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)

1、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%) x7199049.0818667.821510.254.245.57151.9103.12.16199163.1721781.51700.653.85.7176.1103.41.8199293.8626923.482026.653.045.82327.1106.41.8199385.9535333.922577.450.325.95482.2114.7

2、3.151994143.1348197.863496.250.046.07680124.13.151995160.960793.73428350.096.2877.1117.13.151996214.8171176.594838.948.766.411082.4108.31.981997390.4878973.035160.346.66.541339.2102,8 1.711998750.2284402.285425.144.666.71636.999.21.441999878.9589677.055854.0242.076.92108.198.60.99200099099214.556280

3、39.446.962385.6100.40.9920011423.52109655.176859.638.27.12748100.70.9920022274.8120332.697702.837.687.33471.599.20.7220033011135822.768472.237.17.54016.4101.20.7220043194159878.349421.637.77.64627.4103.90.7220053649184937.371049336.77.75401101.80.7220064061216314.4311759.535.87.96583101.50.722007494

4、9.7265810.3113785.836.298.17887.8104.80.7220087338314045.4315780.7637.898.39925.1105.90.3620098144.4340902.8117174.6536.528.512302.699.30.36201010501.1401202.0319109.4435.78.879014.243101.30.3620119560472881.621809.836.39.139547.935105.40.41、 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

5、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

6、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

7、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。X1X2X3X4X5X6X110.995591-0.753970.9549790.94

8、7109-0.26679X20.9955911-0.806340.9770260.959676-0.2963X3-0.75397-0.806341-0.91088-0.79450.514843X40.9549790.977026-0.9108810.941551-0.39444X50.9471090.959676-0.79450.9415511-0.3265X6-0.26679-0.29630.514843-0.39444-0.326512. 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 Square

9、sDate: 06/05/13 Time: 20:21Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb.  X10.0623560.0271342.2981040.0354X2-1.7164880.952013-1.8030080.0903X3190.6488150.88161.2635660.2245X44815.2673016.5981.5962580.1300X50.3827220.1511512.5320610.0222C-36195.4223

10、730.64-1.5252610.1467R-squared0.976812    Mean dependent var2814.867Adjusted R-squared0.969565    S.D. dependent var3315.807S.E. of regression578.4598    Akaike info criterion15.78562Sum squared resid5353852.    Schwarz

11、criterion16.08317Log likelihood-167.6418    Hannan-Quinn criter.15.85571F-statistic134.8008    Durbin-Watson stat1.910836Prob(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：VariableCoefficien

12、tStd. Errort-StatisticProb.*  X10.0249730.00101324.641620.0000X6-9.5160281.918036-4.9613390.0001R-squared0.967105    Mean dependent var2814.867Adjusted R-squared0.965460    S.D. dependent var3315.807S.E. of regression616.2375    A

13、kaike info criterion15.77165Sum squared resid7594973.    Schwarz criterion15.87084Log likelihood-171.4881    Hannan-Quinn criter.15.79502Durbin-Watson stat1.406837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）R²=0.9666

14、85 F=580.3233 对x2=-1835.837 +0.551502x2（271.1357） (20.75179)R²= 0.9555618 F= 430.6369 对x3=x3（5.577219） (-4.759700)R²=0.531119 F= 22.65474 DW=0.172052 对X4X42946.593250.742911.751450.0000C-18188.991805.815-10.072450.0000R-squared0.873495    Mean dependent var2814.867Adjus

15、ted R-squared0.867170    S.D. dependent var3315.807S.E. of regression1208.475    Akaike info criterion17.11861Sum squared resid29208222    Schwarz criterion17.21780Log likelihood-186.3047    Hannan-Quinn criter.17.14198F

16、-statistic138.0967    Durbin-Watson stat0.316946Prob(F-statistic)0.000000=-18188.99+2946.593x4（-10.07245） (11.75145)R²=0.873495 F= 138.0967 DW=0.316946 对x5=0.77532x5（17.6609） R²=0.8893=294 DW=1.109666根据R²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 +0.025

17、092x1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VariableCoefficientStd. Errort-StatisticProb.  X10.0288710.0113592.5416310.0199X2-0.0839030.251106-0.3341350.7419C-882.9879445.3053-1.9828820.0620R-squared0.966879    Mean dependent var2814.867Adjusted R-squar

18、ed0.963393    S.D. dependent var3315.807S.E. of regression634.4133    Akaike info criterion15.86940Sum squared resid7647125.    Schwarz criterion16.01818Log likelihood-171.5634    Hannan-Quinn criter.15.90445F-statistic2

19、77.3292    Durbin-Watson stat1.447167Prob(F-statistic)0.000000Adjusted R-squared0.963393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x5VariableCoefficientStd. Errort-StatisticProb.  X10.0207920.0031636.5735200.0000X50.1589270.1107171.4354280.1674C-984.6087202.5046-4.

