计量经济学eviews操作95分线性回归保费收入模型上机作业2003版 (2)

保费收入的相关数据表年份寿险保费收入(亿元)yGDP(亿元)x1城镇居民家庭人均可支配收入(元) x2 城镇恩格尔系数 x365 岁以上人口占总人口百分数 x4社会保障基金支出(亿元)x5通胀率(居民消费价格指数)x6利率(央行历年存款利率%) x71990 49.08 18667.82 1510.2 54.24 5.57 151.9 103.1 2.161991 63.17 21781.5 1700.6 53.8 5.7 176.1 103.4 1.81992 93.86 26923.48 2026.6 53.04 5.82 327.1 106.4 1.81993 85.95 35333.92 2577.4 50.32 5.95 482.2 114.7 3.151994 143.13 48197.86 3496.2 50.04 6.07 680 124.1 3.151995 160.9 60793.73 4283 50.09 6.2 877.1 117.1 3.151996 214.81 71176.59 4838.9 48.76 6.41 1082.4 108.3 1.981997 390.48 78973.03 5160.3 46.6 6.54 1339.2 102,8 1.711998 750.22 84402.28 5425.1 44.66 6.7 1636.9 99.2 1.441999 878.95 89677.05 5854.02 42.07 6.9 2108.1 98.6 0.992000 990 99214.55 6280 39.44 6.96 2385.6 100.4 0.992001 1423.52 109655.17 6859.6 38.2 7.1 2748 100.7 0.992002 2274.8 120332.69 7702.8 37.68 7.3 3471.5 99.2 0.722003 3011 135822.76 8472.2 37.1 7.5 4016.4 101.2 0.722004 3194 159878.34 9421.6 37.7 7.6 4627.4 103.9 0.722005 3649 184937.37 10493 36.7 7.7 5401 101.8 0.722006 4061 216314.43 11759.5 35.8 7.9 6583 101.5 0.722007 4949.7 265810.31 13785.8 36.29 8.1 7887.8 104.8 0.722008 7338 314045.43 15780.76 37.89 8.3 9925.1 105.9 0.362009 8144.4 340902.81 17174.65 36.52 8.5 12302.6 99.3 0.362010 10501.1 401202.03 19109.44 35.7 8.87 9014.243 101.3 0.362011 9560 472881.6 21809.8 36.3 9.13 9547.935 105.4 0.41、 提出并分析相关问题2、 利用数据，构造计量经济学模型3、 估计并完成模型，对结果给出评价4、 对你的研究给出结论及展望。1. 提出并分析相关问题提出问题：寿险保费收入与其他变量怎样拟合能较好的解释其变化？分析问题：寿险保费收入作为被解释变量，可以在其他 6 个解释变量下，通过一定的设计，做出有经济学意义的回归模型。一、首先要选择合适的与寿险保费收入的经济学理论和行为相关的变量。变量 x1 为 GDP，在 GDP 越高的情况下，生产总值的提升说明社会发展水平提升，对寿险的重视程度很可能也随之提高，因此人们的保费收入也会成正相关变化。变量 x2 为城镇居民家庭人均可支配收入，与 GDP 类似，该变量与保费收入成正相关变化。但其没有包括农村居民收入，因此有些局限性。还要通过进一步分析确定。变量 x3 城镇恩格尔系数越低，说明居民花在食品上的费用占总费用比重越小，其生活水平越高，按该情况居民应更有基础注重保险业务。但从数据上来看，该变量若作为解释变量，其系数应为负。也就是说明，该变量或许与 Y 的关系并不单纯直接，应该还会有其他的因素影响。变量 x4 是 65 岁以上人口占总人口百分数,当该比例越大时，表明需要人寿保险的群体比重增加，保费收入也应该增加。变量 x5 社会保障基金支出的增长，有助于促进保费收入的增加。变量 x6 通胀率(居民消费价格指数)通货膨胀率受很多方面的影响，同时大体上来看，它与保费收入的关系并不密切。变量 x7 利率(央行历年存款利率%)，利率一般是由央行根据整个经济情况决定的，是个比较宏观的（相对来说）变动较小经济变量，同样与保费收入关系不密切，应予以剔除。二、结合散点图，根据经济行为理论，确定变量之间的数学关系。通过散点图，可初步推断 y 与 x1x5 有线性关系。y 与 x1x5 散点图同时，根据经济学意义以及对各变量的分析（见上一标题） ，也可得出y 与各变量成线性相关的关系。三根据经济学意义确定剩下的变量的模型参数估计。同时注意他们之间的独立性。可以通过数据，发现 y 与 x1x5 有正相关关系，故它们前面的系数应该都为正数。另外，通过相关系数矩阵，发现他们之间存在严重的多重共线性。有的相关系数甚至达到了 0.99 以上，对其的相关处理我将在后面进行。X1 X2 X3 X4 X5 X6X1 1 0.995591 -0.75397 0.954979 0.947109 -0.26679X2 0.995591 1 -0.80634 0.977026 0.959676 -0.2963X3 -0.75397 -0.80634 1 -0.91088 -0.7945 0.514843X4 0.954979 0.977026 -0.91088 1 0.941551 -0.39444X5 0.947109 0.959676 -0.7945 0.941551 1 -0.3265X6 -0.26679 -0.2963 0.514843 -0.39444 -0.3265 12. 