計(jì)量經(jīng)濟(jì)學(xué)多元線性回歸模型

1、多元線性回歸模型概述當(dāng)今農(nóng)村農(nóng)民人均純收入與多個(gè)因素存在著嚴(yán)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(fèi)用支出，人均轉(zhuǎn)移性和財(cái)產(chǎn)性收入等。本次將以1995 -2021年農(nóng)村居民純收入與人均工資收入， 人均生產(chǎn)費(fèi)用支出，人均轉(zhuǎn)移性和財(cái) 產(chǎn)性收入等因素的數(shù)據(jù)，通過建立計(jì)量經(jīng)濟(jì)模型來分析上述變量之間的關(guān)系，強(qiáng) 調(diào)農(nóng)村居民生活的重要性，從而促進(jìn)全國經(jīng)濟(jì)的開展。模型構(gòu)建過程1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(fèi)用支出x3人均轉(zhuǎn)移性和財(cái)產(chǎn)性收入x4建立計(jì)量經(jīng)濟(jì)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(fèi)用支出, 人均轉(zhuǎn)移性和財(cái)產(chǎn)性收

2、入的關(guān)系2.模型的數(shù)學(xué)形式設(shè)定農(nóng)民人均純收入與五個(gè)解釋變量相關(guān)關(guān)系模型，樣本回歸模型為：Y +X2i+X®+ X/ei012343數(shù)據(jù)的收集該模型的構(gòu)建過程中共有四個(gè)變量,分別是中國從1995-2021年人均工資收 入，人均農(nóng)林牧漁產(chǎn)值人均生產(chǎn)費(fèi)用支出， 人均轉(zhuǎn)移性和財(cái)產(chǎn)性收入，因此為時(shí) 間序列數(shù)據(jù)，最后一個(gè)即2021年的數(shù)據(jù)作為預(yù)測(cè)比照數(shù)據(jù)，收集的數(shù)據(jù)如下所 示：absYX1X2X3X4obsYX1X2X3X419951302.950234.21001977.920465.400093.6100019961607 720346 35002263 550456 3800107 210

3、0199718087504C5.49002451.090490.150077.9700019981363.060457.17002463.460440.1500104 6100W護(hù)1900.2W470 69002468 0304011000120 0800'2DOO1934.570547.830C2416.650449.1100127.410020012021.000610.650C24S2.250436,0800141 790020022118.0007C7 £8002S700G0526.5100166 170020032117 00081S.920C2563.820617

4、.6800140.970020042449.300884.62003212.360 G98.900QT165.340020052641 0001010.0503236.350K7.41&0T167 710020062969.10011B4.1103449.6301036.960226 6700?0073556.3001470 0503974.3801119.540327 820020214202 5001737 840K66 6901355.220437 360020214604.3001882.4204846.6401334.260477 46004用OLS法估計(jì)模型回歸結(jié)果，散點(diǎn)圖

5、分別如下：Y? =33.632+0.659Xi+0.59 x2-0.274X3+0.152X4d.f.=l0,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)Sample 1595 2021 Included observaljons 15ErrorPrpb33G32£219&26080 1805670 8(030.65W540 1S14693 6317C60 0040 59A2470 1214924 7412560

6、0008 匚 27430202036311 3471160 20771.&239000 S96$62 &Z41830.02330 997116ft/lean dependent var2466 323Adjusted R-squared0.935953S.D dependent varW7 6277S E of regression6021151Akaike info criterion11 2M81Sum squared tesid36254 26Schwarz criterion11 53002Log likeEihood79.711CMF-staiistiG864.430

7、SOut tMnV/atson slai117W67Prpbf-statistico ooooool: Group: UNITTLEO Workfile: UNTm-E&UrTt!tledW 亙 Vte典膽ct Print 糾那世片氈細(xì) 百anplE|ShEgt 15tmts:Epx|20O5O430O0-0V00C00OOO5K1X2X3X4三、模型的檢驗(yàn)與結(jié)果的解釋、評(píng)價(jià)2擬合優(yōu)度檢驗(yàn)與統(tǒng)計(jì)檢驗(yàn)R 2二0.997，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(gè)解釋變量之間總體線性關(guān)系顯著。模型總體性檢驗(yàn)F檢驗(yàn)給定顯著水平=0.05，查自由度為(4,10)的F分布表，得

