計(jì)量經(jīng)濟(jì)學(xué)第五,六章作業(yè)

1、53各地區(qū)農(nóng)村居民家庭人均純收入與家庭人均生活消費(fèi)支出的數(shù)據(jù)（單位：元）（1）試根據(jù)上述數(shù)據(jù)建立2007年我國農(nóng)村居民家庭人均消費(fèi)支出對(duì)人均純收入的線性回歸 模型。（2）選用適當(dāng)方法檢驗(yàn)?zāi)Ｐ褪欠裨诋惙讲?，并說明存在異方差的理由。（3）如果存在異方差，用適當(dāng)方法加以修正。答：散點(diǎn)圖線性回歸分析圖 Equation! UNTITLED Workfik: UNTlTLED-UntitledX衛(wèi)仙 |嚴(yán)oc gee:| Prrn| same|匕曲【皂| 卜crecast Stats | ke$ids|Dependent Variable: XMethod Least SquaresCate 1DH8/

2、14 Time: 18:20Sple 1 31Induced observations: 31VariableCceffoGntStd. Error1-StatisticProb.C179.191622157750.8087090.4253T0 7135000.04570015.744110.0000H-sqtaroaU 8Ui>26UMoan dopenoontvar3376.308Adjusted R0 891649SO dependentar1499 612SF or regression493 5240Acaiire no errenon15303T7Sum SQuarea re

3、sid7066274Schwarz ertterton15 39528Log livelihood-235.2084Hannar-Q jim cite*.1533392F-statstio247.3769Durtin-A'atson stat1 473596Pro bF-st3ti Stic)0 003000由圖建立樣本回歸函數(shù)X=179.1916+0.7195TR2=0.895260F=2478769 Graph: UNTITLED Workfile: UNEL£D:UMitkdrti圖形法町看出殘差平方隨無的變動(dòng)呈增犬趨勢(shì),但還需進(jìn)一步檢驗(yàn).White檢驗(yàn) Equatio

4、r: LNTITLEDWorkfile: UNTTLED:Untitled 1 oI E 應(yīng) JlView | Roc Objeej Print| Name | Freeze | Estmate | Forecast | State | Resids |Heteroskedasticity Test: White厶FlF-stalstic ObswR-squared Scaled explained SS1.8591453.5236014.685299Prob. F(2.10)Prob. Chi-Square(2)Proc. cm-squa(e(2)0.2058 T0.17170.09C1Te

5、st EquationDependentvariable RESIDE Method: Least SquaresDate: 10*18*14 Time: 22:27Sample: 19 31in eluded ooservatons: 13VariableCoefficientStd Error卜 StatisticProb.C-24557702773615.-0.8854040.3067T738 5987872 74020 8402980 41722-0.0400410.062834-0.6372500.5383由上述結(jié)果町知，該模型存在異方差，理由是從數(shù)據(jù)町看出一是截面數(shù)據(jù)，看出各省市經(jīng)

6、濟(jì)發(fā) 展不平衡3）用加權(quán)最小二乘法修正，選用權(quán)數(shù)wlAwZw.則、/VMoth©<l: Coast aqyoroaDate： O8/2A/0D Tir-no： 18 oa bSamplar 1 31inelvtiod otoorvMieno： 31Weigtino son«» W3VarietoleCo<Hr>ei«nc&t<l &rrort-StMietteRrobGX»r.-r»47O.S6T4.721 心.22O.OS673H*io.07aeeO.OOCo.oocwoimacStCtOCl

7、QOM GtlMOrod dKJ&ted R-fuared of rogrogoion Surw ogcjarbd mid Log HkQlirQQci Durbin Wacoon otrxOOJM4ZOO人U今GO2.<«2760/>QQn cSoponaont vur SQ. daponont var AKPlKa info cintQCK>r> Schwarz criterion 卜RroixF atattotio).磯 1166.06 ".22 14.2278O.OOOOCOcAratomod SiatiotleoR. OQuarod