利用数据，构造计量经济学模型首先，对 y 做一个对所有变量的多元回归模型。Dependent Variable: YMethod: Least SquaresDate: 06/05/13 Time: 20:21Sample: 1990 2011Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. X1 0.062356 0.027134 2.298104 0.0354X2 -1.716488 0.952013 -1.803008 0.0903X3 190.6488 150.8816 1.263566 0.2245X4 4815.267 3016.598 1.596258 0.1300X5 0.382722 0.151151 2.532061 0.0222C -36195.42 23730.64 -1.525261 0.1467R-squared 0.976812 Mean dependent var 2814.867Adjusted R-squared 0.969565 S.D. dependent var 3315.807S.E. of regression 578.4598 Akaike info criterion 15.78562Sum squared resid 5353852. Schwarz criterion 16.08317Log likelihood -167.6418 Hannan-Quinn criter. 15.85571F-statistic 134.8008 Durbin-Watson stat 1.910836Prob(F-statistic) 0.000000发现 t 值较为显著的仅有 x1 和 x5.￥%&*（） 可继续说明3. 估计并完成模型，对结果给出评价一、估计并完成模型：思路一：下面运用 Eviews 软件系统自动逐步回归法做出的多元线性模型为：Variable Coefficient Std. Error t-Statistic Prob.* X1 0.024973 0.001013 24.64162 0.0000X6 -9.516028 1.918036 -4.961339 0.0001R-squared 0.967105 Mean dependent var 2814.867Adjusted R-squared 0.965460 S.D. dependent var 3315.807S.E. of regression 616.2375 Akaike info criterion 15.77165Sum squared resid 7594973. Schwarz criterion 15.87084Log likelihood -171.4881 Hannan-Quinn criter. 15.79502Durbin-Watson stat 1.406837分析：可见其思路二：利用向前选择法第一步，用每个解释变量分别对被解释变量做简单回归，得到 Y 与 x1:= -1013.927 +0.025092x1 （24.08990）R= 0.966685 F= 580.3233 对 x2= -1835.837 + 0.551502x2（271.1357） (20.75179)R= 0.9555618 F= 430.6369 对 x3= 17955.12 -354.7465x3（5.577219） (-4.759700)R=0.531119 F= 22.65474 DW=0.172052 对 X4X4 2946.593 250.7429 11.75145 0.0000C -18188.99 1805.815 -10.07245 0.0000R-squared 0.873495 Mean dependent var 2814.867Adjusted R-squared 0.867170 S.D. dependent var 3315.807S.E. of regression 1208.475 Akaike info criterion 17.11861Sum squared resid 29208222 Schwarz criterion 17.21780Log likelihood -186.3047 Hannan-Quinn criter. 17.14198F-statistic 138.0967 Durbin-Watson stat 0.316946Prob(F-statistic) 0.000000=-18188.99+2946.593x4（-10.07245） (11.75145)R=0.873495 F= 138.0967 DW=0.316946 对 x5=0.77532x5（17.6609） R=0.8893=294 DW=1.109666根据 R统计量的大小排序，可见解释变量的重要程度依次为 x1,x2,x5,x4,x3,第二步，以 = -1013.927 +0.025092x1 为基础，依次引入 x2,x5,x4,x3,与逐步回归法不同的是，不再引入已经删除掉的变量。首先把 x2 引入模型回归得Variable Coefficient Std. Error t-Statistic Prob. X1 0.028871 0.011359 2.541631 0.0199X2 -0.083903 0.251106 -0.334135 0.7419C -882.9879 445.3053 -1.982882 0.0620R-squared 0.966879 Mean dependent var 2814.867Adjusted R-squared 0.963393 S.D. dependent var 3315.807S.E. of regression 634.4133 Akaike info criterion 15.86940Sum squared resid 7647125. Schwarz criterion 16.01818Log likelihood -171.5634 Hannan-Quinn criter. 