8、F(4,10)=3.48,可見該模型的F值遠(yuǎn)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(hào)為負(fù)，與經(jīng)濟(jì)意義不符， 因此我們認(rèn)為解釋變量之間存在多重共線性。變量的顯著性檢驗(yàn)t檢驗(yàn)：給定顯著水平=0.05，查自由度為10的t分布表，得t /。二1.812，大于該臨界值的的顯著變量為x1,x2,x4 ; x3解釋變量未通過檢驗(yàn)，說明x3與被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(yàn)相關(guān)系數(shù)檢驗(yàn)法 Group： UNITTLED Workfile: UWTTTLEDLlntitled琛丫艷vjpiroc|gbect| 卩怕町川占恨丁亡已龍| S白mo橙Stat

9、s|&jecCorre-lation MatrixyX4X3X2X1Y1 oooaoo0 98132909657660 9944960 991140X4P 09313291-0000000948077OS7130O0 967125X3P 0.9657&60.948077piSooooo0.9726930 965013X20 9344350 971300FO 97269J1.0000000 962669X1P 0.9911400.9671250.9650130.9828691.000000上圖是Eviews輸出所有變量的相關(guān)系數(shù)矩陣，可發(fā)現(xiàn) 丫與所有解釋變量都是正 相關(guān)的關(guān)系，所

10、以進(jìn)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(gè)解釋變量的相關(guān)性檢驗(yàn)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：VariableCoeHicientStd Error('StatisticProbCJ57.2510173 17624 372721o.ooosX20 4771740.1303173.6616510.0033X302464000 329(30074401B0.4712R-sq Jared0 67629Mean dependent var

11、851 2053Adjusted R*squared0 962118S D dependent var512 3819S.E of99 72701Akaiks info cnterion12 21961Sum squared rgwid1193457Schaaf? critenon12 36122Log likelihood-88 64705Fstatistic170.7821Durt>in-Watson1 150711Prob(F-statistic)oooooooSample 1995 2021 Included obseRatiaFis 15? =-757.251+0.477X i

12、X2+02454 X3R2 = 0.9675 ,2r =0.9621 , F=178.78 ,DW 1.19。t=(-4.373)(3.662)(0.744)可以看到，回歸模型的擬合優(yōu)度非常高，F(xiàn)值也遠(yuǎn)大于臨界值。如果將顯著水平 擴(kuò)大到 =10%勺話，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。1分別用四個(gè)解釋變量對(duì) 丫進(jìn)展回歸，回歸結(jié)果分別如下:Sampie 1995 200&Included ob&eivations 15hVariableCoefficientStd Error t-3tatisU

13、cProbC X190SOD4J1 83306967.0072413.604370 0631326 90491OLOOOO0 ooooRsquared0S82358Uean dependent var2466 323Adjusted Rsquared0.991001S D. dependent varW7 6277S E of regression130 613&Akaike info 亡 ritenon1270601Sum squared rsid2217WJSchwarz cnte non12 80041Lo-g likelihood3.29606F-stahstic723 874

14、2Durbin-Wjt&on stat0 7070J2Pro'Statistic0 000000口tl-I." Sample 1995 2021Included oberi ions: 15VariableCoeflicEentStd Error ( StatisticProb】CX2V45 7S$71 0694 3897 6S245-7 &4 38800 03125234 22033OQOOO00000R-sqvar«dAdj uil ed： R-sq jsrd S E of regrssi on Sum squared resid Log lik

15、elihood Durbin-Wats cn 就卻0W021 0*998176103 0134 138033 3*89 73B0B1.441164M-ean血呼n£訓(xùn)中 S O dfependnL var Akaike mfo cnteri onSchwarz criterion F*statisticPro b(F stall Stic2W 323 &4777 12.2317412 32615 1171 031 0 ooooooSample 1935 SCO?Included obsirvS詢ns 157anbleCoefficientStd Error t-Statisi

16、rcProb.口CSB 9 1248tM.5«393 8110620.0022口X326255460 訝58乃13 423070 0000R-Squaf&d093?7C5Mean ddpendeM var2466 323Adjusted RquredD92T5S8S D deptndvnt var947.«77S.E M regression2&5 WAkak« info critefionId 04481Sum squared resid84E033.4Schwarz ctrtenort14-13931likelihood103 3X1F-sta