20、8621560.0001R-squared0.969944    Mean dependent var2814.867Adjusted R-squared0.966780    S.D. dependent var3315.807S.E. of regression604.3485    Akaike info criterion15.77230Sum squared resid6939506.    Schwarz criterion

21、15.92108Log likelihood-170.4953    Hannan-Quinn criter.15.80735F-statistic306.5770    Durbin-Watson stat1.630647Prob(F-statistic)0.000000上一步的原因相同，剔除x5，引入x4VariableCoefficientStd. Errort-StatisticProb.  X10.0262900.0035917.3218950.0000X4-154.9759443.5

22、722-0.3493810.7306C-92.035372647.097-0.0347680.9726R-squared0.966897    Mean dependent var2814.867Adjusted R-squared0.963413    S.D. dependent var3315.807S.E. of regression634.2404    Akaike info criterion15.86886Sum squared resid7642957.&#

23、160;   Schwarz criterion16.01764Log likelihood-171.5574    Hannan-Quinn criter.15.90390F-statistic277.4856    Durbin-Watson stat1.458254Prob(F-statistic)0.000000剔除x4引入x3VariableCoefficientStd. Errort-StatisticProb.  X10.0256510.0016181

24、5.854170.0000X314.1244130.858780.4577110.6524C-1701.9401517.891-1.1212540.2762R-squared0.967048    Mean dependent var2814.867Adjusted R-squared0.963579    S.D. dependent var3315.807S.E. of regression632.7954    Akaike info criterion15.86430

25、Sum squared resid7608170.    Schwarz criterion16.01307Log likelihood-171.5072    Hannan-Quinn criter.15.89934F-statistic278.7978    Durbin-Watson stat1.456218Prob(F-statistic)0.000000剔除x3 引入x7VariableCoefficientStd. Errort-StatisticProb.

26、60; X10.0245560.00153316.019570.0000X7-104.7564215.6323-0.4858100.6327C-793.3857500.5261-1.5851040.1294R-squared0.967093    Mean dependent var2814.867Adjusted R-squared0.963630    S.D. dependent var3315.807S.E. of regression632.3592    

27、;Akaike info criterion15.86292Sum squared resid7597684.    Schwarz criterion16.01169Log likelihood-171.4921    Hannan-Quinn criter.15.89796F-statistic279.1957    Durbin-Watson stat1.403370Prob(F-statistic)0.000000剔除x7引入x6VariableCoefficient

28、Std. Errort-StatisticProb.  X10.0249460.00110222.643300.0000X6-11.1436822.36418-0.4982830.6240C175.01192395.3630.0730630.9425R-squared0.967114    Mean dependent var2814.867Adjusted R-squared0.963653    S.D. dependent var3315.807S.E. of regression632.

29、1575    Akaike info criterion15.86228Sum squared resid7592839.    Schwarz criterion16.01106Log likelihood-171.4851    Hannan-Quinn criter.15.89733F-statistic279.3799    Durbin-Watson stat1.402881Prob(F-statistic)0.000000

30、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R²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R²和p值，依次保留x1,x2,x5(含截距项)VariableCoefficientStd. Errort-StatisticProb.  X50.2613840.1298062.0136480.0592X2-0.3979950.280448-1.4191410.1729X10.0359450.0111133.2344420.0046C-344.597249

31、2.2582-0.7000340.4929R-squared0.972969    Mean dependent var2814.867Adjusted R-squared0.968463    S.D. dependent var3315.807S.E. of regression588.8406    Akaike info criterion15.75715Sum squared resid6241198.    Schwarz

32、criterion15.95553Log likelihood-169.3287    Hannan-Quinn criter.15.80388F-statistic215.9633    Durbin-Watson stat1.963666Prob(F-statistic)0.000000无常数Dependent Variable: YMethod: Least SquaresDate: 06/01/13 Time: 10:11Sample: 1990 2011Included observations: 22V