15.90445F-statistic 277.3292 Durbin-Watson stat 1.447167Prob(F-statistic) 0.000000Adjusted R-squared 0.963393 因为 x2 的引入是 R 改善幅度较小，且 x2 的系数没有通过 t 显著性检验 所以在模型中剔除 x2,引入 x5Variable Coefficient Std. Error t-Statistic Prob. X1 0.020792 0.003163 6.573520 0.0000X5 0.158927 0.110717 1.435428 0.1674C -984.6087 202.5046 -4.862156 0.0001R-squared 0.969944 Mean dependent var 2814.867Adjusted R-squared 0.966780 S.D. dependent var 3315.807S.E. of regression 604.3485 Akaike info criterion 15.77230Sum squared resid 6939506. Schwarz criterion 15.92108Log likelihood -170.4953 Hannan-Quinn criter. 15.80735F-statistic 306.5770 Durbin-Watson stat 1.630647Prob(F-statistic) 0.000000上一步的原因相同，剔除 x5，引入 x4Variable Coefficient Std. Error t-Statistic Prob. X1 0.026290 0.003591 7.321895 0.0000X4 -154.9759 443.5722 -0.349381 0.7306C -92.03537 2647.097 -0.034768 0.9726R-squared 0.966897 Mean dependent var 2814.867Adjusted R-squared 0.963413 S.D. dependent var 3315.807S.E. of regression 634.2404 Akaike info criterion 15.86886Sum squared resid 7642957. Schwarz criterion 16.01764Log likelihood -171.5574 Hannan-Quinn criter. 15.90390F-statistic 277.4856 Durbin-Watson stat 1.458254Prob(F-statistic) 0.000000剔除 x4 引入 x3Variable Coefficient Std. Error t-Statistic Prob. X1 0.025651 0.001618 15.85417 0.0000X3 14.12441 30.85878 0.457711 0.6524C -1701.940 1517.891 -1.121254 0.2762R-squared 0.967048 Mean dependent var 2814.867Adjusted R-squared 0.963579 S.D. dependent var 3315.807S.E. of regression 632.7954 Akaike info criterion 15.86430Sum squared resid 7608170. Schwarz criterion 16.01307Log likelihood -171.5072 Hannan-Quinn criter. 15.89934F-statistic 278.7978 Durbin-Watson stat 1.456218Prob(F-statistic) 0.000000剔除 x3 引入 x7Variable Coefficient Std. Error t-Statistic Prob. X1 0.024556 0.001533 16.01957 0.0000X7 -104.7564 215.6323 -0.485810 0.6327C -793.3857 500.5261 -1.585104 0.1294R-squared 0.967093 Mean dependent var 2814.867Adjusted R-squared 0.963630 S.D. dependent var 3315.807S.E. of regression 632.3592 Akaike info criterion 15.86292Sum squared resid 7597684. Schwarz criterion 16.01169Log likelihood -171.4921 Hannan-Quinn criter. 15.89796F-statistic 279.1957 Durbin-Watson stat 1.403370Prob(F-statistic) 0.000000剔除 x7 引入 x6Variable Coefficient Std. Error t-Statistic Prob. X1 0.024946 0.001102 22.64330 0.0000X6 -11.14368 22.36418 -0.498283 0.6240C 175.0119 2395.363 0.073063 0.9425R-squared 0.967114 Mean dependent var 2814.867Adjusted R-squared 0.963653 S.D. dependent var 3315.807S.E. of regression 632.1575 Akaike info criterion 15.86228Sum squared resid 7592839. Schwarz criterion 16.01106Log likelihood -171.4851 Hannan-Quinn criter. 