8、o.aeooaK4oan cSoandont var3374.3CQ£ U. depon«n< varS».C. of rDgraaoionSum a<uara<J rooici102547Ourblfi-Waceon oim1 741O5S5.6散點(diǎn)圖回歸結(jié)果忙譏naumdierviueinga|70CbDependent variable YMe:noa： Least squaresDale: 10/23/14 Tine: 18:23Sample: 1978 2011Included observations* 34Variab gCoeff

9、icientStd. EnortStatisticProb.C92.5544342.835572.1622050 0382X0.7462430.01912039.03010oooooR-squared0.979426Mean dependent ar1295.805Adjusted R-squared0 978783S D dependentvar1188 794S.E. cf ragression173.1609Akaike in'o critGfion13.20334Sum squared resid859509.6Schwarz or it© ri on13.29313

10、Log Ikelihood-222.4560Hannanduinn cnier.13.23396F-slalsttc1523349Durbln-Watsonstal1.534480proD(F-stansuc)0.000000Goldfield-quanadt 檢驗(yàn)LJ tquation： uin in Ltu woriaiie: UN in Ltu：untinea o | 凹 |il Vlew|Proc|object| Print|Narae Reezel Estimate|Forecast|S怯ts| Resids|Dependent Variable: YMethod: Least Sq

11、uaresDate 10/23/14 Time: 18:37Sample: 1 13Included observations: 13VariableCoefficientStd Errort-StatisticProbC-18.868618.963780-2.1049840 0591X0.9678390.02687936.007710 0000R squared0.991587"xn dependent var2801377Adjusted R-squared0.990823S.D. dependent var127 0409S.E. of regression12.17039Ak

12、aike info criterion7.976527Sum squared resid1629.301Schwarz criterion8.063442Log likelihood-49.84742Hannan -Quinn criter.7.958662statistic1296.555Durbin-Watson stat1.071505ProbF-statistic)0.000000View | Proc | Object| P-int| Name | Freeze | Estimate | Forecast | Stats ResidsDependent Variable: Y Met

13、hod: Least Squares Date 10/23/14 Time: 18 44 Sample: 22 34Includod ob&orvotions: 13VariableCoefficientStd. Error t-StatisticProb.C179.405820287770.8843050.3954X0.7195660.0M31212.339890.0000R-squarod0.032628Mean depondent var2406.135Adjusted R-squared0.925503S.D. dependent var1022.590S.E. of regr

14、ession277.2268Akaike info criterion14.22819Sum squared resid845401.5Schwarz criterion14.31510Logikelihood-90.43321Hannan-Quinn criter.14.21032F-slatislic Prot>：F-statistic)15227280.003000Durbin-Watson stat1.058399F=845401.5/16293041=518 872所以模型存在異方差Vcw|Proc| Otject| Print|r4orre F-ccre | Estimate

15、 Forecast S»ts| Rcsics|DGpondontVanaolo: YMethod: Least SauaresDate: 10/23/14 Time: 18:57Sample 1 34Included observations 34Weightino series W3griAbloCoefficientStd Errort-StatisticProbC8.8908693.60429924567400.0192X0.8521930.02015342293380.0000VSeightec StatislcsR-squaredAdjusted R squared S.E

16、. ol recression Sum squared resid Log lir 創(chuàng)山 ood F-statistic0.9824250.90187516.202720400.904 -141 90941708.730Mean aepenaertvar S.D. dependentvar AKaikeinfc cmerion Schwarz criterion Hannan-Ou inn enter Durbin-V/atson stat230.2434247.17198.465258G.55504484958780.604648 4 |_IIIIt檢驗(yàn)，F(xiàn)檢驗(yàn)顯著5?=8 890869+0

17、.852193xrt= (2.4667) (42.2933) 7?2=0.9824> DW=0.6046 =1788.730剔除價(jià)格變動(dòng)因素后的回歸結(jié)果如下6.1卜表是北京市連續(xù)19年城鎮(zhèn)居民家庭人均收入與人均支出的數(shù)據(jù)。表略（1）建立居民收入一消費(fèi)函數(shù)：殘差圖> 800-1.400-r2001.200-1.000-600-400-400600800 1,000 1,200 1,400 1.600 1.800> 800-> 800-DopondontVariablG Y Method: Least Squares Date: 10/25*14 Time: 22:38 S

