计量经济学试验报告能源指数多重线性回归

1、河用士林计量经济学实验报告-经济贸易系国际经济与贸易专业 2014级2班41号实验人王超实验地点:实训楼 B305实验日期:2016.10实验题目：线性回归模型实验类型：基本操作实验目的： 掌握Eviews的基本操作；散点图的绘制；线性回归模型中的参数估计、 模型检验、回归预测的基本操作；并能够针对回归结果及检验结果做出正确的分析。 实验内容：（按要求完成下面题目）2.1表中是16支公益股票某年的每股帐面价值和当年红利:公司序号帐面价值（元）红利（元）公司序号帐面价值（元）红利（元）122.442.4912.140.80220.892.981023.311.94322.092.061116.2

2、33.00414.481.09120.560.28520.731.96130.840.84619.251.551418.051.80720.372.161512.451.21826.431.601611.331.07根据上表资料：（1）绘制散点图（2）建立每股帐面价值和当年红利的回归方程；（3）解释回归系数的经济意义；（4）对所建立的回归模型进行检验。实验步骤：2.1建立工作文彳建立 Workfile 后，在主界面命令栏键入 data y x,其中x代表账面价值，y代表红 利，录入数据。(1)散点图3.53.02.52.01.51.00.50.00481216202428估计参数Depende

3、nt Variable: YMethod: Least SquaresDate: 09/25/16 Time: 11:48Sample: 1 16Included observations: 16VariableCoefficientStd. Errort-StatisticProb.C0.4797750.3474401.3808830.1890X0.0728760.0194313.7505620.0022R-squared0.501189Mean dependent var1.671250Adjusted R-squared0.465559S.D. dependent var0.769813

4、S.E. of regression0.562775Akaike info criterion1.804596Sum squared resid4.434023Schwarz criterion1.901169Log likelihood-12.43676Hannan-Quinn criter.1.809541F-statistic14.06672Durbin-Watson stat1.976956Prob(F-statistic)0.002151Residual Actual FittedEstimation Command:=LS Y C XEstimation Equation: =Y

5、= C(1) + C(2)*XSubstituted Coefficients: =Y = 0.479774593451 + 0.0728758993263*X(2)回归方程为 丫 = 0.479774593451 + 0.0728758993263*X(3)回归系数的经济意义：所估计的参数BA1=0.4798 , BA2=0.072876 ,说明账面价值每增加 1元，平均来说红利增加了0.072826 ,这与预期的经济意义相符。（4）进行检验:Forecast: YFActual: YForecast sample: 1 16Included observations: 16Root Mea

6、n Squared Error0.526428Mean Absolute Error0.387470Mean Abs. Percent Error28.45368Theil Inequality Coefficient0.146944Bias Proportion0.000000Variance Proportion0.170997Covariance Proportion0.829003YF 2 S.E.统计检验1,拟合优度：由表中数据可知RY=0.5011，修正的可决系数为0.4656,这说明模型对样本的拟合不是很好。t检验（P值检验）由回归结果可知 P=0.0022a=0.05,表明在a

7、=0.05的显著性水平下每股账面价值对每股红利的影响是显著的。2.2研究青春发育与远视率（对数视力）的变化关系，测得结果如下表:年龄（岁）x远视率（%） y对数视力丫=ln y663.644.153761.064.112838.843.659913.752.6211014.502.674118.072.088124.411.484132.270.82142.090.737151.020.02162.510.92173.121.138182.981.092试建立曲线回归方程? = aebx （Y?= lna + bx）并进行计量分析。Dependent Variable: LNYMethod:

8、Least SquaresDate: 11/22/16 Time: 16:43Sample: 6 18Included observations: 13VariableCoefficientStd. Errort-StatisticProb.C5.7301980.6057009.4604630.0000X-0.3139400.048187-6.5150440.0000R-squared0.794184Mean dependent var1.962923Adjusted R-squared0.775473S.D. dependent var1.371926S.E. of regression0.

