计量经济学第二版 第四章答案.doc

4.1 (1) 存在。因为当之间的相关系数为零时，离差形式的有同理有：(2) 因为 ，且，由于，则 则 (3) 存在。因为当时，同理，有4.3(1)建立中国商品进口额为Y与国内生产总值x1、居民消费价格指数x2得回归模型 估计模型参数，结果为Dependent Variable: LNYMethod: Least SquaresDate: 05/16/12 Time: 19:15Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-3.0601490.337427-9.0690590.0000LNX11.6566740.09220617.967030.0000LNX2-1.0570530.214647-4.9246180.0001R-squared0.992218 Mean dependent var9.155303Adjusted R-squared0.991440 S.D. dependent var1.276500S.E. of regression0.118100 Akaike info criterion-1.313463Sum squared resid0.278952 Schwarz criterion-1.165355Log likelihood18.10482 F-statistic1275.093Durbin-Watson stat0.745639 Prob(F-statistic)0.000000参数估计结果如下：（2）)数据中有多重共线性，居民消费价格指数的回归系数的符号不能进行合理的经济意义解释，且其简单相关系数呈现正向变动。（3）Dependent Variable: LNYMethod: Least SquaresDate: 05/16/12 Time: 19:17Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-4.0906670.384252-10.645790.0000LNX11.2185730.03519634.622220.0000R-squared0.982783 Mean dependent var9.155303Adjusted R-squared0.981963 S.D. dependent var1.276500S.E. of regression0.171438 Akaike info criterion-0.606254Sum squared resid0.617208 Schwarz criterion-0.507515Log likelihood8.971921 F-statistic1198.698Durbin-Watson stat0.364369 Prob(F-statistic)0.000000Dependent Variable: LNYMethod: Least SquaresDate: 05/16/12 Time: 19:18Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-5.4424201.253662-4.3412180.0003LNX22.6637900.22804611.680910.0000R-squared0.866619 Mean dependent var9.155303Adjusted R-squared0.860268 S.D. dependent var1.276500S.E. of regression0.477166 Akaike info criterion1.441037Sum squared resid4.781435 Schwarz criterion1.539775Log likelihood-14.57192 F-statistic136.4437Durbin-Watson stat0.152312 Prob(F-statistic)0.000000Dependent Variable: LNX1Method: Least SquaresDate: 05/16/12 Time: 19:19Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-1.4379840.734328-1.9582310.0636LNX22.2459710.13357716.814000.0000R-squared0.930855 Mean dependent var10.87007Adjusted R-squared0.927563 S.D. dependent var1.038480S.E. of regression0.279498 Akaike info criterion0.371300Sum squared resid1.640506 Schwarz criterion0.470039Log likelihood-2.269955 F-statistic282.7107Durbin-Watson stat0.142984 Prob(F-statistic)0.000000单方程拟合效果都很好，回归系数显著，可决系数较高，GDP和CPI对进口分别有显著的单一影响,在这两个变量同时引入模型时影响方向发生了改变；GDP对CPI进行回归分析，回归系数显著，判定系数较高，说明GDP和CPI有很强的线性关系，这正是原模型多重共线性的原因。（4）如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意。4.6 (1)建立对数线性多元回归模型，引入全部变量建立对数线性多元回归模型如下:变量对数线性多元回归,结果为:Dependent Variable: LNYMethod: Least SquaresDate: 05/16/12 Time: 19:29Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C3.4420512.7061121.2719540.2228LNX111.838202.3097225.1253770.0001LNX2-11.337801.932927-5.8656090.0000LNX3-0.3714500.719447-0.5163000.6132LNX40.2198910.1520831.4458570.1688LNX5-0.1821640.105332-1.7294340.1042LNX60.2255080.3029230.7444390.4681LNX71.2700520.4847282.6201340.0193R-squared0.993930 Mean dependent var11.78641Adjusted R-squared0.991097 S.D. dependent var0.343125S.E. of regression0.032375 Akaike info criterion-3.754629Sum squared resid0.015722 Schwarz criterion-3.359675Log likelihood51.17824 F-statistic350.8771Durbin-Watson stat1.539809 Prob(F-statistic)0.000000从修正的可决系数和F统计量可以看出，全部变量对数线性多元回归整体对样本拟合很好，各变量联合起来对能源消费影响显著。可是其中的lnX4、lnX6对lnY影响不显著,而且lnX2、lnX3、lnX5的参数为负值，在经济意义上不合理。所以这样的回归结果并不理想。 (2)解释变量国民总收入(亿元)X1(代表收入水平)、国内生产总值(亿元)X2(代表经济发展水平)、工业增加值(亿元)X3、建筑业增加值(亿元)X4、交通运输邮电业增加值(亿元)X5(代表产业发展水平及产业结构)、人均生活电力消费 (千瓦小时)X6(代表人民生活水平提高)、能源加工转换效率(%)X7(代表能源转换技术)等很可能线性相关,计算相关系数如下变量LNX1LNX2LNX3LNX4LNX5LNX6LNX7LNX110.9999740.9997330.9969130.9935760.997170.708415LNX20.99997410.9997460.9971770.9938390.9968190.709065LNX30.9997330.99974610.9978870.9917010.9955110.71606LNX40.9969130.9971770.99788710.9895910.9899320.708962LNX50.9935760.9938390.9917010.98959110.9939370.664793LNX60.997170.9968190.9955110.9899320.99393710.685726LNX70.7084150.7090650.716060.7089620.6647930.6857261可以看出lnx1与lnx2、lnx3、lnx4、lnx5、lnx6之间高度相关，许多相关系数高于0.900以上。如果决定用表中全部变量作为解释变量，很可能会出现严重多重共线性问题。（3）因为存在多重共线性，解决方法如下：Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 19:49Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-76917.33103078.4-0.7462020.4671X115.232234.6587863.2695700.0052X2-15.905044.478372-3.5515230.0029X3-2.6333783.649937-0.7214860.4817X426.2643911.126342.3605610.0322X50.0747593.6752040.0203410.9840X6890.4204364.50722.4428060.0274X72155.1851498.8041.4379370.1710R-squared0.989342 Mean dependent var139423.9Adjusted R-squared0.984368 S.D. dependent var51806.33S.E. of regression6477.323 Akaike info criterion20.65821Sum squared resid6.29E+08 Schwarz criterion21.05316Log likelihood-229.5694 F-statistic198.9049Durbin-Watson stat1.278853 Prob(F-statistic)0.000000由图可以看出还是有严重多重共线性。我会采用逐步回归的办法，去检验和解决多重共线性问题:Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 19:59Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C79949.572951.12027.091260.0000X10.7344870.02791626.310490.0000R-squared0.970557 Mean dependent var139423.9Adjusted R-squared0.969155 S.D. dependent var51806.33S.E. of regression9098.624 Akaike info criterion21.15258Sum squared resid1.74E+09 Schwarz criterion21.25131Log likelihood-241.2546 F-statistic692.2419Durbin-Watson stat0.317238 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 19:57Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C79577.183085.51625.790560.0000X20.7365210.02917625.243910.0000R-squared0.968097 Mean dependent var139423.9Adjusted R-squared0.966578 S.D. dependent var51806.33S.E. of regression9471.027 Akaike info criterion21.23280Sum squared resid1.88E+09 Schwarz criterion21.33154Log likelihood-242.1772 F-statistic637.2550Durbin-Watson stat0.303167 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 19:59Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C81615.092696.63430.265550.0000X31.7331670.06113928.347930.0000R-squared0.974533 Mean dependent var139423.9Adjusted R-squared0.973321 S.D. dependent var51806.33S.E. of regression8461.964 Akaike info criterion21.00749Sum squared resid1.50E+09 Schwarz criterion21.10623Log likelihood-239.5862 F-statistic803.6049Durbin-Watson stat0.331246 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 19:59Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C79251.873030.26326.153460.0000X413.214080.51229625.793850.0000R-squared0.969402 Mean dependent var139423.9Adjusted R-squared0.967945 S.D. dependent var51806.33S.E. of regression9275.342 Akaike info criterion21.19105Sum squared resid1.81E+09 Schwarz criterion21.28979Log likelihood-241.6971 F-statistic665.3228Durbin-Watson stat0.314072 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:00Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C82253.985537.91614.852880.0000X510.921770.81045913.476030.0000R-squared0.896349 Mean dependent var139423.9Adjusted R-squared0.891414 S.D. dependent var51806.33S.E. of regression17071.46 Akaike info criterion22.41115Sum squared resid6.12E+09 