18、ample: 1 19Induded obserations: 19VariableCoeffiaentStd Error t-StatisticProbC79.9300412.399196.4463900.0000X0.6904880.01287753.620630.0000R-squared0.994122Mean dependent var700.2747Adjusted R-squared0.993776S.D. dependentvar246.4491S.E of regression19.44245Akaike info criterion8.872095Sum squared r

19、esid6426.149Schwarz criterion8.971510Log likelihood-82.28490Hsnnan-Quinn criter.8.888920F-statistic2875.178Durbin-Watson stat0.574663Prob(F statistic)0.000000 = 79 90 + 0 690Se = (11399)(0.013)t =(6 446) (53 621)R2 = 0 994 DW = 0 575（2）檢驗(yàn)?zāi)Ｐ椭写嬖诘膯栴}，并采取適肖的補(bǔ)救措施預(yù)以處理：（2 ） DW=0.575.取 a = 5%.査 DW 上下界 dL =1.

20、1 & * = 1.40, DW V1.18,說明誤 差項(xiàng)存在正自相關(guān)（3）對(duì)模型結(jié)果進(jìn)行經(jīng)濟(jì)解釋。采用科克倫奧科特迭代法廣義差分Dependent VariablesMethod: Least SquaresDate: 10/25/14 Time: 22:43Sample (adjusted): 2 19In eluded observations: 18 after adjustments Convergence achieved after 5 iterationsVariableCoefficientStd. Errort-StatisticProb.C104.044923.8

21、76184.3576870.0006X0.6692620.02083132.127570.0000AR(1)0.6300150.1642183.8364620.0016R-squared0.997097Mean dependentvar719.1867Adjusted R-squared0.996710S.D. dependent var238.9866S.E. of regression13.70843Akaike info criterion8.224910Sum squared resid2818.814Schwarz criterion8.373306Log likelihood-71

22、.02419Hannan-Quinn criter.8.245372F-statistic2575.896Durbin-Watson stat1787878Prob(F-statistic)0.000000Inverted AR Roots.63因此原回歸模型應(yīng)為X =104985+0.669X,其經(jīng)濟(jì)盤義為:北京市人均實(shí)際收入增加1元時(shí)，平均說來人均實(shí)際生活消費(fèi)支出將增加63為了探討股票市場繁榮程度與宏觀經(jīng)濟(jì)運(yùn)行情況之間的關(guān)系，取股票價(jià)格指數(shù)與GDP開 展探討,表6.7為美國1981-2006年股票價(jià)格指數(shù)(y)和國內(nèi)生產(chǎn)總值GDP (x)的數(shù)據(jù)。估計(jì)回歸模型y_t=p _l+p _2X_t

23、+»_t檢驗(yàn)(1)中模型是否存在自相關(guān)，若存在，用廣義差分法消除自柑關(guān)ViewProcObjectPrintNameFrceicDefaultOption:Position | Sample | Sh14,0002.00012.000 -10,000 -6.000 -4,000 -3,0005 0007 0009 000/> 8.000 -0 1 000Dependent Variable: Y Method: Least Squares Date: 10/25/14 Time: 20:55 Sample: 1981 2006 In duded observations: 26

24、VariableCoefficientStd Error t-StatisticProb.C3002527300.41749.9945180.0000X1.1684970.06829817.108750.0000R-squared0.924221Mean dependentvar7305.946Adjusted R-SQuared0.921063S.D. dependent var2981.130S.E. of regression837.5690Akaike info criterion16.37269Sum squared resid16836523Schwarz criterion16.

25、46946Log likelihood-210.8449Han nan-Quinn criter.16.40056F-statistic292.7093Durbin-Watson stat0.444511Prob(F-statistic)0.000000最小乘法估計(jì)回歸模型為£=3002527+1.1685/Se=(300.4174)(0.0683)t=(9.9945)(17.1087)R2=o.9242F=2927093DW=04445PMidual AouaI FittedBreusch-Godfrey Serial Correlation LM Teststatistic22.