9、650076Akaike info criterion2.117184Sum squared resid4.648592Schwarz criterion2.204100Log likelihood-11.76170Hannan-Quinn criter.2.099319F-statistic42.44580Durbin-Watson stat0.662056Prob(F-statistic)0.000043lna=5.7302 b=-0.3139，所以 y=lna+bx=5.7302-0.3139x从回归结果来看，RA2=0.7942 ,所以模型拟合一般。RA2=0.7942 ,t值为9.4

10、605-6.5150 ,斜率项为-0.3139, 这表明孩子的对数视力随着年龄的增加呈平均下降趋势。3.1下表给出的是1960 1982年间7个OECD国家的能源需求指数（丫）、实际GDP指数（X1）、能源价格指数（X2）的数据，所有指数均以1970年为基准（ 1970=100）年份能源需求指数Y实际GDP指数X1能源价格指数X2年份能源需求指数Y实际GDP指数X1能源价格指数X2196054.154.1111.9197297.294.398.6196155.456.4112.41973100.0100.0100.0196258.559.4111.1197497.3101.4120.11963

11、61.762.1110.2197593.5100.5131.0196463.665.9109.0197699.1105.3129.6196566.869.5108.31977100.9109.9137.7196670.373.2105.31978103.9114.4133.7196773.575.7105.41979106.9118.3144.5196878.379.9104.31980101.2119.6179.0196983.383.8101.7198198.1121.1189.4197088.986.297.7198295.6120.6190.9197191.889.8100.3(1)建

12、立能源需求与收入和价格之间的对数需求函数lnY = Po + A In X1t + 02 1nx2 +5 ,解释各回归系数的意义，用P值检验所估计回归系数是否显著。(2)再建立能源需求与收入和价格之间的线性回归模型Yt = Po + PiXIt + p2X2t + u ,解释各回归系数的意义，用P值检验所估计回归系数是否显著。(3)比较两个模型参数估计结果的经济意义有什么不同？(4)如果两个模型结论不同，你将选择哪个模型，为什么？Dependent Variable: LNYMethod: Least SquaresDate: 11/22/16 Time: 21:44Sample: 1 23I

13、ncluded observations: 23VariableCoefficientStd. Errort-StatisticProb.C1.5495040.09011317.195090.0000LNX10.9969230.01911052.166360.0000LNX2-0.3313640.024310-13.630870.0000R-squared0.994130Mean dependent var4.412077Adjusted R-squared0.993543S.D. dependent var0.224107S.E. of regression0.018008Akaike in

14、fo criterion-5.074917Sum squared resid0.006486Schwarz criterion-4.926809Log likelihood61.36154Hannan-Quinn criter.-5.037668F-statistic1693.654Durbin-Watson stat0.807847Prob(F-statistic)0.000000实验结果：对模型的参数进行估计，根据回归结果得：LnAYt=1.549504+0.996923lnX1t-0.331364lnX2tt=(17.19508) (52.16634) (-13.63086)RA2=0.

15、99413 - RA2=0.993543 F=1693.652S.E.=0.018008 DW=0.807846经济意义：在能源价格指数不变的情况下，实际GDP旨数的对数每增加一个单位，能源需求指数的对数平均增加0.996923个单位；在实际GD指数不变的情况下，能源价格指数的对数每增加一个单位，能源需求指数的对数平均减少0.331364个单位。B A1, 3人2的P值均为0.0000 ,远远小于0.05 ,说明回归系数均显著。实验步骤：Dependent Variable: YMethod: Least SquaresDate: 11/22/16 Time: 21:50Sample: 1 2

16、3Included observations: 23VariableCoefficientStd. Errort-StatisticProb.C28.255061.42148819.877090.0000X10.9808490.01945450.419000.0000X2-0.2584260.015282-16.910310.0000R-squared0.993890Mean dependent var84.34348Adjusted R-squared0.993279S.D. dependent var17.50999S.E. of regression1.435479Akaike info

17、 criterion3.681982Sum squared resid41.21199Schwarz criterion3.830090Log likelihood-39.34279Hannan-Quinn criter.3.719230F-statistic1626.707Durbin-Watson stat0.977840Prob(F-statistic)0.000000实验结果：对模型的参数进行估计，根据回归结果得：LnAYt=28.25506+0.980849lnX1t-0.30.258426lnX2tt=(19.87709) (50.419) (-16.91031)RA2=0.99389 - RA2=0.993279 F=1626.707S.E.=1.435479 DW=0.977840经济意义：在能源价格指数不变的情况下，实际GDP旨数的对数每增加一个单位，能源需求指数的对数平均增加0.9808049个单位；在实际GDP旨数不变的情况下，能源价格指数的对数每增加