EViews計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)報(bào)告多重共線性的診斷與修正的討論

試驗(yàn)題目多重共線性的診斷與修正一、試驗(yàn)?zāi)康呐c要求：要求目的：1、對(duì)多元線性回歸模型的多重共線性的診斷;2、對(duì)多元線性回歸模型的多重共線性的修正。二、試驗(yàn)內(nèi)容依據(jù)書上第四章引子“農(nóng)業(yè)的進(jìn)展反而會(huì)削減財(cái)政收入，197－2023業(yè)增加值等數(shù)據(jù)，運(yùn)用EV三、試驗(yàn)過程:〔實(shí)踐過程、實(shí)踐全部參數(shù)與指標(biāo)、理論依據(jù)說明等)〔一)模型設(shè)定及其估量爭(zhēng)論“農(nóng)業(yè)的進(jìn)展反而會(huì)削減財(cái)政收入”這個(gè)問題。1設(shè)定如下形式的計(jì)量經(jīng)濟(jì)模型:Y=+ X+ X + X + X + X + X +1i 2 2 3 3 4 4 5 5 6 6 7 7 ii

為財(cái)政收入CS/億元；X2

為農(nóng)業(yè)增加值NZ/億元；X3

為工業(yè)增加值GZ/億元；X4

為建筑業(yè)增加值JZZ/億元；X 為總?cè)丝赥POP/X5

為最終消費(fèi)CUM/億元；X7

為受災(zāi)面積SZM/千公頃。圖1： 1978~2023年財(cái)政收入及其影響因素?cái)?shù)據(jù)年份 億元

農(nóng)業(yè)增工業(yè)增加GZ/億NZ/億元元

億元

總?cè)丝谌?/p>

最終消費(fèi)受災(zāi)面億元千公頃19781132。31027。51607138。2962592239。15079019791146。41270。21769。7143。8975422633.73937019801159.91371.61996.5195。5987053007。94452619811175.81559.52048。4207。11000723361。53979019821212.31777。42162。3220。71016543714.833130198313671978。42375。6270.61030084126。43471019841642。92316.12789316。71043574846。33189019852023。82564。43448.7417。91058515986。344365198621222788.73967525.71075076821.84714019872199.432334585。8665.81093007804.64209019882357.23865。45777。28101110269839.55087019892664。94265.9648479411270411164。24699119902937。150626858859.411433312090。53847419913149。485342。28087。11015。111582314091.95547219923483。375866。610284.5141511717117203。35133319934348.956963。8141882266。511851721899.94882919945218。19572。719480。72964。711985029242.25504319956242.212135824950。63728.812112136748。24582119967407.9914015429447。64387。412238943919。54698919978651.1414441932921。44621。612362648140.65342919989875。9514817.634018.44985。812476151588.250145199911444.081477035861。55172.112578655636。949981202313395.2314944.7400365522。31267436151654688202316386.0415781.343580.65931。712762766878.352215202318903641653747431.36465.512845371691.2471192023217152517381754945.57490.812922777449。55450620232639647214127652108694.312998887032。937106202331649.292242076912.910133813075696918.138818202338760.22404091310。9118511131448110595.3410912023513217828095107367.2140141132129128444648992EVY、XX、X、X、XX等數(shù)據(jù)，承受這些數(shù)據(jù)對(duì)模型進(jìn)展OLS回歸。i 2 3 4 5 6 7(二)診斷多重共線性1EviewFile/Open/EVWorkfil—Excexls2、在EVlsycx2x3x4x5x6xEnteOLS：圖2： OLS回歸結(jié)果DependentVariable:YMethod：LeastSquaresDate:10/12/10 Time:17:07Sample：19782023Includedobservations：30Variable