Schwarz criterion22.50988Log likelihood-255.7282 F-statistic181.6035Durbin-Watson stat0.382638 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:00Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C66876.703935.72416.992220.0000X6679.225330.4119922.334130.0000R-squared0.959601 Mean dependent var139423.9Adjusted R-squared0.957677 S.D. dependent var51806.33S.E. of regression10657.87 Akaike info criterion21.46893Sum squared resid2.39E+09 Schwarz criterion21.56766Log likelihood-244.8926 F-statistic498.8135Durbin-Watson stat0.291768 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:00Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C-1191355.283030.8-4.2092780.0004X719372.594118.6424.7036360.0001R-squared0.513034 Mean dependent var139423.9Adjusted R-squared0.489846 S.D. dependent var51806.33S.E. of regression37002.72 Akaike info criterion23.95831Sum squared resid2.88E+10 Schwarz criterion24.05705Log likelihood-273.5206 F-statistic22.12419Durbin-Watson stat0.665335 Prob(F-statistic)0.000121分别作一元回归得到：变量 X1 X2X3X4X5X6X7参数估计值0.73450.73651.733213.214110.9218679.225319372.59t 统计量26.310525.243928.347925.793913.476022.33414.70360.97060.96810.97450.96940.89630.95960.51300.96920.96660.97330.96790.89140.95770.4898以X1为基础加入其他变量, 结果为:Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:01Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C83843.322740.21230.597380.0000X17.0543211.9695403.5817090.0019X2-6.3458171.977500-3.2090090.0044R-squared0.980564 Mean dependent var139423.9Adjusted R-squared0.978621 S.D. dependent var51806.33S.E. of regression7574.958 Akaike info criterion20.82419Sum squared resid1.15E+09 Schwarz criterion20.97230Log likelihood-236.4782 F-statistic504.5147Durbin-Watson stat0.464981 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:02Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C84231.503279.59625.683500.0000X1-1.0594060.784911-1.3497160.1922X34.2266251.8483692.2866790.0333R-squared0.976659 Mean dependent var139423.9Adjusted R-squared0.974325 S.D. dependent var51806.33S.E. of regression8301.111 Akaike info criterion21.00727Sum squared resid1.38E+09 Schwarz criterion21.15538Log likelihood-238.5837 F-statistic418.4359Durbin-Watson stat0.378850 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:03Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C79700.503065.92625.995570.0000X10.5125660.5191100.9873930.3352X44.0009739.3448150.4281490.6731R-squared0.970824 Mean dependent var139423.9Adjusted R-squared0.967907 S.D. dependent var51806.33S.E. of regression9280.880 Akaike info criterion21.23041Sum squared resid1.72E+09 Schwarz criterion21.37852Log likelihood-241.1497 F-statistic332.7520Durbin-Watson stat0.314608 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:03Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C80505.092595.24131.020280.0000X11.0547430.1208328.7289780.0000X5-5.0602561.869664-2.7065050.0136R-squared0.978450 Mean dependent var139423.9Adjusted R-squared0.976295 S.D. dependent var51806.33S.E. of regression7976.346 Akaike info criterion20.92746Sum squared resid1.27E+09 Schwarz criterion21.07556Log likelihood-237.6657 F-statistic454.0346Durbin-Watson stat0.568319 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 05/16/12 Time: 20:03Sample: 1985 2007Included observations: 23VariableCoefficientStd. Errort-StatisticProb. C85053.327168.65411.864610.0000X11.0076470.3501212.8779950.0093X6-254.8718325