計量經(jīng)濟學多元線性回歸模型x

1、多元線性回歸模型一.概述當今農(nóng)村農(nóng)民人均純收入與多個因素存在著緊密的聯(lián)系，例如人均工資收入，人均農(nóng)林牧漁產(chǎn)值人均生產(chǎn)費用支出，人均轉(zhuǎn)移性和財產(chǎn)性收入等。本次將以安徽 1995 2009年農(nóng)村居民純收入與人均工資收入,人均生產(chǎn)費用支出,人均轉(zhuǎn)移性 和財產(chǎn)性收入等因素的數(shù)據(jù)，通過建立計量經(jīng)濟模型來分析上述變量之間的關(guān)系， 強調(diào)農(nóng)村居民生活的重要性，從而促進全國經(jīng)濟的發(fā)展。二、 模型構(gòu)建過程L變量的定義被解釋變量：農(nóng)民人均純收入y解釋變量：人均工資收入x1,人均農(nóng)林牧漁產(chǎn)值x2人均生產(chǎn)費用支出x3 人均轉(zhuǎn)移性和財產(chǎn)性收入x40建立計量經(jīng)濟模型：解釋農(nóng)民人均純收入與人均工資收入，人均生產(chǎn)費用支出， 人

2、均轉(zhuǎn)移性和財產(chǎn)性收入的關(guān)系2 .模型的數(shù)學形式設(shè)定農(nóng)民人均純收入與五個解釋變量相關(guān)關(guān)系模型，樣本回歸模型為：Y =+ Xii+ X2i+ X3i+X4i+e012343 .數(shù)據(jù)的收集該模型的構(gòu)建過程中共有四個變量，分別是中國從19952009年人均工資 收入，人均農(nóng)林牧漁產(chǎn)值人均生產(chǎn)費用支出，人均轉(zhuǎn)移性和財產(chǎn)性收入，因此為 時間序列數(shù)據(jù)，最后一個即2009年的數(shù)據(jù)作為預測對比數(shù)據(jù)，收集的數(shù)據(jù)如下 所示：obsYX1X2X3X4obsYX1X2X3X419951302.950234.21 DC1977.920465.400093.6100019961&07.720346J5DC2263.S504

3、56.8800107 2100；193718087504C5.490C2451.090第0J50Q77,9700019981363.060457.170C246S.460440.1500104.fi 100:19931900 290470,690(2468.030409.1000120 060020001S3J 57054/8300241&.650J48 1100127.410020012020.000510.650C2482.250406.0800141.790020022116.000707,58002570.050526.5100166 170020032117.000818 92002

4、563 820517.5000140 870020042449.300884.62003212.360696.9000165.340020062641 0001010 0503236390B9L4100187 710020062969 10。11M.11O3449 630103RMQ226 70020073556.300U70.0603974.3801119.540327.8200120084202 5001737 04C4666 6901395 220437 360020094.504 3001B3242C4846 5401334.260477.45004 .用OLS法估計模型歸結(jié)果，散點圖

5、分別如T JDepend2nl Variable. YMethod: Least SquaresDate 11/17/11 Time 18 07Sample 1995 2009included obser/ations. 15Variable Coefficient Std Errart-StatisticPobCx1nx3x433 63262186.26080.1805S70 8603。5905411214 的3.G3176G0,C04G0.5902470.1244924.741256OflOOB-0 2743820 203681-1.3471160 20771 6239000 569856

6、2 6741830 0233R-squared0.99711 GMean dependent var2466J23Adjusted Rvqgrfd0.995963S D. dependent var947 6277S.E. of regression60,21151Akaike info crikrion1129481Sum squared resid36254.26Schwarz criterion11.53082Log likelihood-79.71104F-statistic864.4308Durbin-Watson stat1 179357Prob(F-st atistic0 000

7、000Y? =33.632+0.659X 1+0.59 X 2 -0.274X 3+0.152 X 4 d.f.=10 ,R2 =0.997116 , Se=(186.261) (0.1815 (0.1245) (0.2037) (0.5699) t=(0.1805) (3.632) (4.741) (-1.347) (2.674) Group: ENTITLE & Workfile: U N TITLE DUnt；tled互 IS 口Vtewl Proc| Otject| PrhtjMaine|Reege| Nar甲相SheeH 弓tats|Spg|X1X2X3X4三、模型的檢驗及結(jié)果的解釋

