計(jì)量經(jīng)濟(jì)學(xué)·多元線性回歸模型

計(jì)量經(jīng)濟(jì)學(xué)·多元線性回歸模型

應(yīng)用作業(yè)1985~2014年中國GDP與進(jìn)口、出口貿(mào)易總額的關(guān)系一、

概述

在當(dāng)今市場(chǎng)上，一國的GDP與多個(gè)因素存在著緊密的聯(lián)系，例如進(jìn)口總額和出口總額等都是影響一國GDP的重要因素。本次將以中國1985－2014年GDP和進(jìn)口總額、出口總額兩個(gè)因素因素的數(shù)據(jù)，通過建立計(jì)量經(jīng)濟(jì)模型來分析上述變量之間的關(guān)系，強(qiáng)調(diào)

貿(mào)易對(duì)GDP

的重要性，從而促進(jìn)國內(nèi)生產(chǎn)總值的發(fā)展。二、

模型構(gòu)建過程

⒈變量的定義

解釋變量：X1進(jìn)口貿(mào)易總額，X2出口貿(mào)易總額

被解釋變量：Y國內(nèi)生產(chǎn)總值

建立計(jì)量經(jīng)濟(jì)模型：解釋原油產(chǎn)量與進(jìn)口貿(mào)易總額、出口貿(mào)易總額之間的關(guān)系。

⒉模型的數(shù)學(xué)形式

設(shè)定GDP與兩個(gè)解釋變量相關(guān)關(guān)系模型，樣本回歸模型為：

⒊數(shù)據(jù)的收集

該模型的構(gòu)建過程中共有兩個(gè)變量,分別是中國從1990－2006年民用汽車擁有量、電力產(chǎn)量、國內(nèi)生產(chǎn)總值以及能源消費(fèi)總量，因此為時(shí)間序列數(shù)據(jù)，最后一個(gè)即2006年的數(shù)據(jù)作為預(yù)測(cè)對(duì)比數(shù)據(jù)，收集的數(shù)據(jù)如下所示時(shí)間國內(nèi)生產(chǎn)總值(億元)出口總額(人民幣億元)進(jìn)口總額(人民幣億元)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316751.7100394.9479526.532009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數(shù)據(jù)來源：國家統(tǒng)計(jì)局模型的檢驗(yàn)及結(jié)果的解釋、評(píng)價(jià)(一）OLS法的檢驗(yàn)相關(guān)系數(shù)：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.9975652794446187X20.9835242294506280.99756527944461871

線性圖：估計(jì)參數(shù)：DependentVariable:YLOG(X1)0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared0.9877359836279073

Meandependentvar11.38310574067848AdjustedR-squared0.9868275379707153

S.D.dependentvar1.306196606830758S.E.ofregression0.1499139436548128

Akaikeinfocriterion-0.8628711662239941Sumsquaredresid0.6068031435577368

Schwarzcriterion-0.7227514280577785Loglikelihood15.94306749335991

Hannan-Quinncriter.-0.8180456580836856F-statistic1087.28130935309

Durbin-Watsonstat0.4125950217515378Prob(F-statistic)1.572322907613123e-26檢驗(yàn)?zāi)Ｐ偷漠惙讲睿簣D形法

（goldfeld-Quandt檢驗(yàn)）DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:16:04Sample:111Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C5479.8790806823941364.2892958688484.0166547500415090.003859098436432651X11.4331353437969051.7592030257396050.81465034042582160.4388484070935154X23.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared0.9848299439189845

Meandependentvar25135.82727272728AdjustedR-squared0.9810374298987306

S.D.dependentvar16782.16114325512S.E.ofregression2310.981594158292

Akaikeinfocriterion18.55573317233263Sumsquaredresid42725087.42830722

Schwarzcriterion18.664250064914Loglikelihood-99.05653244782944

Hannan-Quinncriter.18.48732847210918F-statistic259.6773376866937

Durbin-Watsonstat2.590461609402877Prob(F-statistic)5.296009374728331e-08

DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:16:05Sample:2030Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C-131209.061546085344951.25277685769-2.9189189052732220.01932324601265213X10.90801015214794812.5137156596208070.36122230001340770.7272868120760894X24.8280901698092332.8182139453930281.713173755917920.1250330211123522R-squared0.9492597452885157

Meandependentvar376906.7363636364AdjustedR-squared0.9365746816106446

S.D.dependentvar165542.7249904584S.E.ofregression41690.91509980208

Akaikeinfocriterion24.34095492221962Sumsquaredresi87124

Schwarzcriterion24.449471814801Loglikelihood-130.8752520722079

Hannan-Quinncriter.24.27255022199618F-statistic74.8328719030782

Durbin-Watsonstat2.016741299693539Prob(F-statistic)6.628428440105899e-06

（三）WHITE檢驗(yàn)HeteroskedasticityTest:WhiteF-statistic8.065639360788028

Prob.F(5,24)0.0001401031747031907Obs*R-squared18.80739651082681

Prob.Chi-Square(5)0.002087524503307292ScaledexplainedSS24.48540340808745

Prob.Chi-Square(5)0.0001751046944911128TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/14/15Time:16:18Sample:130Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C-172076058.1206036441097474.8325652-0.39010891682370530.6998968080763495X1-434816.1859048981264665.0535233542-1.6428923279307430.1134443283056973X1^2-14.0260807141404617.43640515048546-0.80441355847652770.4290549805564741X1*X241.0314734815675239.804889285300281.0308149128986580.3129044598250328X2532589.0240447041306551.76908160161.7373542669164410.09514332316116304X2^2-28.6178784222710922.88697651710863-1.2504001304356840.2232078922692591R-squared0.6269132170275604

Meandependentvar1103900782.743284AdjustedR-squared0.5491868039083021

S.D.dependentvar2013044843.410424S.E.ofregression1351611130.658886

Akaikeinfocriterion45.06385981098074Sumsquaredresid4.384446356450382e+19

Schwarzcriterion45.34409928731318Loglikelihood-669.9578971647112

Hannan-Quinncriter.45.15351082726136F-statistic8.065639360788028

Durbin-Watsonstat1.62042765626833Prob(F-statistic)0.0001401031747031907

所以存在異方差異方差修正：自相關(guān)的檢驗(yàn)與修正：一圖示檢驗(yàn)法DW檢驗(yàn)DW0.54328498對(duì)樣本容量為30、兩個(gè)解釋變量的模型，5%的顯著水平，查DW統(tǒng)計(jì)表可知，=1.567=1.284模型中DW<,顯然模型中有自相關(guān)。BG檢驗(yàn)

Breusch-GodfreySerialCorrelationLMTest:F-statistic19.24107

Prob.F(2,25)0.0000Obs*R-squared18.18566

Prob.Chi-Square(2)0.0001TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:12/20/15Time:20:42Sample:19852014Includedobservations:30Presampl