1、保費(fèi)收入的相關(guān)數(shù)據(jù)表年份壽險(xiǎn)保費(fèi)收入(億元)yGDP(億元) x1城鎮(zhèn)居民家庭人均可支配收入(元) x2 城鎮(zhèn)恩格爾系數(shù) x365歲以上人口占總?cè)丝诎俜謹(jǐn)?shù) x4社會(huì)保障基金支出(億元)x5通脹率(居民消費(fèi)價(jià)格指數(shù))x6利率(央行歷年存款利率%) 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、 提出并分析相關(guān)問(wèn)題2、 利用數(shù)據(jù)，構(gòu)造計(jì)量經(jīng)濟(jì)學(xué)模型3、 估計(jì)并完成模型，對(duì)結(jié)果給出評(píng)價(jià)4、 對(duì)你的研究給出結(jié)論及

5、展望。1. 提出并分析相關(guān)問(wèn)題提出問(wèn)題：壽險(xiǎn)保費(fèi)收入與其他變量怎樣擬合能較好的解釋其變化？分析問(wèn)題：壽險(xiǎn)保費(fèi)收入作為被解釋變量，可以在其他6個(gè)解釋變量下，通過(guò)一定的設(shè)計(jì)，做出有經(jīng)濟(jì)學(xué)意義的回歸模型。一、首先要選擇合適的與壽險(xiǎn)保費(fèi)收入的經(jīng)濟(jì)學(xué)理論和行為相關(guān)的變量。變量x1為GDP，在GDP越高的情況下，生產(chǎn)總值的提升說(shuō)明社會(huì)發(fā)展水平提升，對(duì)壽險(xiǎn)的重視程度很可能也隨之提高，因此人們的保費(fèi)收入也會(huì)成正相關(guān)變化。變量x2為城鎮(zhèn)居民家庭人均可支配收入，與GDP類似，該變量與保費(fèi)收入成正相關(guān)變化。但其沒(méi)有包括農(nóng)村居民收入，因此有些局限性。還要通過(guò)進(jìn)一步分析確定。變量x3城鎮(zhèn)恩格爾系數(shù)越低，說(shuō)明居民花在食品

6、上的費(fèi)用占總費(fèi)用比重越小，其生活水平越高，按該情況居民應(yīng)更有基礎(chǔ)注重保險(xiǎn)業(yè)務(wù)。但從數(shù)據(jù)上來(lái)看，該變量若作為解釋變量，其系數(shù)應(yīng)為負(fù)。也就是說(shuō)明，該變量或許與Y的關(guān)系并不單純直接，應(yīng)該還會(huì)有其他的因素影響。變量x4是65歲以上人口占總?cè)丝诎俜謹(jǐn)?shù),當(dāng)該比例越大時(shí)，表明需要人壽保險(xiǎn)的群體比重增加，保費(fèi)收入也應(yīng)該增加。變量x5社會(huì)保障基金支出的增長(zhǎng)，有助于促進(jìn)保費(fèi)收入的增加。變量x6通脹率(居民消費(fèi)價(jià)格指數(shù))通貨膨脹率受很多方面的影響，同時(shí)大體上來(lái)看，它與保費(fèi)收入的關(guān)系并不密切。變量x7利率(央行歷年存款利率%)，利率一般是由央行根據(jù)整個(gè)經(jīng)濟(jì)情況決定的，是個(gè)比較宏觀的（相對(duì)來(lái)說(shuō)）變動(dòng)較小經(jīng)濟(jì)變量，同樣與

