計量經濟學多元回歸分析案例

1、計量經濟學案例分析多元回歸分析案例財政收入規(guī)模的影響因素被解釋變量：財政收入（億元）解釋變量：稅收（億元），經濟活動人口（億元），國內生產總值（億元）樣本：2000年一2011年的財政收入，稅收（億元），經濟活動人口（億元），國內生產總值（億元）數(shù)據(jù)來源:中華人民共和國國家統(tǒng)計局（單位：億元）財政收入Y2,937.103,149.483,483.374,348.955,218.106,242.207,407.998,651.149,875.9511,444.0813,395.2316,386.0418,903.6421,715.2526,396.4731,649.2938,760.2051,3

2、21.7861,330.3568,518.3083,101.51103,874.43各項稅收經濟活動人口X1X22,821.862,990.173,296.914,255.305,126.886,038.046,909.828,234.049,262.8010,682.5812,581.5115,301.3817,636.4520,017.3124,165.6828,778.5434,804.3545,621.9754,223.7959,521.5973,210.7989,738.3965,323.0066,091.0066,782.0067,468.0068,135.0068,855.006

3、9,765.0070,800.0072,087.0072,791.0073,992.0073,884.0074,492.0074,911.0075,290.0076,120.0076,315.0076,531.0077,046.0077,510.0078,388.0078,579.00國民生產總值X318,668.0021,618.0026,924.0035,334.0048,198.0060,794.0071,177.0078,973.0084,402.0089,677.0099,215.00109,655.00120,333.00135,823.00159,878.00183,085.00

4、211,923.00257,306.00307,064.00335,353.00362,181.00471,564.001990199119921993199419951996199719981999200020012002200320042005200620072008200920102011對數(shù)據(jù)進行回歸，得出回歸模型:國亙叵變量間的關系：口Group:UNTITLEDWorkfile:UNTITLED;Untitled、Vie榭|所配|Object|Print|Mame|FreezeSamptejShset|Stats|Spec|500,000-400,000-300,000-200,0

5、00-d100,000-40,00080,000120.000OLS古計結果:Equation:UNELE口WorkfiletUNTITLED：Untied、o|回E3ObjEH|Print|NamuFreuzeEMtjmdteFmca允Stats|Res也DependentVariable:YMethodLeastSquaresDate:125/13Time:22:08Sample:19902011IncludedODservations:22VariableCoefTicientStd.Errort-StatisticProb.C17296.872507,0696.8967620.0000

6、X110739530.031Q6S34,570670.0000X2-0.2719360.038292-7.10168900000X30.0237720.0070103391090Q.Q033Rsquared0999927Meandependentvar27186.86AdjustedR-squared0999915S.D.dependentvar28848.33SEofregression3665214Akaikeinfocriterion1417175Sumsquaredresid1278606.Schwarzcriterion14,37012Loglikelihood-151.8S93Ha

7、nnan-Quinncriter.14,21848F-statstic82005.58Durbin-Watsonstat1.471300Prob(F-statistic)0.000000ML估計結果:Equation:UNTITLEDWorlcfile：UNnTLED：UnthledView|Proc|OtJect|Print|Name|Freeze|Estimate|Fonecast|ftats|Nesids|Dep&ndentVarlable:YMettiod,HL-CensoredNormal(TOEIFT)(Quadratichillclimbing)Date:12/25/13Time

8、:22:10Sample:19902011Includedobservations.22.Leftcensoring(value)atzeroConvergenceachievedafter4iterationsCovariancernalrixcomputedusingsecondderivativesVariableCoefficientStdError衛(wèi)-StatisticPrOD.X11.0739530.02810033.219300.0000X2-Q2719360.034636-7B512080.0000X30,0237720.0063413.74S9S90.0002C17295.8

9、72268.5457.6246540.00Q0ErrorDistributionSCALE：C(5)241.077736,343E76.6332415000。*rirMM古計結果:OEquation:UNTTTLEDWorkfile:UNnTLED:UrtitledVi&v?IProcIObjectIPrintINameIFreezeIEstmateIForecastStatsIResidsIDepend&ntVariable:YMethodGeneralizedMettiodofMomentsDate:12/25/1STime:22:10Sample:19902011Includedobse

10、rvations22Kemel:BartlettBandwidth:Fixed(2),Noprewhrt&ningSimuliarousweighingmatrix&coeniclentrleratlonConverflenceachievedafter1weightmatrix,2totalcoefiterationsInstrumentlist:CX1X2X3VariableCoefficientStdErrort-StatisiicProbX11073953002517942652990DOUDX2-02719360.042261-64347230.0000X30,0237720.006