8、、評價2 .擬合優(yōu)度檢驗及統(tǒng)計檢驗R2 = 0.997,可以看到模型的擬合優(yōu)度非常高，說明農(nóng)民人均純收入與上述四個解釋變量之間總體線性關(guān)系顯著。模型總體性檢驗（F檢驗）：給定顯著水平=0.05,查自由度為（4,10）的F分布表，得F（4,10）=3.48，可見該,g型的F值遠大于臨界值，因此該回歸方程 很明顯是顯著的。但由于 X3系數(shù)不顯著且符號為負，與經(jīng)濟意義不符，因 此我們認為解釋變量之間存在多重共線性。變量的顯著性檢驗（t檢驗）：給定顯著水平=0.05,查自由度為10的t分布表，得t /210=1.812,大于該臨界值白的顯著變量為x1,x2,x4; x3解釋變量未通過檢驗，說明x3與被

9、解釋變量之間不存在顯著的線性相關(guān)關(guān)系。3 .多重共線性的檢驗 相關(guān)系數(shù)檢驗法VfeTproc| Object Print|MameFreeze5ame | ShueE5tats|&ecCorrection Matrixa Group： UNTITLED Workfile: UNTTTlEDLlrrtHledyX4X3X2X1Y1 oooooo0.M132909657960 9944950 99114CX40.9813291.0000000948077。.刎 3M0.967125X3F 0.9657&60.9430771.0000000.9726930.965013 X2F 0 9944350.

10、9713000.9726931.000&000 982869X10 9911400.967125,0 965013 _0 932S691 000000上圖是Eviews輸出所有變量的相關(guān)系數(shù)矩陣，可發(fā)現(xiàn) Y與所有解釋變量都是正 相關(guān)的關(guān)系，所以進一步確定了上面的回歸存在共線性問題。另外，我們發(fā)現(xiàn) X1和X2的相關(guān)系數(shù)很高，兩變量很可能存在共線性。多個解釋變量的相關(guān)性檢驗由上面的分析可知，X1和X2有很高的相關(guān)性，那么我們這里就用X1做被解釋 變量，X2和X3做解釋變量，可得回歸模型如下：Viev,s - Equation UNTITLED WorlcfilUNTlTLEDUnfeitledEs

11、tmte Forecast Stats - ResidsEdit Object View Prtxr Quick Options Window Hel|Hiuw Prgf 田閨 Name FreejeDependent Variable- X1 Method Least Squares Date: 11/17/11 Time: 19:14 Sample 1996 2009Included obsen-ations- 15VariableCoefficientStd. Error t-StatisticProb.C-7S7.26101T31752 4 372721OC009X204771740

12、1303173 由 616510 0033X3S245mG.329S3C0.74401B0.4712R-squsred0 96752&Mean depencieni var851 2053Adjusted R-squared0 362118S.D dependent var512 3819S.E. of regressiori99.72701Akaike info criterion12.21961Sum squared resid119345 1Schwarz ertienon12.36122Lag Jikelihcod-B8 64705F-statistic178 7821urbin-Wa

13、tson stat1 190711ProbfF-statistic)0 OOOOOO? =-757.251+0.477X1X2 +0.2454X3t=(-4.373)(3.662)(0.744)R2 =0.9675, R2 =0.9621, F=178.78, DW=1.19?？梢钥吹?，回歸模型的擬合優(yōu)度非常高，F(xiàn)值也遠大于臨界值。如果將顯著水平擴大到=10%的話，X2系數(shù)顯著，X3系數(shù)不顯著。因此x 1 ,x2存在共線性。四、模型的建立這里我們用逐步回歸法得到農(nóng)民人均純收入模型L分別用四個解釋變量對 Y進行回歸，回歸結(jié)果分別如下：口 Equation: UNTITLED Workfile:

14、UNTITLEDUrrtitled | 0 回View|Prod Object Print|Nanie|l=tieeFe| Estinate| Erecast Itais ResidslDependent Variable: YJ Msthad: Least SquaresDate 11/17/11 Time 1943Sample: 1995 2009Included observations: 15VanableCaffictenlStd. Error t-Stati sticProb.C906 0C4367 0372413.504870 0000X11J33C690.06813126904

15、910.0000F?-sc|uared0 82358Pear dependent var2466.323Adjusted R-squared0.9810013 D dependent var947 6277S E. of regression130 6186Akaike infc criterion12.70601Sum squared resjd221795.9Schwarz criterian12.80041Log likelihood-932 死 05F-statistic723 3742Durbin-Watson stat0 707042ProbfR-statistK)0 OOOCOO

16、 Equation: UNTITLED Workfile: UNTTTLEDUntitled a | E 次 Vjevv|Poc|8j6cti Print | NameFreeze | Estiinate | Forecast Stats | Nesi:is |Dependent Variable: YMethod Least SquaresDate: 11/17/11 Time: 19:44Sample: 1995 2009Included observations: 15VariableCoefficientStd. Error t-StatisticProb.C745 755797 56

17、245 764388c0 0000X21.0694380.03125234.220330.0000R-squared0.989021Mean dependent var2466 323Adjusted R-squared0 988176S D dependent var947 6277S.E of regression103.0434Akaike info criterion12,23174Sum squared resid138033.3Schwarz criterion12.32616Log likelihood-8973808F-statist ic1171 031Durbin-Wats

18、on stat1 461168Prob(F-statistic)0000000 Equation: UNHTLED Workfile: UNTITLEDUntitled亙View|ProcJ Object Print| Name Freeze Esbmiate|Foreca5tlStats|Rasids|Dependent Variable: YMethod. Least SquaresDate: 11/17/11 Time: 19.45Sample: 1995 2009Included observations: 15VariableCoefficientStd. Error t-Stati

19、sticProb.C589 1289154.58393 8110620 0022X32.6285460.19582313.423070.0000R-squared0.932705Mean dependent var2466 323Adjusted R-squared0 927528S D dependent var947 62S E of regression255.1068Akaike info criterion14 04481Sum squared resid846033.4Schwarz criterion14.13921Log likelihood-103.3361F-statist

20、ic180.1788Durbin-Watson stat0.777246Prob(F-statistic)0.000000 Equation; UNTITLED Workfile: UNTITLEDUntitled國 疝Vie/. Poc ；Qbjec hE NsrnejFreeze | E?*mdte -orecst Sta:s： R&sidsJDependent Variable. YMethod: Lea5t SquaresDate 11/17711 Timer 19 46Sample: 1995 2009Included observations. 15VariableCoeff ci

21、 entStd Error t-StatisticProtC1013.437926586810.9137G0.0000X47.509564040922018.395870.0000RSquared0.9C3006Mean dependent var2456.323Adjusted R-squared0.%0160S.D. dependent var947.6277S E. of regression189.1456Akai ke info critericn13.44M8Sum squared resid46so882Schwarz critenon13 54 088Log likelihoo

22、d98 64S57F-statistic338.4079Durbin-Watson stat0.804301Probf-slatistic)0 000000可以看出，Y與X2擬合優(yōu)度R2最大，因此將這個方程作為基本方程，然后往里 加入其他變量。2.引入第二個變量匚心加口二 LNTjTLED 世飛人口齒 LNTnEDALntitledaVfew|Ptoc|Object| *it|NameFre金* Ectnwte Forecast Stats|ftesidsDependent Variable Y Method Least Squafog Date： 11/17711 Time: 19:61Sa

23、mple 1996 2009Included observations: 15Varrable Coefficient Std. Error t-Statistic Prob.cX1X201.22950.7449930.64374319S.7348 -0.5093700.2142273.4771230.1245615.1B80890.51970.00450 0002R-squared0 994531Mean dependent var2466 323Adjusted R-squared0.993619S O dependent var947 方 277S.E. of regression75

24、69550Akaike info criierion11,658 17Sum squared resid63757 71Schwarz critenon11 80578Log fikelihood-S4.61128F-statistic1091 063Durbin Watson stat0 677182Prob(F-statistic)0.000000引入變量Xi后，t值3.17 臨界值3.18,其系數(shù)通不過顯著性檢驗。 Equation； UNTITLID Workfile: UNTITLElUrtitled豆 -1目.Wf kI k0cI object | Prirtl Nanne | F