7、保費(fèi)收入關(guān)系不密切，應(yīng)予以剔除。二、結(jié)合散點(diǎn)圖，根據(jù)經(jīng)濟(jì)行為理論，確定變量之間的數(shù)學(xué)關(guān)系。通過(guò)散點(diǎn)圖，可初步推斷y與x1x5有線性關(guān)系。y與x1x5散點(diǎn)圖同時(shí)，根據(jù)經(jīng)濟(jì)學(xué)意義以及對(duì)各變量的分析（見上一標(biāo)題），也可得出y與各變量成線性相關(guān)的關(guān)系。三根據(jù)經(jīng)濟(jì)學(xué)意義確定剩下的變量的模型參數(shù)估計(jì)。同時(shí)注意他們之間的獨(dú)立性。可以通過(guò)數(shù)據(jù)，發(fā)現(xiàn)y與x1x5有正相關(guān)關(guān)系，故它們前面的系數(shù)應(yīng)該都為正數(shù)。另外，通過(guò)相關(guān)系數(shù)矩陣，發(fā)現(xiàn)他們之間存在嚴(yán)重的多重共線性。有的相關(guān)系數(shù)甚至達(dá)到了0.99以上，對(duì)其的相關(guān)處理我將在后面進(jìn)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. 利用數(shù)據(jù)，構(gòu)造計(jì)量經(jīng)濟(jì)學(xué)模型首先，對(duì)y做一個(gè)對(duì)所有變量的多元回歸模型。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發(fā)現(xiàn)t值較為顯著的僅有x1和x5.￥%&*（）可繼續(xù)說(shuō)明3. 估計(jì)并完成模型，對(duì)結(jié)果給出評(píng)價(jià)一、估計(jì)并完成模型：思路一：下面運(yùn)用Eviews軟件系統(tǒng)自動(dòng)逐步回歸法做出的多元線性模型為：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：可見其思路二：利用向前選擇法第一步，用每個(gè)解釋變量分別對(duì)被解釋變量做簡(jiǎn)單回歸，得到 Y與x1:=-1013.927 +0.025092x1 （24.08990）R²=0.9666

14、85 F=580.3233 對(duì)x2=-1835.837 +0.551502x2（271.1357） (20.75179)R²= 0.9555618 F= 430.6369 對(duì)x3=x3（5.577219） (-4.759700)R²=0.531119 F= 22.65474 DW=0.172052 對(duì)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 對(duì)x5=0.77532x5（17.6609） R²=0.8893=294 DW=1.109666根據(jù)R²統(tǒng)計(jì)量的大小排序，可見解釋變量的重要程度依次為x1,x2,x5,x4,x3,第二步，以= -1013.927 +0.025

17、092x1為基礎(chǔ)，依次引入x2,x5,x4,x3,與逐步回歸法不同的是，不再引入已經(jīng)刪除掉的變量。首先把x2引入模型回歸得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?yàn)閤2的引入是R 改善幅度較小，且x2的系數(shù)沒(méi)有通過(guò)t 顯著性檢驗(yàn) 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、結(jié)果排除了x2x5所有變量，最后僅剩下x1的一元回歸。思考：雖然這樣擬合效果很好，但這種情況喪失了其他變量對(duì)Y的解釋能力。 因此，當(dāng)R²的變化并沒(méi)有顯著減小的時(shí)候，可以考慮保留該變量。如此例中，根據(jù)R²和p值，依次保留x1,x2,x5(含截距項(xiàng))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無(wú)常數(shù)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根據(jù)t值以及擬合度的比較，選擇更好的不含截距項(xiàng)=0.042498x1-0.577857x2+0.3

35、10739x5Ra²=0.969310 DW=1.992356進(jìn)一步分析：雖然擬合效果很好，但是x2的系數(shù)是負(fù)值，這與之前的期望不同，猜想這是由于與x1的嚴(yán)重的多重共線性造成的。處理：刪除變量x2,再次做出擬合。發(fā)現(xiàn)含截距項(xiàng)的比不含時(shí)擬合程度更很高。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、給出評(píng)價(jià)多重共線角度X1和X5之間的多重共線性還是沒(méi)有消除，相信學(xué)習(xí)了“差分法”操作后，會(huì)有對(duì)模型的進(jìn)一步優(yōu)化。異方差性角度殘差變化圖 用x1、x5擬合的殘差圖異方差檢驗(yàn)（White 檢驗(yàn)）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綜合兩種情況，同方差的原假設(shè)被推翻，即認(rèn)為存在異方差情況。利用WLS方法修正異方差，得到如下結(jié)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通過(guò)修正，各方面的數(shù)據(jù)都得到了一定程度的改善。=0.015830x1+0.292116x5-819.3659Ra²=0.998400 DW=1.5502675. 對(duì)你的研究給出結(jié)論及展望。根據(jù)以上分析，y最終與x1、x5擬合，得出比較優(yōu)良的結(jié)果，在此基礎(chǔ)上，得出20122015年的預(yù)測(cè)估計(jì)值。用t值分別