15.89733F-statistic 279.3799 Durbin-Watson stat 1.402881Prob(F-statistic) 0.000000结果排除了x2x5所有变量，最后仅剩下x1的一元回归。思考：虽然这样拟合效果很好，但这种情况丧失了其他变量对 Y 的解释能力。因此，当 R的变化并没有显著减小的时候，可以考虑保留该变量。如此例中，根据 R和 p 值，依次保留 x1,x2,x5(含截距项)Variable Coefficient Std. Error t-Statistic Prob. X5 0.261384 0.129806 2.013648 0.0592X2 -0.397995 0.280448 -1.419141 0.1729X1 0.035945 0.011113 3.234442 0.0046C -344.5972 492.2582 -0.700034 0.4929R-squared 0.972969 Mean dependent var 2814.867Adjusted R-squared 0.968463 S.D. dependent var 3315.807S.E. of regression 588.8406 Akaike info criterion 15.75715Sum squared resid 6241198. Schwarz criterion 15.95553Log likelihood -169.3287 Hannan-Quinn criter. 15.80388F-statistic 215.9633 Durbin-Watson stat 1.963666Prob(F-statistic) 0.000000无常数Dependent Variable: YMethod: Least SquaresDate: 06/01/13 Time: 10:11Sample: 1990 2011Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. X5 0.310739 0.107517 2.890137 0.0094X1 0.042498 0.005909 7.192296 0.0000X2 -0.577857 0.110891 -5.211038 0.0000R-squared 0.972233 Mean dependent var 2814.867Adjusted R-squared 0.969310 S.D. dependent var 3315.807S.E. of regression 580.8847 Akaike info criterion 15.69311Sum squared resid 6411114. Schwarz criterion 15.84188Log likelihood -169.6242 Hannan-Quinn criter. 15.72815Durbin-Watson stat 1.992356根据 t 值以及拟合度的比较，选择更好的不含截距项= 0.042498x1 -0.577857x2+0.310739x5Ra=0.969310 DW=1.992356进一步分析：虽然拟合效果很好，但是x2的系数是负值，这与之前的期望不同，猜想这是由于与x1的严重的多重共线性造成的。处理：删除变量x2,再次做出拟合。发现含截距项的比不含时拟合程度更很高。Dependent Variable: YMethod: Least SquaresDate: 06/01/13 Time: 21:03Sample (adjusted): 1990 2011Included observations: 22 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob. X5 0.158927 0.110717 1.435428 0.1674X1 0.020792 0.003163 6.573520 0.0000C -984.6087 202.5046 -4.862156 0.0001R-squared 0.969944 Mean dependent var 2814.867Adjusted R-squared 0.966780 S.D. dependent var 3315.807S.E. of regression 604.3485 Akaike info criterion 15.77230Sum squared resid 6939506. Schwarz criterion 15.92108Log likelihood -170.4953 Hannan-Quinn criter. 15.80735F-statistic 306.5770 Durbin-Watson stat 1.630647Prob(F-statistic) 0.000000= 0.020792x1 -0.158927x5-984.6087Ra=0.966780 DW=1.6306474. 二、给出评价多重共线角度X1 和 X5 之间的多重共线性还是没有消除，相信学习了“差分法”操作后，会有对模型的进一步优化。