Coefficient Std。Error

t—Statistic Prob.C—6646。6946454。156—1.0298320。3138X2-0.9706880.330409—2。9378410。0074X31.0846540。2285214。7463970.0001X4-2.7639282.076994—1。3307350。1963X50。0776130.0679741。1418080。2653X6-0.0471190。081509-0。5780840.5688X70.0075800。0350390.2163290。8306R-squared0。994565Meandependentvar10049.04AdjustedR-squared0.993147S.D.dependentvar12585。51S.E.ofregression1041.849Akaikeinfocriterion16.93634Sumsquaredresid24965329Schwarzcriterion17。26329Loglikelihood-247.0452F—statistic701.4747Durbin—Watsonstat2.167410Prob(F-statistic〕0.000000由此可見，該模型的可決系數(shù)為0.9950.993，模型擬和很好,F統(tǒng)計(jì)量為701。47，模型擬和很好，回歸方程整體上顯著。但是當(dāng)=0。05時(shí)，t (nk)=t (23)=2。069,不僅X4、X5、X6、X7的系數(shù)t檢驗(yàn)不顯著,而且X2、X4、X6系/2 0.025數(shù)的符號(hào)與預(yù)期相反，這說明很可能存在嚴(yán)峻的多重共線性〔即除了農(nóng)業(yè)增加值X 、工業(yè)增加值X外，其他因素對(duì)2 3財(cái)政收入的影響都不顯著,且農(nóng)業(yè)增加值X、建筑業(yè)增加值X、最終消費(fèi)X的回歸系數(shù)還是負(fù)數(shù)，這說明很可能存2 4 6在嚴(yán)峻的多重共線性.)3、計(jì)算各解釋變量的相關(guān)系數(shù)：Workfile窗口，選擇X2、X3、X4、X5、X6、X7Quick”-GroupStatistics—Correlations-OK，消滅3:圖3：相關(guān)系數(shù)矩陣X2X3X4X5X6X70。0。0.9729806145982660623490.92797842940.988962619722619996587X2161479789067452466724650。0。0。0.9729806145998521808390.84390020659926412367112944371033X361471318868758178462150。0。0。982660623490.99852180830.86415213599960568434415464571840X4978993188128051159643530。0.92797842940.8439002065864152135920.88884805550.3877672648X506745687588051146979087870。0。0。0.988962619799264123671996056843440.88884805551858085X6246671784159646979115820。0。0。0.22619996580.129443710315464571840387767264801858085X772465362154353878715821由相關(guān)系數(shù)矩陣可以看出，各解釋變量相互之間的相關(guān)系數(shù)較高，特別是農(nóng)業(yè)增加值X2

、工業(yè)增加值X3

、建筑業(yè)增加值X4

、最終消費(fèi)之間X6

0.8以上。這說明模型存在著多重共線性。〔三〕修正多重共線性1Y對(duì)X2、X3、X4、X5、X6、X7的一元回歸,結(jié)果如以以下圖4:在EVlsycx2DependentVariable：YMethod:LeastSquaresDate:10/12/10 Time:17:49Sample:19782023Includedobservations:30Variable

Coefficient

Std.Error t-Statistic Prob。C—4086。5441463。091—2.7930900.0093X21.4541860。11723512.403980.0000R—squared0.846034Meandependentvar10049。04AdjustedR-squared0.840536S.Ddependentvar12585.51S。E.ofregression5025.770Akaikeinfocriterion19.94689SumsquaredresidLoglikelihood707E+08—297。2033SchwarzcriterionF—statistic20.04030153.8588Durbin-Watsonstat0。166951Prob(F-statistic〕0.000000依次如上推出X3、X4、X5、X6、X74:4。一元回歸估量結(jié)果變量X2X3X4X5X6X7參數(shù)估量值1.45418604268173186851082978903303540.111530t12.40398289016822.67733620602518.128950320338R20.84603409675670.94836405790410.9214940003651R20。8405360966408094652005640060.918690-0.0319322、其中，參與X的R2最大,以X為根底，順次參與其他變量逐步回歸。結(jié)果如以以下圖5：3 3DependentVariable:YLeastSquaresDate：10/13/10 Time：01:27Sample:19782023Includedobservations：30Variable

Coefficient

Std.Error

t-Statistic

Prob。C1976。086388。24135。0898410。0000—1.10533X290。105222—10.504860.0000X30.7219890。02887925.000560。0000R-squared0.993624Meandependentvar10049.04AdjustedR-squared0.993152S。Ddependentvar12585。51S.E.ofregression1041.474Akaikeinfocriterion16。82930Sumsquaredresid29286057Schwarzcriterion16。96942Loglikelihood-249.4395F—statistic2103.946Durbin-Watsonstat1.662637Prob(F—statistic〕0。000000依照上面,在順次參與X4、X5、X6、X7，進(jìn)展逐步回歸。綜合結(jié)果如以以下圖5：變量X2X3X4變量X2X3X4X5X6X7R2-1.1053390。721989X3X20.993152X3X40.990547X3X50。98301X3,X60。985025X3X70.970053〔—10.50486〕〔25.00056)1。65227—9。255748(11.46367〕0.514796〔-8.514941〕-0。261997〔26.29703〕0.910503〔-5。325453〕-0。386459〔11.18199〕0.430639(—5。984236〕—0.125579〔30。62427〕〔-2。099504)經(jīng)比較，參與X的方程R2=0.993152，改進(jìn)最大，但是X得系數(shù)為負(fù)，這明顯不符題意。2 在X的根底上分別參與其他變量后覺察，XX2 3 2 4