17、tistic150 1788Durbin-VJat$on daL0 777246Pr-obF statistic0,000000Sample 1995 2021Included oberv-alions 15VariableCoelfieientStd Error l-St atist 忙PrcbC1013.437 ? 50956442.8«868W.913760 J08220 W 335070 00000 ooooAdjusled R-s quared SE. oFregression Slim $quafed resid Log likelihood Darbm-Watsort

18、stat0.9650 MT89-98 34&570804301Mean depend &nrt S 0 dependenl var Akarke info entrion Schwarz criterion F-staiistic Prob(F-statisiic)2466323 W 5277 13 446J8 13.5408B 338 4079 0 OQCOOOdn可以看出，丫與X2擬合優(yōu)度R2最大，因此將這個(gè)方程作為根本方程，然后往里 參加其他變量。2引入第二個(gè)變量xiSample 1396 2059 included obseratFons 15

19、gn甜©C廚砧旳iSW E吋PrOb,口c*101 229519E 73480 50S370C 6197口XI0 7448930 2142273 4771230 0W6X20 6437430 1245615 16S03S0 0002R-squared0 994631Mean dependent var2466 323Adjusted R-squared0993G19S 0 pen-detM 岀rW 62775.E. of regression75 69550Akik& i(if& cnt&non11.S6S17Surnreswi68767 71Sch-wan

20、匚 nterton11 B0S73log likelihood« 51128F-siatigtic1091 068Durbiri-Walsan 百0 677162PfqIKF-slati&bc j0 0M0003.17 臨界值3.18，其系數(shù)通不過顯著性檢驗(yàn)。Sample 19% 2021 Included otxi«rvati&ns15VariableCoefficient$td Enor c-SUti3LicPmbCX2X3-730 72261.O9957C-0 079445185.&519-4 2007780 13&&S5 7

21、8&S057 G 35372 -0 2244400J912O.IXXJQ0 0262IIR-tquirtdAdjustedS E_ of regression Sum squared Log ! kehhoMi Durbin-Watson at at0.9990661071374663 8牛 70&E1.62&41fiMandependeni vgj S O dependent var Akaike info Graerion Schwarz fntnartF-slatisticPrabfF-ststiatic)2466 323J47 W7712 350B9115425

22、0M2 7«98Q OCMflCO引入變量x3后，t值-0.22444V臨界值3.18，其系數(shù)通不過顯著性檢驗(yàn)。Sample. 1996 2021Ircfuded otsrvationtVan?bl«CoeficiemSid Eirori-StatisticPlob.C295 5507TW-1 6Q5W20 1343吃0 78557$0 107S297 2«血0 0000K42079&770 76&90627153150 0188R-squared0 993199F3ean dependent vsr2466 323Adjusted0 992066

23、5 D 賓弊rpnL varW &277S E of regression34 41(X36AXaik? info enteion11 B8611Sum squared resptf85500 70Schwa rr criterion1202772Leg bkdihood86 U5B0F-statisticS76 23«70jfbn-WatSQn 歙前1 386$閔Prob<Fsl5tiSUC)0 000040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(yàn)。綜上所述，本次模型只引入變量X2，其最終輸出結(jié)果如下:Sampie 1&95 202

24、1Indudad observations 1SVariableCoefficientSid Enof t-StaTi$tjcProbC-745 755797 56245" &I3理00,0000X21 0694390 0312璇34 220330 0000R-squared09&W51Mean dependent var24鏈 323Adjusted辛d0JB817SS.D depemlwt varW 7.6277S t of regression103 0434Akaike info cnenon12 Z3174Sum squawd ruid1380333Schw

25、arz1232615Log lik*bhMd89 73808F* 5tati«ie1171 031Durbin-Watsan st 9t1 461168Prob(F stati&uc)moooooa模型的最終結(jié)果為Y = -745.76+1.069 X2R2 = 0.989 ,-7.644 34.22=0.988 , F=1171.031,DW=1.4611S*mple 1 15included &bse(vgtifl(i3； 15VariablyCoeffiewMStd Errorp«bCT28B0 3365224 J6 J 1173770 2857X252 4262840 467321 2S552202195JC20 0077350 005353 d 32U31D2110R squared0125350kan dependent var5202 220抑用軾訊R-squared0