1、精選文檔計量經(jīng)濟學(xué)多元線性回歸模型應(yīng)用作業(yè)19852014年中國GDP與進口、出口貿(mào)易總額的關(guān)系一、概述在當(dāng)今市場上，一國的GDP與多個因素存在著緊密的聯(lián)系，例如進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19852014年GDP和進口總額、出口總額兩個因素因素的數(shù)據(jù)，通過建立計量經(jīng)濟模型來分析上述變量之間的關(guān)系，強調(diào)貿(mào)易對GDP的重要性，從而促進國內(nèi)生產(chǎn)總值的發(fā)展。二、模型構(gòu)建過程變量的定義解釋變量：X1進口貿(mào)易總額，X2出口貿(mào)易總額 被解釋變量：Y國內(nèi)生產(chǎn)總值建立計量經(jīng)濟模型：解釋原油產(chǎn)量與進口貿(mào)易總額、出口貿(mào)易總額之間的關(guān)系。模型的數(shù)學(xué)形式設(shè)定GDP與兩個解釋變量相關(guān)關(guān)

2、系模型，樣本回歸模型為：數(shù)據(jù)的收集該模型的構(gòu)建過程中共有兩個變量,分別是中國從19902006年民用汽車擁有量、電力產(chǎn)量、國內(nèi)生產(chǎn)總值以及能源消費總量，因此為時間序列數(shù)據(jù)，最后一個即2006年的數(shù)據(jù)作為預(yù)測對比數(shù)據(jù)，收集的數(shù)據(jù)如下所示時間國內(nèi)生產(chǎn)總值(億元)出口總額(人民幣億元)進口總額(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.

3、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1

4、36564.636287.934195.62004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.

5、52014年636138.7143911.66120422.84數(shù)據(jù)來源：國家統(tǒng)計局3、 模型的檢驗及結(jié)果的解釋、評價(一）OLS法的檢驗相關(guān)系數(shù)：YX1X2Y10.97999191759670260.983524229450628X10.979991917596702610.9975652794446187X20.9835242294506280.99756527944461871線性圖：估計參數(shù)：Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 14:47Sample: 1985 2014Included obse

6、rvations: 30VariableCoefficientStd. Errort-StatisticProb.C3775.3193593260248769.92804671830.43048464471025450.6702600664360232X1-0.91272630855511891.938518631883585-0.47083700591944140.6415389475333828X25.522785592511612.2548570541426052.4492841275083020.021087030146243R-squared0.9675860494429319Mea

7、n 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 criter.23.90

8、481848460881F-statistic402.9873385683694Durbin-Watson stat0.5432849836158895Prob(F-statistic)7.850214650723685e-21統(tǒng)計檢驗：（1） 擬合優(yōu)度：從上表可以得到R2=0.9675860494429319，修正后的可決系數(shù)R2=0.9651850160683343，這說明模型對樣本的擬合很好。（2） F檢驗：針對H0：（二）多重共線性的檢驗及修正 相關(guān)系數(shù)矩陣：X1X2X110.9975652794446187X20.99756527944461871輔助回歸的R2值Dependent

9、Variable: X1Method: Least SquaresDate: 12/14/15 Time: 15:13Sample: 1985 2014Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-236.1503079858336853.796869002943-0.27658839773166180.7841276813528842X21.1603536176166710.015330102952961675.691182321284056.205455045312624e-34R-squar

10、ed0.9951364867534203Mean dependent var43924.96633333334Adjusted R-squared0.9949627898517566S.D. dependent var48106.05415975261S.E. of regression3414.245696799649Akaike info criterion19.17364126464171Sum squared resid326398062.9872178Schwarz criterion19.26705442341918Log likelihood-285.6046189696256H

11、annan-Quinn criter.19.20352493673524F-statistic5729.155081193856Durbin-Watson stat0.730903182658975Prob(F-statistic)6.205455045312711e-34因為方差擴大因子VIF大于等于10 為204.081，所以存在嚴(yán)重的多重共線性。對多重共線性的處理：Dependent Variable: LOG(Y)Method: Least SquaresDate: 12/14/15 Time: 15:35Sample: 1985 2014Included observations:

12、30VariableCoefficientStd. Errort-StatisticProb.C3.2221181949992160.233348310985516513.808191631604349.378486825750091e-14LOG(X1)0.29961479256469490.23109796252290661.2964839209043080.2057807637271318LOG(X2)0.53925469393756130.24855479727493982.169560595288220.03901090355174436R-squared0.987735983627

13、9073Mean 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

14、 criter.-0.8180456580836856F-statistic1087.28130935309Durbin-Watson stat0.4125950217515378Prob(F-statistic)1.572322907613123e-26檢驗?zāi)Ｐ偷漠惙讲睿海ㄒ唬?圖形法（goldfeld-Quandt檢驗）Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:04Sample: 1 11Included observations: 11VariableCoefficientStd. Errort-S

15、tatisticProb.C5479.8790806823941364.2892958688484.0166547500415090.003859098436432651X11.4331353437969051.7592030257396050.81465034042582160.4388484070935154X23.2482294959499731.9835618267750021.6375741114312250.1401455299675676R-squared0.9848299439189845Mean dependent var25135.82727272728Adjusted R

16、-squared0.9810374298987306S.D. dependent var16782.16114325512S.E. of regression2310.981594158292Akaike info criterion18.55573317233263Sum squared resid42725087.42830722Schwarz criterion18.664250064914Log likelihood-99.05653244782944Hannan-Quinn criter.18.48732847210918F-statistic259.6773376866937Dur

17、bin-Watson stat2.590461609402877Prob(F-statistic)5.296009374728331e-08Dependent Variable: YMethod: Least SquaresDate: 12/14/15 Time: 16:05Sample: 20 30Included observations: 11VariableCoefficientStd. Errort-StatisticProb.C-131209.061546085344951.25277685769-2.9189189052732220.01932324601265213X10.90

18、801015214794812.5137156596208070.36122230001340770.7272868120760894X24.8280901698092332.8182139453930281.713173755917920.1250330211123522R-squared0.9492597452885157Mean dependent var376906.7363636364Adjusted R-squared0.9365746816106446S.D. dependent var165542.7249904584S.E. of regression41690.915099

19、80208Akaike info criterion24.34095492221962Sum squared resi87124Schwarz criterion24.449471814801Log likelihood-130.8752520722079Hannan-Quinn criter.24.27255022199618F-statistic74.8328719030782Durbin-Watson stat2.016741299693539Prob(F-statistic)6.628428440105899e-06（三）WHITE檢驗Heteroskedas

20、ticity Test: WhiteF-statistic8.065639360788028Prob. 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

21、 Time: 16:18Sample: 1 30Included observations: 30VariableCoefficientStd. Errort-StatisticProb.C-172076058.1206036441097474.8325652-0.39010891682370530.6998968080763495X1-434816.1859048981264665.0535233542-1.6428923279307430.1134443283056973X12-14.0260807141404617.43640515048546-0.80441355847652770.4

22、290549805564741X1*X241.0314734815675239.804889285300281.0308149128986580.3129044598250328X2532589.0240447041306551.76908160161.7373542669164410.09514332316116304X22-28.6178784222710922.88697651710863-1.2504001304356840.2232078922692591R-squared0.6269132170275604Mean dependent var1103900782.743284Adj

23、usted R-squared0.5491868039083021S.D. dependent var2013044843.410424S.E. of regression1351611130.658886Akaike info criterion45.06385981098074Sum squared resid4.384446356450382e+19Schwarz criterion45.34409928731318Log likelihood-669.9578971647112Hannan-Quinn criter.45.15351082726136F-statistic8.065639360788028Durbin-Watson stat1.62042765626833Prob(F-statistic)0.0001401031747031907所以存在異方差 異方差修正：自相關(guān)的檢驗與修正：一 圖示檢驗法DW檢驗DW 0.54328498 對樣本容量為30、兩個解釋變量的模型，5%的顯著水平，查DW統(tǒng)計表可知， =1.567 =1.284 模型中DW ,顯然模型中有自相關(guān)。BG檢驗Breusch-Godfrey Serial Correlation LM Test:F-statistic19.2