11、3893.7205631X0018C17296.372737930631749900000R-squared0.999927Meandependentvar27186.3&AdjustedR-squared0.999915S.O.d&pendentvar2384833S.E.orregression26652T4Sumsquaredresid1276606m根據(jù)回歸結果進行模型檢驗：Y:財政收入（億元）X1:稅收（億元），X2:經濟活動人口（人）X3:國民生產總值（億元）1、系數(shù)的顯著性水平檢驗Y=1.07395313854*X1-0.271936276384*X2+0.02377230149

12、46*X3+17296.8669142t值（34.57）（-7.10）（3.39）（6.90）從上面的t值來看：“稅收”系數(shù)的t統(tǒng)計值大于4,p0.01,表示拒絕在此模型中“稅收”與“財政收入”無關的原假設，而得出二者間有明顯關系存在的結論?！敖洕顒尤丝凇毕禂?shù)的t統(tǒng)計值大于2,p0.01,說明“國民生產總值”與“財政收入”間存在明顯線性關系。“國民生產總值”系數(shù)的t值大于4,p0.01,拒絕在此模型中“國民生產總值”與“財政收入”無關的原假設，而得出二者間有明顯關系存在的結論。從R2來看：R2=0.999927,R2=0.999915,可以看出，非線性擬合的效果較好從F值來看：針對H0:Pi

13、=P2=&=0,給定顯著性水平=0.01,在F分布表中查出自由度為k-1=2和n-k-1=20的臨界值4（2,20）=5.85。由題中得到F=82005,遠遠高于臨界值，應拒絕原假設H0:Bi=P2=P3=0,說明回歸方程顯著，即“稅收，經濟活動人口，國民生產總值”等變量聯(lián)合起來確實對“財政收入”有顯著影響。2、經濟意義檢驗Y=12640.9418561+1X1-0.197660517414*X2+0.00661207908605*X3模型估計結果說明，在假定其它變量不變的情況下，當年稅收收入每增長1億元，財政收入增長1.074億元；在假定其它變量不變的情況下，當年經

14、濟活動人口每增長1人，財政收入減少0.27億元；在假定其它變量不變的情況下，當國民生產總值每增加1億元，財政收入就會增加0.0237億元。對回歸模型進行是否符合經典假設進行檢驗1 .多重共線性檢驗方法：OGroup:UNELEDWorkfile:UNTTTLED:Untitled|口|回ViuTPrtxObjectPrintNameFreezeSampleSheetStats|Spec|CorrelationX1X2X3kxi1oooooo0.B235380.994513,X20.8235381.0000000,864925|X30.9945130.8649251oooooo一般而言，每個解釋

15、變量的簡單相關系數(shù)大于0.8,則認為存在嚴重的多重共線性。由相關系數(shù)矩陣可以看出，確實存在嚴重的多重共線性。共線性的修正：采用逐步回歸的辦法分別做Y對X1,X2,X3的一元回歸，結果如下：Y對X1的一元回歸：VariableCoefficientStdErrort-StatisticProbC-899.66311598872-5.62311100000XI1154493D.D04639248.344100000R-squared0999677Meandependentvar2713686AdjustedR-squared0.999561Ddependentvar2884833S.E.ofreg

16、ression531.1691Akaikeinfocriterion15.47455Sumsquaredresid5B42813.Schwarzcriterion15.57373Loglikelihood-168.2200Hannan-Quinncriter.15.49791F-statistic6192338Durbin-Watsonstat1.038768Prob(F-statistic)0.000000Y對X2的一元回歸:VariableCoefficientStd.Errort-StatisticProbC-377989.464443.43-5,8654400.0000X25.5671

17、540.8S4Q386.2974150.0000R-squared0664753Meandependentvar27186.36AdjustedR-squared0647990SD.dependentvar2884B33S.E.ofregression1711583AkaikeInfocriterion22.41990Sumsquaredresid5.86E+09Schwarzcriterian22.51909Loglikelihood-2446169Hannan-QuinnEter.22.44327F-statistic39.65744Durin.Vatsonstat0152642Prot)

18、(F-statistic)0.000004Y對X3的一回歸：VariableCoefficientStd.Errort-StatisticProb.C-70619851119.902-63053870.0000X30,229079000579939.5Q17800000R-squared0.907345Meandependentwar27186.86AdjustedR-squared0.986712S.D.dependentvar28843.33S.E.ofregression3325432AKaikeinfocriterion191430gSumsquaredresid2.21E+08Sch

