計量經(jīng)濟學(xué)·多元線性回歸模型

-.z.計量經(jīng)濟學(xué)·多元線性回歸模型應(yīng)用作業(yè)1985~2014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與多個因素存在著嚴(yán)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1985－2014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，從而促進國生產(chǎn)總值的開展。二、模型構(gòu)建過程⒈變量的定義解釋變量：*1進口貿(mào)易總額，*2出口貿(mào)易總額被解釋變量：Y國生產(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。⒉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)系模型，樣本回歸模型為：⒊數(shù)據(jù)的收集該模型的構(gòu)建過程中共有兩個變量,分別是中國從1990－2006年民用汽車擁有量、電力產(chǎn)量、國生產(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)測比照數(shù)據(jù)，收集的數(shù)據(jù)如下所示時間國生產(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21895.53827.13398.71992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)計局模型的檢驗及結(jié)果的解釋、評價(一〕OLS法的檢驗相關(guān)系數(shù)：Y*1*2Y10.670260.0628*10.6702610.46187*20.06280.461871線性圖：估計參數(shù)：DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:14:47Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C3775.48769.92804671830.025450.60232*1-0.511891.3585-0.944140.33828*25.1612.26052.83020.6243R-squared0.29319

Meandependentvar173871.8233333334AdjustedR-squared0.83343

S.D.dependentvar187698.4414104575S.E.ofregression35022.

Akaikeinfocriterion23.85Sumsquaredresid.29852

Schwarzcriterion24.471Loglikelihood-354.74

Hannan-Quinncriter.23.881F-statistic402.94

Durbin-Watsonstat0.58895Prob(F-statistic)7.3685e-21統(tǒng)計檢驗：擬合優(yōu)度：從上表可以得到R2=0.29319，修正后的可決系數(shù)R2=0.83343，這說明模型對樣本的擬合很好。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：*1*2*110.46187*20.461871輔助回歸的R2值DependentVariable:*1Method:LeastSquaresDate:12/14/15Time:15:13Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C-236.36853.3-0.166180.28842*21.66710.2961675.4056.2624e-34R-squared0.34203

Meandependentvar43924.AdjustedR-squared0.17566

S.D.dependentvar48106.S.E.ofregression3414.9

Akaikeinfocriterion19.171Sumsquaredresid326398062.9872178

Schwarzcriterion19.918Loglikelihood-285.56

Hannan-Quinncriter.19.524F-statistic5729.6

Durbin-Watsonstat0.8975Prob(F-statistic)6.2711e-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：DependentVariable:LOG(Y)Method:LeastSquaresDate:12/14/15Time:15:35Sample:19852014Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C3.92160.5516513.4349.0091e-14LOG(*1)0.469490.290661.43080.71318LOG(*2)0.756130.493982.8220.R-squared0.79073

Meandependentvar11.848AdjustedR-squared0.07153

S.D.dependentvar1.0758S.E.ofregression0.48128

Akaikeinfocriterion-0.39941Sumsquaredresid0.77368

Schwarzcriterion-0.77785Loglikelihood15.991

Hannan-Quinncriter.-0.36856F-statistic1087.

Durbin-Watsonstat0.15378Prob(F-statistic)1.3123e-26檢驗?zāi)Ｐ偷漠惙讲睿簣D形法〔goldfeld-Quandt檢驗〕DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:16:04Sample:111Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C5479.41364.84.15090.1*11.69051.96050.582160.35154*23.99731.50021.12250.75676R-squared0.89845

Meandependentvar25135.AdjustedR-squared0.87306

S.D.dependentvar16782.S.E.ofregression2310.2

Akaikeinfocriterion18.263Sumsquaredresid42725087.42830722

Schwarzcriterion18.4Loglikelihood-99.944

Hannan-Quinncriter.18.918F-statistic259.37

Durbin-Watsonstat2.2877Prob(F-statistic)5.8331e-08DependentVariable:YMethod:LeastSquaresDate:12/14/15Time:16:05Sample:2030Includedobservations:11VariableCoefficientStd.Errort-StatisticProb.

C-131209.061546085344951.-2.32220.*10.794812.08070.340770.60894*24.92332.30281.7920.23522R-squared0.85157

Meandependentvar376906.7363636364AdjustedR-squared0.06446

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

Akaikeinfocriterion24.962Sumsquaredresid.87124

Schwarzcriterion24.1Loglikelihood-130.79

Hannan-Quinncriter.24.618F-statistic74.82

Durbin-Watsonstat2.3539Prob(F-statistic)6.5899e-06〔三〕WHITE檢驗HeteroskedasticityTest:WhiteF-statistic8.8028

Prob.F(5,24)0.07Obs*R-squared18.681

Prob.Chi-Square(5)0.2Scalede*plainedSS24.745

Prob.Chi-Square(5)0.28TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/14/15Time:16:18Sample:130Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.

C-172076058.1206036441097474.8325652-0.370530.63495*1-434816.1859048981264665.0535233542-1.07430.56973*1^2-14.04617.546-0.652770.64741*1**241.75239.0281.86580.50328*2532589.0240447041306551.76908160161.64410.*2^2-28.10922.863-1.56840.92591R-squared0.75604

Meandependentvar1103900782.743284AdjustedR-squared0.83021

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

Akaikeinfocriterion45.074Sumsquaredresid4.0382e+19

Schwarzcriterion45.318Loglikelihood-669.12

Hannan-Quinncriter.45.136F-statistic8.8028

Durbin-Watsonstat1.833Prob(F-statistic)0.07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DW0.54328498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-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:1985201