，X ，X6

的系數(shù)都為負(fù)，與預(yù)期估量違反。因此這些變量都會(huì)引起嚴(yán)峻的多重共線性，全部剔除，只保存X3DependentVariable：YMethod:LeastSquaresDate：10/12/10 Time:17:50Sample：19782023Includedobservations:30

。修正的回歸結(jié)果為：Variable

Coefficient

Std.Error t—Statistic Prob.C X3

570。5337 -1。8847080.014768 28。90168

0.06990.0000R—squaredAdjustedR—squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

0。967567 Meandependentvar0。966408 S。D。dependentvar2306。678 Akaikeinfocriterion149E+08 Schwarzcriterion-2738402 F-statistic0。292531 Prob〔F-statistic)

10049。0412585.5118。3893518.48276835.30740.000000Y?=-1075。289+ 0.426817Xi 3〔-1。884708〕〔28。90168〕R2=0。967567 R2=0.966408 F=835.3074這說明在其他因素不變的狀況下，工業(yè)增加值每增加10.426817億元。四、實(shí)踐結(jié)果報(bào)告:為爭(zhēng)論“農(nóng)業(yè)的進(jìn)展反而會(huì)削減財(cái)政收入”的問題，依據(jù)1978－2023年的財(cái)政收入，農(nóng)業(yè)增加值,工業(yè)增加值,建筑業(yè)增加值等數(shù)據(jù)，運(yùn)用EV最終修正的回歸結(jié)果為：Y?=—1075.289+ 0.426817Xi 3(-1.884708〕〔28.90168〕R2=0.967567 R2=0.966408 F=835。307410.4268170.967567,較高，說明模型擬合優(yōu)度高；F835。3074，說明整個(gè)方程顯著;t28。90168，t統(tǒng)計(jì)量，t檢驗(yàn)顯著，符合題意.逐步回歸后的結(jié)果雖然實(shí)現(xiàn)了減輕多重共線性的目的,但反映農(nóng)業(yè)增加值，建筑業(yè)增加值的X2，X3等也一并從模型中剔除出去了,可能會(huì)帶來設(shè)定偏誤,這是在使用逐步回歸時(shí)需要留意的問題。附加:1Y對(duì)X2、X3、X4、X5、X6、X7的一元回歸，結(jié)果如下：lsycx2DependentVariable:YMethod:LeastSquaresDate：10/12/10 Time：17:49Sample:19782023Includedobservations：30Variable

Coefficient

Std.Error t—Statistic Prob?！?086。C 544

1463。091

0.0093X2 1.454186 0.117235 12.40398 0.0000R—squaredAdjustedR-squaredS。E.ofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

0.846034 Meandependentvar0。840536 S。D。dependentvar5025。770 Akaikeinfocriterion7.07E+08 Schwarzcriterion-297.2033 F-statistic0.166951 Prob〔F-statistic)

10049。0412585.5119。9468920。04030153.85880。000000lsycx3DependentVariable：YMethod:LeastSquaresDate:10/12/10 Time：17:50Sample:19782023Includedobservations:30VariableCX3

Coefficient0。426817

Std.Error0。014768

t-Statistic-1.884708

Prob。0.06990。0000R—squared0.967567Meandependentvar10049.04AdjustedR-squared0.966408S。D.dependentvar12585.51S。E.ofregression2306。678Akaikeinfocriterion18.38935Sumsquaredresid1.49E+08Schwarzcriterion18。48276—273。Loglikelihood8402F—statistic835。3074Durbin—Watsonstat0.292531Prob〔F-statistic)0。000000lsycx4DependentVariable:YLeastSquaresDate：10/12/10 Time:17：50Sample：19782023Includedobservations:30VariableCoefficientStd。Errort-StatisticProb.C—1235。177727.9896-1。6966950.1008X43。1868510.14053022。677330.0000R—squaredAdjustedR—squared

