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1、编号：时间：2021年x月x日书山有路勤为径，学海无涯苦作舟页码：第8页 共8页一、 研究课题：通过对19842003年某国GDP和出口的分析，研究GDP和出口量的相关关系并对参数估计值进行检验。二、 模型及数据来源：GDP为因变量，出口量为自变量。选择模型是一元线性回归模型y=c0+c1x+u（y代表GDP，x代表出口量，u表示残差项）数据来自计量经济学软件eviews的使用135页表12.1。提取其进口和国内生产总值两列数据：annualexportgdp1984580.571711985808.98964.419861082.110202.21987147011962.519881766
2、.714928.31989195616909.219902985.818547.919913827.121617.819924676.326638.119935284.834634.4199410421.846759.4199512451.858478.1199612576.467884.6199715160.774462.6199815233.678345.2199916159.882067.5200020634.489468.1200122024.497314.8200226947.4105172.3200336287.9117251.9三、 作业1、 根据表格得到曲线图、散点图、X-Y曲
3、线图：曲线图散点图X-Y曲线图2、数据描述统计分析3、简单的回归估计Dependent Variable: GDPMethod: Least SquaresDate: 06/14/09 Time: 16:38Sample: 1984 2003Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C11772.772862.4194.1128730.0007EXPORT3.5477900.19791917.925480.0000R-squared0.946953 Mean dependent var49439
4、.02Adjusted R-squared0.944006 S.D. dependent var36735.19S.E. of regression8692.656 Akaike info criterion21.07298Sum squared resid1.36E+09 Schwarz criterion21.17256Log likelihood-208.7298 F-statistic321.3229Durbin-Watson stat0.604971 Prob(F-statistic)0.000000根据输出结果，写出OLS估计式，并进行分析说明：yt=-11772.77+3.547
5、790xt R2=0.946953 df=18检验回归系数显著性的原假设和备择假设是（给定a = 0.05）H0：c1= 0； H1：c1 0。因为t = 17.92548 t0.025 (18) = 2，所以检验结果是拒绝c1=0，即认为进口额和GDP之间存在回归关系，二者正方向变化。上述模型的经济解释是，对于出口量每增加1亿元，GDP将平均增加3.54779亿元。拟合优度为0.946953说明上式的拟合情况较好。GDP变动的94.7%可以由出口量的变动解释。 4、自相关及其解决残差：残差序列图717113832.2580652-6661.25806521| . * | . |8964.41
6、4642.5733286-5678.17332857| . * | . |10202.215611.8295893-5409.62958929| . * | . |11962.516988.0173767-5025.51737674| . * | . |14928.318040.6467053-3112.34670528| . * | . |16909.218712.2433749-1803.04337495| . *| . |18547.922365.7576403-3817.85764028| . * | . |21617.825350.513468-3732.71346804| . *
7、| . |26638.128363.2968377-1725.19683774| . *| . |34634.430522.12712564112.27287438| . | * . |46759.448747.1249708-1987.72497084| . *| . |58478.155949.1389142528.96108604| . |* . |67884.656391.193562911493.4064371| . | .* |74462.665559.74756948902.85243061| . | * |78345.265818.381469112526.8185309| .
8、 | .* |82067.569104.34467812963.155322| . | . * |89468.184979.28634794488.81365206| . | * . |97314.889910.71461447404.08538558| . | *. |105172.3107376.485374-2204.18537401| . *| . |117251.9140514.618988-23262.7189877|* . | . |由图看出残差具有较明显的自相关趋势，同时由简单回归估计的D-W值0.604971，远小于2，也可推出模型存在自相关可能。AR（1）模型的估计消除自相
9、关的回归分析Dependent Variable: GDPMethod: Least SquaresDate: 06/14/09 Time: 15:46Sample(adjusted): 1985 2003Included observations: 19 after adjusting endpointsConvergence achieved after 30 iterationsVariableCoefficientStd. Errort-StatisticProb. C-80417.9387670.31-0.9172770.3726EXPORT0.7969100.3427642.324
10、9550.0336AR(1)1.0361310.02818436.763690.0000R-squared0.994780 Mean dependent var51663.65Adjusted R-squared0.994127 S.D. dependent var36331.34S.E. of regression2784.259 Akaike info criterion18.84529Sum squared resid1.24E+08 Schwarz criterion18.99441Log likelihood-176.0303 F-statistic1524.449Durbin-Wa
11、tson stat0.560294 Prob(F-statistic)0.000000Inverted AR Roots 1.04Estimated AR process is nonstationary经过GLS处理以后，我们可以看出G-W的值由原来的0.604971改进为0.560294，基本上消除了自相关性。GDP = -80417.93181 + 0.7969104937*EXPORT + AR(1)=1.0361305915、异方差性及其修正先看散点图：由图可以看出，残差随着GDP的增大其分散程度也增大，这是存在异方差性的初步经验证据。怀特检验：White Heteroskedast
12、icity Test:F-statistic14.97532 Probability0.000178Obs*R-squared12.75835 Probability0.001697Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/14/09 Time: 23:22Sample: 1984 2003Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C41955477317976011.3194540.2045EXP
13、ORT-7517.7835261.145-1.4289250.1711EXPORT20.5061300.1617753.1286120.0061R-squared0.637918 Mean dependent var68006039Adjusted R-squared0.595320 S.D. dependent var1.23E+08S.E. of regression78013471 Akaike info criterion39.32014Sum squared resid1.03E+17 Schwarz criterion39.46950Log likelihood-390.2014
14、F-statistic14.97532Durbin-Watson stat1.737044 Prob(F-statistic)0.000178辅助回归模型中，取显著性水平a=0.05，由于Obs*R-squared=12.75835Xa/20.05（10）=18.31，所以函数不存在异方差性。由输出结果的概率值（P值）可以看出，函数不存在异方差性。因为存在异方差性，OLS所估计出来的参数标准有误，我们采用怀特法重新估计参数解决这一问题。Dependent Variable: GDPMethod: Least SquaresDate: 06/14/09 Time: 20:08Sample: 19
15、84 2003Included observations: 20White Heteroskedasticity-Consistent Standard Errors & CovarianceVariableCoefficientStd. Errort-StatisticProb. C11772.772757.3044.2696660.0005EXPORT3.5477900.34264110.354260.0000R-squared0.946953 Mean dependent var49439.02Adjusted R-squared0.944006 S.D. dependent var36
16、735.19S.E. of regression8692.656 Akaike info criterion21.07298Sum squared resid1.36E+09 Schwarz criterion21.17256Log likelihood-208.7298 F-statistic321.3229Durbin-Watson stat0.604971 Prob(F-statistic)0.000000GDP = 11772.7659 + 3.54779012*EXPORT6、总结研究发现，出口量与国民生产总值（GDP）存在正相关关系，即可以通过各种优惠政策刺激出口来有效地促进GDP的增长。同时出口量存在明显的自相关性，也就是说当年的出口量受前几年出口量的影响很大。第 8 页 共 8 页