33、ariableCoefficientStd. Errort-StatisticProb.  X50.3107390.1075172.8901370.0094X10.0424980.0059097.1922960.0000X2-0.5778570.110891-5.2110380.0000R-squared0.972233    Mean dependent var2814.867Adjusted R-squared0.969310    S.D. dependent var3315.807S.E

34、. of regression580.8847    Akaike info criterion15.69311Sum squared resid6411114.    Schwarz criterion15.84188Log likelihood-169.6242    Hannan-Quinn criter.15.72815Durbin-Watson stat1.992356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+0.3

35、10739x5Ra²=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 adjustmentsVariableCoefficientStd. Errort-

36、StatisticProb.  X50.1589270.1107171.4354280.1674X10.0207920.0031636.5735200.0000C-984.6087202.5046-4.8621560.0001R-squared0.969944    Mean dependent var2814.867Adjusted R-squared0.966780    S.D. dependent var3315.807S.E. of regression604.3485 &#

37、160;  Akaike info criterion15.77230Sum squared resid6939506.    Schwarz criterion15.92108Log likelihood-170.4953    Hannan-Quinn criter.15.80735F-statistic306.5770    Durbin-Watson stat1.630647Prob(F-statistic)0.000000=0.020792x1-

38、0.158927x5-984.6087Ra²=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-statistic6.899998    Prob. F(5,16)0.0013Obs*R-squared15.02970   

39、60;Prob. Chi-Square(5)0.0102Scaled explained SS20.34198    Prob. Chi-Square(5)0.0011Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/05/13 Time: 23:34Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb.  C-32057.81

40、384761.4-0.0833190.9346X119.0445613.868611.3732130.1886X12-0.0002105.74E-05-3.6529210.0021X1*X50.0151640.0043033.5241170.0028X5-804.7381406.3217-1.9805440.0651X52-0.2389800.075270-3.1749800.0059R-squared0.683168    Mean dependent var315432.1Adjusted R-squared0.584158  &

41、#160; S.D. dependent var615053.6S.E. of regression396622.2    Akaike info criterion28.84636Sum squared resid2.52E+12    Schwarz criterion29.14391Log likelihood-311.3099    Hannan-Quinn criter.28.91645F-statistic6.899998  

42、0; Durbin-Watson stat2.029000Prob(F-statistic)0.001308No cross termHeteroskedasticity Test: WhiteF-statistic6.043855    Prob. F(2,19)0.0093Obs*R-squared8.554172    Prob. Chi-Square(2)0.0139Scaled explained SS11.57766    Prob. Chi-Squar

43、e(2)0.0031Test Equation:Dependent Variable: RESID2Method: Least SquaresDate: 06/05/13 Time: 23:36Sample: 1990 2011Included observations: 22VariableCoefficientStd. Errort-StatisticProb.  C134931.9132617.11.0174550.3217X121.04E-053.46E-063.0181130.0071X52-0.0080510.004930-1.6330000.1189R-squ

44、ared0.388826    Mean dependent var315432.1Adjusted R-squared0.324492    S.D. dependent var615053.6S.E. of regression505508.3    Akaike info criterion29.23064Sum squared resid4.86E+12    Schwarz criterion29.37942Log likel

45、ihood-318.5370    Hannan-Quinn criter.29.26569F-statistic6.043855    Durbin-Watson stat2.607760Prob(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)VariableCoefficientStd. Errort-Statis

46、ticProb.  X10.0158300.0025516.2051200.0000X50.2921160.0674054.3337270.0004C-819.365981.03558-10.111190.0000Weighted StatisticsR-squared0.998553    Mean dependent var2036.956Adjusted R-squared0.998400    S.D. dependent var3604.586S.E. of regression153

47、.4799    Akaike info criterion13.03114Sum squared resid447565.8    Schwarz criterion13.17992Log likelihood-140.3425    Hannan-Quinn criter.13.06619F-statistic6553.884    Durbin-Watson stat1.121655Prob(F-statistic)0.00000

48、0Unweighted StatisticsR-squared0.964401    Mean dependent var2814.867Adjusted R-squared0.960653    S.D. dependent var3315.807S.E. of regression657.7240    Sum squared resid8219415.Durbin-Watson stat1.550267通过修正，各方面的数据都得到了一定程度的改善。=0.015830x1+0.292116x5-819.3659Ra²=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，在此基础上，得出20122015年的预测估计值。用t值分别