25、rsze Esf mate: FprecaEU .也t$ HesidaDependent Variable: D fJlethod. Least Squares Date: 11/17/11 Time： 1&：57 Sample: 1995 2009 Included observations 15VariableCoefficientStd. ErrorProb.C-7&07225185.851942007780 0012X21.09&9700.1396557.8650570.0000X34079445045襯 7262244400 8262R-squared0.989066Mean dep

26、endent var2466 323Adjusted R-squared0.96T244S D dependent var947.6277S.E. of regression107.3266Akaike info criterion12,36089Sum squaredpsid137456 3Schwarz critenon1Z60250Log likelihood-8970666Fstatistic542 7698Durbin4/Vatson stat1.52541&ProbfF -statist ic)0 DOOOOO引入變量X3后，t值-0.22444臨界值3.18,其系數(shù)通不過顯著性檢

27、驗。 Equation: UN7TTLED Workfile: UNTmEDUntitled - u1 回 法VieA PcObject Print 網(wǎng)的日| Freeze | Estimate | Foreca | tais Resids |Dep&n-dnt Variable: YMethod. Least SquaresDate: 11/17/11 Time 19:58Sampla: 1995 2009Included observatians. 1SVariable Coefficient Sid Error t-Statistic ProbC-295.5387現(xiàn) 0626 J.506

28、6420.1.343X20 7655790.107G297.2999720.0000X42Q796770J659Q6 271S3150.0138squared0.993199Mean dependent var2466.323Adjust eri R-squared0.992066S D dependent var347 6277SE of regression8441006Akaike info g rite ri on11 誠 11Sum squared resid35500 70Schwarz criterion12 02772Log likelihood*36.14580F 噂 tat

29、istic376.2367urtjin-Watson start1 386558Prob(F-stati5tic)0.000000引入變量X4后，t值2.715臨界值3.18,其系數(shù)通不過顯著性檢驗。綜上所述，本次模型只引入變量X2,其最終輸出結(jié)果如下: Equation! UN7TT1ED Worldlie! UNTm.EDUnrtled 0 B 過 止科伊其|8灰戊1 Pmt|hlaEe|Freeae| E&tirnatEj Forec85tlstats Resids jDap&ndent Variable YMethod Least SquaresDate： 11/17/11 Time：

30、 19.44Sample: 1595 2009Included observations: 15VariableCoefficientStd_ Error t-StatisticProb.1C-745 755797 56245-7.6438800 0030X21.9694300 03125234.220330.0030R-squared0989021Mean dependent var2466 323Adjusted Rsquared0J68176S D dependent var347 62S E of regression用 3 0434Akaike info criterion12 23

31、174Sum squar&d resid138033.3Schv/arz criterion12.32615Log likelihood加9.73808F-statistic1171 031Durbin-Watson stat1.46116aProbfF-atatisticoooooao模型的最終結(jié)果為Y =-745.76+1.069X2R2 = 0.989,(-7.644)(34.22)=0.988 , F=1171.031, DW=1.4611異方差檢驗（懷特檢驗）EViews - Equation UNTITLED .Vorl4i!e: UN-TITLED-1.UntiIed 口 Fil

32、e Edit Object View Proc Quick Options Window Help,ie a1 | Proci Object Print| Name Freeze1 Estamate Forecast Stats ;ResdsjWhite HeteraskedasticityTest-F-siatistic0.387616Prcbabiliiy0.4-37061Obs*R-squared1.932877Pro bsbility0.380436Test Equation:pendant Vanable: RESIDEMMh附 Least SquaresDate- 11/17/11

33、 Tims 20 22Sample 1 15Included observations 15Vanable Coefficrent Sid Error t-Statistic Prob.CX2X2空-729S0 33 52 42628-0X0773565224.4E-1.11737740.457321.2955220.005353 13214310.28670.2196O. 2110R-squared0.128853Mean dependent var9202.220Adjusted R-squ日期4016332S.D. dependent var14225.16S E of regression14340 35Akaike info criterion22