441097474.8325652-0.39010891682370530.6998968080763495X1-434816.1859048981264665.0535233542-1.6428923279307430.1134443283056973X12-14.0260807141404617.43640515048546-0.80441355847652770.4290549805564741X1*X2.0314*39.8048892853

22、00281.0308149128986580.3129044598250328X2.024*306551.76908160161.737354266916441.0951*X22-28.6178784222710922.88697651710863-1.2504001304356840.2232078922692591R-squared0.6269132170275604Mean dependent var1103900782.743284Adjusted R-squared0.5491868039083021S.D. dependent var2013044843.410424S.E. of

23、 regression1351611130.658886Akaike info criterion45.06385981098074Sum squared resid4.384446356450382e+19Schwarz criterion45.34409928731318Log likelihood-669.9578971647112Hannan-Quinn criter.45.153*136F-statistic8.065639360788028Durbin-Watson stat1.62042765626833Prob(F-statistic)0.0001401031747031907

24、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 Variable: RESIDMethod: Least

25、 SquaresDate: 12/20/15 Time: 20:42Sample: 1985 2014Included observations: 30Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C-3494.4895807.583-0.6017110.5528X13.5415291.6418532.1570320.0408X2-3.8932071.870051-2.0818720.0477RESID(-1)0.9712560.2030854.7825110.0001RESID(-2)0.1490140.2717090.5484320.5883