EViews計量經(jīng)濟學(xué)試驗報告

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試驗題目多重共線性的診斷與修正

一、試驗?zāi)康呐c要求：

要求目的：1、對多元線性回歸模型的多重共線性的診斷；

2、對多元線性回歸模型的多重共線性的修正。

二、試驗內(nèi)容

根據(jù)書上第四章引子“農(nóng)業(yè)的發(fā)展反而會減少財政收入〞，1978－2023年的財政收入，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)，運用EV軟件，做回歸分析，判斷是否存在多重共線性，以及修正。

三、試驗過程：（實踐過程、實踐所有參數(shù)與指標(biāo)、理論依據(jù)說明等）

（一）模型設(shè)定及其估計

經(jīng)分析，影響財政收入的主要因素，除了農(nóng)業(yè)增加值，工業(yè)增加值，建筑業(yè)增加值以外，還可能與總?cè)丝诘纫蛩赜嘘P(guān)。研究“農(nóng)業(yè)的發(fā)展反而會減少財政收入〞這個問題。

設(shè)定如下形式的計量經(jīng)濟模型：Yi=1+2X2+3X3+4X4+5X5+6X6+7X7+i

其中，Yi為財政收入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；

X5為總?cè)丝赥POP/萬人；X6為最終消費CUM/億元；X7為受災(zāi)面積SZM/千公頃。

圖1：1978～2023年財政收入及其影響因素數(shù)據(jù)

年份

197819791980198119821983198419851986198719881989199019911992199319941995

建筑業(yè)

農(nóng)業(yè)增工業(yè)增加總?cè)丝?/p>

財政收入增加值

加值值GZ/億TPOP/萬

CS/億元JZZ/億

NZ/億元元人

元

1132.31027.51607138.2962591146.41270.21769.7143.8975421159.91371.61996.5195.5987051175.81559.52048.4207.11000721212.31777.42162.3220.710165413671978.42375.6270.61030081642.92316.12789316.71043572023.82564.43448.7417.910585121222788.73967525.71075072199.432334585.8665.81093002357.23865.45777.28101110262664.94265.964847941127042937.150626858859.41143333149.485342.28087.11015.11158233483.375866.610284.514151171714348.956963.8141882266.51185175218.19572.719480.72964.71198506242.212135.824950.63728.8121121

受災(zāi)面

最終消費

積SZM/

CUM/億元

千公頃2239.12633.73007.93361.53714.84126.44846.35986.36821.87804.69839.511164.212090.514091.917203.321899.929242.236748.2

507903937044526397903313034710318904436547140420905087046991384745547251333488295504345821

1996199719981999200020232023202320232023202320237407.998651.149875.9511444.0813395.2316386.0418903.6421715.2526396.4731649.2938760.251321.7814015.414441.914817.61477014944.715781.31653717381.721412.722420240402809529447.64387.432921.44621.634018.44985.835861.55172.1400365522.343580.65931.747431.36465.554945.57490.8652108694.376912.910133.891310.911851.1107367.214014.112238912362612476112578612674312762712845312922712998813075613144813212943919.548140.651588.255636.96151666878.371691.277449.587032.996918.1110595.3128444.6469895342950145499815468852215471195450637106388184109148992

利用EV軟件，生成Yi、X2、X3、X4、X5、X6、X7等數(shù)據(jù)，采用這些數(shù)據(jù)對模型進行OLS回歸。

（二）診斷多重共線性

1、雙擊“Eviews〞，進入主頁。輸入數(shù)據(jù)：點擊主菜單中的File/Open/EVWorkfile—Excel—多重共線性的數(shù)據(jù).xls；2、在EV主頁界面的窗口，輸入“l(fā)sycx2x3x4x5x6x7〞，按“Enter〞.出現(xiàn)OLS回歸結(jié)果,圖2：圖2：OLS回歸結(jié)果

DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:07Sample:19782023Includedobservations:30

VariableCX2X3X4X5X6X7

R-squared

Coefficient

-6646.694-0.9706881.084654-2.7639280.077613-0.0471190.007580

Std.Error

6454.1560.3304090.2285212.0769940.0679740.0815090.035039

t-Statistic

-1.029832-2.9378414.746397-1.3307351.141808-0.5780840.216329

Prob.

0.31380.00740.00010.19630.26530.56880.8306

10049.0412585.5116.9363417.26329701.47470.000000

0.994565Meandependentvar0.993147S.D.dependentvar1041.849Akaikeinfocriterion24965329Schwarzcriterion-247.0452F-statistic2.167410Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

由此可見，該模型的可決系數(shù)為0.995，修正的可決系數(shù)為0.993，模型擬和很好，F(xiàn)統(tǒng)計量為701.47，模型擬和很好，

回歸方程整體上顯著。

但是當(dāng)=0.05時，t/2(nk)=t0.025(23)=2.069，不僅X4、X5、X6、X7的系數(shù)t檢驗不顯著，而且X2、X4、X6系數(shù)的符號與預(yù)期相反，這說明很可能存在嚴(yán)重的多重共線性。（即除了農(nóng)業(yè)增加值X2、工業(yè)增加值X3外，其他因素對財政收入的影響都不顯著，且農(nóng)業(yè)增加值X2、建筑業(yè)增加值X4、最終消費X6的回歸系數(shù)還是負(fù)數(shù)，這說明很可能存在嚴(yán)重的多重共線性。）