19、warzcriterion192422BLoglikelihood-208.5740Hannan-Quinncriter.19,16646F-statistic1560391DurbinWatsonstat0499033Prot)(Fatalistic)0000000由上表可知：加入xi的R2最大，以X1為基礎，順次加入其他變量逐步回歸，結果為:Y對X1,X2的回歸:VariableCoefficientStd.Errort-StatisticProb.C11000.232100.645523659500000X111783760.005113230.447900000X241,1714920

20、.03023S-5.67139500000R-squared0.999880Meandependentwar271S6.85AdjustedR-squared0.999867S.D.dependentvar2S848.33S.E.ofregression332.0951Akaikeinfocriterion14.57484Sumsquaredresid2095457.Schwarzcriterion1472362Loglikelihood-1573233Hannan-Quinncriter14.60989F-statistlc79223.39Durbin-Watsonstat2.443966P

21、rotiF-statistic)0.000000丫對X1,X3的回歸：VariableCoefficientStd.ErrorStatisticProb.C-432.3856283.2413-1.7030900.1049X11,227903004223029.0707500000X3-0.0147380008432-1.74794S00966R-squared0999722Meandependentvar27186.86AdjustedR-squared0,999593S.D.dependentvar28848.33S.E.ofregression5058144Akaikeinfocriter

22、ion15.41634Sumsquaredresid4861116.Schwarzcriterion15.56512Loglikelihood-166.5797Hannan-Quinncriter.15.45139F-statistic34145.02Durbin-Watsonstat1919466Prot)F-statiStic)0.000000加入X2,X3后回歸結果都要比一元的要好，但相對來說加入X2的R2比X3要高，所以將變量X3去掉，采用Y對X1,X2的回歸，即：VariableCoefficientStd.Errort-St3tisticProb.C11000232100.6455

23、23659500000X111783750.005113230.447900000X2-0.1714920.030238-567139500000R-squareJ0,999880Meandependentvar27186.86AdjustedR-squared0.999867SD.dependentvar28848.33S.Eofregression332.0951Akaikeinfocriterion14.57484Sumsquaredresid2095457.Schwarzcriterion1472362Loglikelihood-1573233Hannan-Quinncriter14.

24、60989F-statistlc79223.39Durbin-Watsonstat2.443966ProtiF-statistic)00000002 .異方差異方差檢驗：采用white檢驗方法：得到結果為:HeteroskedasticityTest:WhiteF-statistic5.374-906Prob.F(3,130.0056Obs*R-squared10884112Prob.Chi-Square3)0.0124ScaledexplainedSS5.310490Prob.Chi-Square(30.1504TestEquation:DependentVariable:RESIDA2Me

25、thod:LeastSquaresate:12/25713Time:23:25Sample:19902011Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C105701.7160953.00,6567240.5197X1A2-0.0001695.96E-05-2.B435680.0103X2A2-2.02E-053.29E-05-0.6147440.5464X3A27.00E-06233E-063.0021160.0077R-squared0.4-94733Meandependentvar58118.44A

26、djustedR-squared0410522S.D.dependentvar71820.99S.E.ofregression55142.36Akaikeinfocriterion2483619Sumsquaredresid5.47E-H10Schwarzcriterion25,03456Loglikelihood-269.19S1Hannan-Cluinncriter.24,33292F-statistic5.374-906urbin-Watsonstat1.614923Prob(F-statistic)0.005500從上圖可以看出，nR2=10.88412，由white檢驗可知，在顯著性

27、水平為a=0.05下，臨界值4.05(9)=16.919,比較臨界值與統(tǒng)計量，nR2sX1X2X3E1990282186065323.OQ1366800-70.40026119912990170660910021618.0099.9414619923296.9106S7B20026924.00166.179219934255300674600035334.00-10.88351199451263806S135004819800-202.19501995603B04068855Otl6079400-260279919966909.32069755.0071177口口-30.10657199782

28、34,04070800007B973.00-112.9816199B92S2.80072037.DO84402.00227.9105199910682.58727910089677.00337.307B200012581.51739920099215.0034S.9510200115301.33738340010365501411961200217636457449200120333062537002003200173174911.00135S23.06292323200424165.687529D00159S7SO-179.7906200528778.547S12000183085O-206.942720061-1-然后輸入：SCATE(-1)E得到et-et-1的散點圖-600*400*2000200400600EE)PLOTE還可繪制et的趨勢圖口Graph:UNTITLEDWorkfile：UMTrTLED:Urrtitled|=|回|1Viu隊|Proc|%ect|m閨雨畫AddT,xt|Linu/Shadu|Rum。鼠eTemplate|Options.8時由回歸方程的殘差