异方差性角度残差变化图 用 x1、x5 拟合的残差图异方差检验（White 检验）Include cross termHeteroskedasticity Test: WhiteF-statistic 6.899998 Prob. F(5,16) 0.0013Obs*R-squared 15.02970 Prob. Chi-Square(5) 0.0102Scaled explained SS 20.34198 Prob. Chi-Square(5) 0.0011Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/05/13 Time: 23:34Sample: 1990 2011Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C -32057.81 384761.4 -0.083319 0.9346X1 19.04456 13.86861 1.373213 0.1886X12 -0.000210 5.74E-05 -3.652921 0.0021X1*X5 0.015164 0.004303 3.524117 0.0028X5 -804.7381 406.3217 -1.980544 0.0651X52 -0.238980 0.075270 -3.174980 0.0059R-squared 0.683168 Mean dependent var 315432.1Adjusted R-squared 0.584158 S.D. dependent var 615053.6S.E. of regression 396622.2 Akaike info criterion 28.84636Sum squared resid 2.52E+12 Schwarz criterion 29.14391Log likelihood -311.3099 Hannan-Quinn criter. 28.91645F-statistic 6.899998 Durbin-Watson stat 2.029000Prob(F-statistic) 0.001308No cross termHeteroskedasticity Test: WhiteF-statistic 6.043855 Prob. F(2,19) 0.0093Obs*R-squared 8.554172 Prob. Chi-Square(2) 0.0139Scaled explained SS 11.57766 Prob. Chi-Square(2) 0.0031Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/05/13 Time: 23:36Sample: 1990 2011Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 134931.9 132617.1 1.017455 0.3217X12 1.04E-05 3.46E-06 3.018113 0.0071X52 -0.008051 0.004930 -1.633000 0.1189R-squared 0.388826 Mean dependent var 315432.1Adjusted R-squared 0.324492 S.D. dependent var 615053.6S.E. of regression 505508.3 Akaike info criterion 29.23064Sum squared resid 4.86E+12 Schwarz criterion 29.37942Log likelihood -318.5370 Hannan-Quinn criter. 29.26569F-statistic 6.043855 Durbin-Watson stat 2.607760Prob(F-statistic) 0.009302综合两种情况，同方差的原假设被推翻，即认为存在异方差情况。利用 WLS 方法修正异方差，得到如下结果Included observations: 22Weighting series: 1/ABS(RESID)Variable Coefficient Std. Error t-Statistic Prob. X1 0.015830 0.002551 6.205120 0.0000X5 0.292116 0.067405 4.333727 0.0004C -819.3659 81.03558 -10.11119 0.0000Weighted StatisticsR-squared 0.998553 Mean dependent var 2036.956Adjusted R-squared 0.998400 S.D. dependent var 3604.586S.E. of regression 153.4799 Akaike info criterion 13.03114Sum squared resid 447565.8 Schwarz criterion 13.17992Log likelihood -140.3425 Hannan-Quinn criter. 13.06619F-statistic 6553.884 Durbin-Watson stat 1.121655Prob(F-statistic) 0.000000Unweighted StatisticsR-squared 0.964401 Mean dependent var 2814.867Adjusted R-squared 0.960653 S.D. dependent var 3315.807S.E. of regression 657.7240 Sum squared resid 8219415.Durbin-Watson stat 1.550267通过修正，各方面的数据都得到了一定程度的改善。= 0.015830x1 +0.292116x5-819.3659Ra=0.998400 DW=1.5502675. 对你的研究给出结论及展望。根据以上分析，y 最终与 x1、x5 拟合，得出比较优良的结果，在此