0。948364 Meandependentvar0.946520 S.D。dependentvar

10049。0412585.51S.EofregressionSumsquaredresidLoglikelihoodDurbin—Watsonstat

2910.486 Akaikeinfocriterion2.37E+08 Schwarzcriterion—280.8155 F-statistic0。215531 Prob〔F-statistic)

18。8543718。94778514。26140.000000lsycx5DependentVariable：YMethod:LeastSquaresDate:10/12/10 Time：17：51Sample：19782023Includedobservations:30VariableCoefficientStd.Errort-StatisticProb。C—86420。4215618。35-5。5332600。0000X50。8297890.1337076。2060250。0000R—squared0。579041Meandependentvar10049.04AdjustedR—squared0。564006S.D.dependentvar12585。51S。Eofregression8310.188Akaikeinfocriterion20。95269SumsquaredresidLoglikelihood1.93E+09—312.2904SchwarzcriterionF—statistic21.0461138.51474Durbin—Watsonstat0。132458Prob(F—statistic〕0.000001lsycx6DependentVariable：YLeastSquaresDate:10/12/10 Time：17:51Sample：19782023Includedobservations:30Variable

Coefficient Std。Error

t—Statistic Prob.C X6 0.330354

934.3495—2。1692810.018222

0.03870.0000R-squaredAdjustedR—squared

0。921494 Meandependentvar0。918690 S.D。dependentvar

10049。0412585。51S。E。ofregression 3588。750 Akaikeinfocriterion 19.27334SumsquaredresidLoglikelihood

361E+08 Schwarzcriterion—287.100 F—statistic

19。36675328。65890Durbin—Watsonstat 0。189127 Prob(F—statistic) 0.000000lsycx7DependentVariable:YMethod:LeastSquaresDate：10/12/10 Time：18:36Sample：19782023Includedobservations：30Variable

Coefficient Std。Error

t—Statistic

Prob。C X7 0。111530

16135。44

0。3058250.320338

0。76200.7511R-squared0。003651Meandependentvar10049。04AdjustedR-squared-0031932S。D.dependentvar12585。51S。E.ofregression12784.87Akaikeinfocriterion21。81425Sumsquaredresid4.58E+09Schwarzcriterion21。90767—325。Loglikelihood2138F-statistic0。102616Durbin-Watsonstat0。065981Prob〔F-statistic〕0.7510912、以X3為根底，順次參與其他變量逐步回歸。X3、X2：DependentVariable：YMethod：LeastSquaresDate:10/13/10 Time:01：27Sample:19782023Includedobservations:30VariableCoefficientStd。Errort-StatisticProb.C1976.086388.24135.0898410。0000X2—1。1053390.105222—10.504860。0000X30。7219890.02887925.000560。0000R-squared0.993624Meandependentvar10049。04AdjustedR—squared0。993152S.D.dependentvar12585.51S。Eofregression1041。474Akaikeinfocriterion16.82930Sumsquaredresid29286057Schwarzcriterion16.96942Loglikelihood-249.4395F—statistic2103.946Durbin—Watsonstat1.662637Prob〔F—statistic)0.000000X3、X4:DependentVariable:YLeastSquaresDate：10/13/10 Time:01：27Sample：19782023Includedobservations：30Variable

Coefficient Std。Error

t-Statistic

Prob.C-2414297318。0985-0。7589780。4544X31.6522700.14413111.463670.0000X4—9.2557481。087001—8.5149410。0000R—squared0.991199Meandependentvar10049.04AdjustedR—squared0.990547S.D.dependentvar12585.51S。E.ofregression1223。617Akaikeinfocriterion17。15165SumsquaredresidLoglikelihood40425409—254.2747SchwarzcriterionF—statistic17.291771520。477Durbin—Watsonstat1.669559Prob〔F—statistic〕0.000000X3、X5：DependentVariable：YMethod:LeastSquaresDate：10/13/10 Time：01：28Sample：19782023Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C27090.895304.5145.1071380.0000X30.5147960。01957626.297030.0000X5—0.2619970。049197—5。3254530.0000R-squared0.984182Meandependentvar10049.04AdjustedR-squared0。983010S。Ddependentvar12585.51S。Eofregression1640.462Akaikeinfocriterion17。73798Sumsquaredres