3、計算各解釋變量的相關(guān)系數(shù)：

在Workfile窗口，選擇X2、X3、X4、X5、X6、X7數(shù)據(jù)，點擊“Quick〞—GroupStatistics—Correlations—OK,出現(xiàn)相關(guān)系數(shù)矩陣，如圖3：

圖3：相關(guān)系數(shù)矩陣

X2X3X4X5X6X7

X210.9729806145

614799789067452466772465

193188687581178436215

0.98266062340.9985218083

1280514159604353

0.92797842940.84390020650.8641521359

0.98896261970.99264123670.99605684340.8888480555

151582

0.22619996580.1294437103038776726480.1851728808

1

X36147

X49978993188

X5067456875828051

X624667117844159646979

X7724653621504353087870.1851728808

51582

0.97298061450.98266062340.92797842940.98896261970.2261999658

0.99852180830.84390020650.99264123670.1294437103

0.86415213590.99605684340.1546457184

0.88884805550.3877672648

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、最終消費之間X6，相關(guān)系數(shù)都在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

1、采用逐步回歸法，去檢驗和解決多重共線性問題。分別作Y對X2、X3、X4、X5、X6、X7的一元回歸，結(jié)果如下圖4：在EV主頁界面的窗口，輸入“l(fā)sycx2〞，“回車鍵〞。

DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:49Sample:19782023Includedobservations:30

VariableCX2

Coefficient

-4086.5441.454186

Std.Error

1463.0910.117235

t-Statistic

-2.79309012.40398

Prob.

0.00930.0000

R-squared

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

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

10049.0412585.5119.9468920.04030153.85880.000000

依次如上推出X3、X4、X5、X6、X7的一元回歸。綜上所述，結(jié)果如下圖4：

圖4.一元回歸估計結(jié)果

2、其中，參與X3的R最大，以X3為基礎(chǔ)，順次參與其他變量逐步回歸。結(jié)果如下圖5：

DependentVariable:YMethod:LeastSquaresDate:10/13/10Time:01:27Sample:19782023Includedobservations:30

VariableCX2X3

R-squared

Coefficient

1976.086-1.1053390.721989

Std.Error

388.24130.1052220.028879

t-Statistic

5.089841-10.5048625.00056

Prob.

0.00000.00000.0000

10049.0412585.5116.8293016.969422103.9460.000000

2

0.993624Meandependentvar0.993152S.D.dependentvar1041.474Akaikeinfocriterion29286057Schwarzcriterion-249.4395F-statistic1.662637Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

依照上面，在順次參與X4、X5、X6、X7，進行逐步回歸。綜合結(jié)果如下圖5：

圖5.參與新變量的回歸結(jié)果（一）

經(jīng)比較，新參與X2的方程R=0.993152，改進最大，但是X2得系數(shù)為負(fù)，這顯然不符題意。在X3的基礎(chǔ)上分別參與其他變量后發(fā)現(xiàn)，X2，X4，X5，X6，X7的系數(shù)都為負(fù)，與預(yù)期估計違背。因此這些變量都會引起嚴(yán)重的多重共線性，全部剔除，只保存X3。修正的回歸結(jié)果為：

DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:50Sample:19782023Includedobservations:30

VariableCX3

R-squared

Coefficient

-1075.2890.426817

Std.Error

570.53370.014768

t-Statistic

-1.88470828.90168

Prob.

0.06990.0000

10049.0412585.5118.3893518.48276835.30740.000000

2

0.967567Meandependentvar0.966408S.D.dependentvar2306.678Akaikeinfocriterion1.49E+08Schwarzcriterion-273.8402F-statistic0.292531Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

=-1075.289+0.426817X3Yi

（-1.884708）（28.90168）

2

R2=0.967567R=0.966408F=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1億元，財政收入平均增加0.426817億元。

四、實踐結(jié)果報告：

為研究“農(nóng)業(yè)的發(fā)展反而會減少財政收入〞的問題，根據(jù)1978－2023年的財政收入，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)，運用EV軟件，做回歸分析，判斷是否存在多重共線性，以及修正。最終修正的回歸結(jié)果為：

=-1075.289+0.426817X3Yi

（-1.884708）（28.90168）

2

R2=0.967567R=0.966408F=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1億元，財政收入平均增加0.426817億元。

可決系數(shù)為0.967567，較高，說明模型擬合優(yōu)度高；F值為835.3074，說明整個方程顯著；斜率系數(shù)的t值28.90168，大于t統(tǒng)計量，t檢驗顯著，符合題意。

逐步回歸后的結(jié)果雖然實現(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，可能會帶來設(shè)定偏誤，這是在使用逐步回歸時需要注意的問題。

附加：

1、分別作Y對X2、X3、X4、X5、X6、X7的一元回歸，結(jié)果如下：

lsycx2

DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:49Sample:19782023Includedobservations:30

VariableCX2

R-squared

Coefficient

-4086.5441.454186

Std.Error

1463.0910.117235

t-Statistic

-2.79309012.40398

Prob.