26、78058Prob. F(2,22)0.0000Obs*R-squared17.53360Prob. Chi-Square(2)0.0002Test Equation:Dependent Variable: RE SIDMethod: Least SquaresDate; 10/25/14 Time:21:11Sample: 1981 2006Included observations: 26Presample missing value lagged residuals set to zero.VariableCoefficientStd. Errort-StatisticProb.C2.9

27、59362180.26060.0164170.9870X-0.0023630 040873-0.0578110.9544RESID(-1)1.1299130.1874226.0286980.0000RESID(-2)0.4964920.192408-2.5804160.0171R-squarea0.674369Mean depenaemvar1.27E-12Adjusted R-squared0.629965S.D. dependentvar820.6466S.E. erf regression499.2036Akaike info criterion15.40454Sum squared r

28、esid5482492.Schwarz criterion15.59810Log likelihood-196.2591Hanna nd inn criier.15.46028F-statistic15.18705Durbin-Watson stat1.978124Prob(F-statistic)0.000014LM=T/?2=26*0.6744=17 5344 P值為0.00014 t檢驗(yàn)和F檢驗(yàn)不可信。所以需要補(bǔ)救廣義差分法用科克倫奧科特迭代法Dependent Variable: YMethod: Least SquaresDate 10/25/14 Time: 21:54Sample

29、 (adjusted): 1983 2006Included observations: 24 after adjustmentsCunveigence duliieved after 15 iterationsVariableCoefficientStd. Errort-StatisticProb.C2020.2802019.372-1.0004500.3290X0.0914160.0349762.6136960.0166AR(1)1.3033790.2151086.0591780.0000AR-0.2712550.224475-1.2083980.2410R-squared0.999229

30、Mean dependent燉7548.800Adjusted R-squared0.999114S.D. dependentvar2339.896S.E. of regression84.54348Akaike info criterion11.86342Sum squared resid142952.0Schwarz criteri on12.05976Log likelihood-138.3610Hannan -Quinn enter.11.91551F-statistic8644.033Durbin-Watso n stat1731745ProbF-statistic>0.000

31、000Inverted AR Roots1.04.26Estimated AR process is nonstationary=.2020.280,0.0914x； se= (2019372) (0.0349) t= (4.000) (7.2931)R2=o.9992 F=8644033 DW=1.7317所以美國國內(nèi)生產(chǎn)總值每增加10億美元，股票價(jià)格指數(shù)增加0.09146.4卜表給出了某地區(qū)1980-2000年的地區(qū)生產(chǎn)總值（V）與固定資產(chǎn)投資額（X）的數(shù)據(jù)表略 要求：（2）使用對(duì)數(shù)線性模型 U1X = A + LliX, + ut進(jìn)行回歸，并檢驗(yàn)回歸模型的 自相關(guān)性：（2）采用廣義差分法

32、處理模型中的自相關(guān)問題。（3）令X； = X, / X,.,（固定資產(chǎn)投資指數(shù)），（地區(qū)生產(chǎn)總值增長指數(shù)），使用模型 LnY =0+佚LnX+v;，該模型中是否有自相關(guān)？答:散點(diǎn)圖如下9.28.88.4g 8.0767.26.848525660646872LNXiXLJ 1AxJ LAXAJDependent Variable: LNYMethod: Least SquaresDate: 10/25/14 Time 22:14Sample: 1980 2000Included observations: 21VariableCoefficientStd. Error t-StatisticPr

33、ob.C2.1710410.2410259.0075290.0000LNX0.9510900.02889724.451230.0000R-squared0.969199Mean dependent var8.039307Adjusted R-squared0.967578S.D. dependent var0.565486S E of regression0101822Akaike info criterion-1640785Sum squared resid0.196987Schwarz criterion-1.541307Log likelihood19.22825Hannan-Quinn