0.00930.0000

10049.0412585.5119.9468920.04030153.85880.000000

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

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

lsycx3

DependentVariable:YMethod:LeastSquaresDate:10/12/10Time:17:50Sample:19782023Includedobservations:30

VariableCX3

R-squared

Coefficient

-1075.2890.426817

Std.Error

570.53370.014768

t-Statistic

-1.88470828.90168

Prob.

0.06990.0000

10049.0412585.5118.3893518.48276835.30740.000000

0.967567Meandependentvar0.966408S.D.dependentvar2306.678Akaikeinfocriterion1.49E+08Schwarzcriterion-273.8402F-statistic0.292531Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

lsycx4

DependentVariable:YMethod:LeastSquares

Std.Error

727.98960.140530

t-Statistic

-1.69669522.67733

Coefficient

-1235.1773.186851

Prob.

0.10080.0000

10049.0412585.5118.8543718.94778514.26140.000000

Date:10/12/10Time:17:50Sample:19782023Includedobservations:30

VariableCX4

R-squared

0.948364Meandependentvar0.946520S.D.dependentvar2910.486Akaikeinfocriterion2.37E+08Schwarzcriterion-280.8155F-statistic0.215531Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

lsycx5

DependentVariable:YMethod:LeastSquares

Date:10/12/10Time:17:51Sample:19782023Includedobservations:30

VariableCX5

R-squared

Coefficient

-86420.420.829789

Std.Error

15618.350.133707

t-Statistic

-5.5332606.206025

Prob.

0.00000.0000

10049.0412585.5120.9526921.0461138.514740.000001

0.579041Meandependentvar0.564006S.D.dependentvar8310.188Akaikeinfocriterion1.93E+09Schwarzcriterion-312.2904F-statistic0.132458Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

lsycx6

DependentVariable:YMethod:LeastSquares

Std.Error

934.34950.018222

t-Statistic

-2.16928118.12895

Coefficient

-2026.8670.330354

Prob.

0.03870.0000

10049.0412585.5119.2733419.36675328.65890.000000

Date:10/12/10Time:17:51Sample:19782023Includedobservations:30

VariableCX6

R-squared

0.921494Meandependentvar0.918690S.D.dependentvar3588.750Akaikeinfocriterion3.61E+08Schwarzcriterion-287.1000F-statistic0.189127Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

lsycx7

DependentVariable:YMethod:LeastSquares

Std.Error

16135.440.348162

t-Statistic

0.3058250.320338

Coefficient

4934.6160.111530

Prob.

0.76200.7511

10049.04

Date:10/12/10Time:18:36Sample:19782023Includedobservations:30

VariableCX7

R-squared

0.003651Meandependentvar

S.E.ofregressionSumsquaredresidLoglikelihoodDurbin-Watsonstat

12784.87Akaikeinfocriterion4.58E+09Schwarzcriterion-325.2138F-statistic0.065981Prob(F-statistic)

21.8142521.907670.1026160.751091

2、以X3為基礎(chǔ)，順次參與其他變量逐步回歸。X3、X2:

DependentVariable:YMethod:LeastSquaresDate:10/13/10Time:01:27Sample:19782023Includedobservations:30

VariableCX2X3

R-squared

Coefficient

1976.086-1.1053390.721989

Std.Error

388.24130.1052220.028879

t-Statistic

5.089841-10.5048625.00056

Prob.

0.00000.00000.0000

10049.0412585.5116.8293016.969422103.9460.000000

0.993624Meandependentvar0.993152S.D.dependentvar1041.474Akaikeinfocriterion29286057Schwarzcriterion-249.4395F-statistic1.662637Prob(F-statistic)

AdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatX3、X4:

DependentVariable:YMethod:LeastSquares

Std.Error

318.09850.1441311.087001

t-Statistic

-0.75897811.46367-8.514941

Coefficient

-241.42971.652270-9.255748

Prob.

0.45440.00000.0000

10049.0412585.5117.15165

Date:10/13/10Time:01:27Sample:19782023Includedobservations:30

VariableCX3X4

R-squared

0.991199Meandependentvar0.990547S.D.dependentvar1223.617Akaikeinfocriterion

AdjustedR-squaredS.E.ofregression

LoglikelihoodDurbin-WatsonstatX3、X5:

DependentVariable:YMethod:LeastSquares

-254.2747F-statistic1.669559Prob(F-statistic)

1520.4770.000000

Std.Error

5304.5140.0195760.049197

t-Statistic

5.10713826.29703-5.325453

Coefficient

27090.890.514796-0.261997

Prob.

0.00000.00000.0000

10049.0412585.5117.7379817.87810839.94790.000000

Date:10/13/10Time:01:28Sample:19782023Includedobservations:30

VariableCX3X5

R-squared

0.984182Meandependentvar0.983010S.D.dependentvar1640.462Akaikeinfocriterion72660152Schwarzcriterion-263.0698F-statistic0.451996Prob(F-statistic)

Adj