1、實驗題目 多重共線性的診斷與修正 一、實驗目的與要求：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、實驗內(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”，19782007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、實驗過程：（實踐過程、實踐所有參數(shù)與指標、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

2、經(jīng)濟模型：=+其中，為財政收入CS/億元；為農(nóng)業(yè)增加值NZ/億元；為工業(yè)增加值GZ/億元；為建筑業(yè)增加值JZZ/億元；為總?cè)丝赥POP/萬人；為最終消費CUM/億元；為受災面積SZM/千公頃。圖1： 19782007年財政收入及其影響因素數(shù)據(jù)年份財政收入CS/億元農(nóng)業(yè)增加值NZ/億元工業(yè)增加值GZ/億元建筑業(yè)增加值JZZ/億元總?cè)丝赥POP/萬人最終消費CUM/億元受災面積SZM/千公頃19781132.31027.51607138.2962592239.15079019791146.41270.21769.7143.8975422633.73937019801159.91371.61996.

3、5195.5987053007.94452619811175.81559.52048.4207.11000723361.53979019821212.31777.42162.3220.71016543714.833130198313671978.42375.6270.61030084126.43471019841642.92316.12789316.71043574846.33189019852004.82564.43448.7417.91058515986.344365198621222788.73967525.71075076821.84714019872199.432334585.866

4、5.81093007804.64209019882357.23865.45777.28101110269839.55087019892664.94265.9648479411270411164.24699119902937.150626858859.411433312090.53847419913149.485342.28087.11015.111582314091.95547219923483.375866.610284.5141511717117203.35133319934348.956963.8141882266.511851721899.94882919945218.19572.71

5、9480.72964.711985029242.25504319956242.212135.824950.63728.812112136748.24582119967407.9914015.429447.64387.412238943919.54698919978651.1414441.932921.44621.612362648140.65342919989875.9514817.634018.44985.812476151588.250145199911444.081477035861.55172.112578655636.949981200013395.2314944.740036552

6、2.31267436151654688200116386.0415781.343580.65931.712762766878.352215200218903.641653747431.36465.512845371691.247119200321715.2517381.754945.57490.812922777449.554506200426396.4721412.7652108694.312998887032.937106200531649.292242076912.910133.813075696918.138818200638760.22404091310.911851.1131448

7、110595.341091200751321.7828095107367.214014.1132129128444.648992利用EV軟件，生成、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 /EV WorkfileExcel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)s y c x2 x3 x4 x5 x6 x7”，按“Enter”.出現(xiàn)OLS回歸結(jié)果,圖2： 圖2： OLS 回歸結(jié)果Dependent Variable: YMethod: Least SquaresDate:

8、 10/12/10 Time: 17:07Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-6646.6946454.156-1.0298320.3138X2-0.9706880.330409-2.9378410.0074X31.0846540.2285214.7463970.0001X4-2.7639282.076994-1.3307350.1963X50.0776130.0679741.1418080.2653X6-0.0471190.08

9、1509-0.5780840.5688X70.0075800.0350390.2163290.8306R-squared0.994565    Mean dependent var10049.04Adjusted R-squared0.993147    S.D. dependent var12585.51S.E. of regression1041.849    Akaike info criterion16.93634Sum squared resid24965329&#

10、160;   Schwarz criterion17.26329Log likelihood-247.0452    F-statistic701.4747Durbin-Watson stat2.167410    Prob(F-statistic)0.000000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=0.05時，=2.069，不僅X4、X5、X6、X7的系數(shù)t檢驗不顯著，而且

11、X2、X4、X6系數(shù)的符號與預期相反，這表明很可能存在嚴重的多重共線性。（即除了農(nóng)業(yè)增加值、工業(yè)增加值外，其他因素對財政收入的影響都不顯著，且農(nóng)業(yè)增加值、建筑業(yè)增加值、最終消費的回歸系數(shù)還是負數(shù)，這說明很可能存在嚴重的多重共線性。）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”Group StatisticsCorrelationsOK,出現(xiàn)相關(guān)系數(shù)矩陣，如圖3：圖3： 相關(guān)系數(shù)矩陣X2X3X4X5X6X7X210.972980614561470.9826606234997890.9279784294067450.98896

12、26197246670.226199965872465X30.9729806145614710.9985218083931880.8439002065687580.9926412367117840.129443710336215X40.9826606234997890.99852180839318810.8641521359280510.9960568434415960.154645718404353X50.9279784294067450.8439002065687580.86415213592805110.8888480555469790.387767264808787X60.988962

13、6197246670.9926412367117840.9960568434415960.88884805554697910.185172880851582X70.2261999658724650.1294437103362150.1546457184043530.3877672648087870.1851728808515821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、工業(yè)增加值、建筑業(yè)增加值、最終消費之間，相關(guān)系數(shù)都在0.8以上。這表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

14、、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)s y c x2”，“回車鍵”。Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:49Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-4086.5441463.091-2.7930900.0093X21.4541860.11723512.403980.0000R-squared0.846034&

15、#160;   Mean dependent var10049.04Adjusted R-squared0.840536    S.D. dependent var12585.51S.E. of regression5025.770    Akaike info criterion19.94689Sum squared resid7.07E+08    Schwarz criterion20.04030Log likelihood-297.203

16、3    F-statistic153.8588Durbin-Watson stat0.166951    Prob(F-statistic)0.000000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)果變量參數(shù)估計值1.4541860.4268173.1868510.8297890.3303540.111530t統(tǒng)計量12.4039828.9016822.677336.20602518.128950.3203380.8460340.9675670.9483640

17、.5790410.9214940.0036510.8405360.9664080.9465200.5640060.918690-0.0319322、其中，加入的最大，以為基礎(chǔ)，順次加入其他變量逐步回歸。結(jié)果如下圖5：Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C1976.086388.24135.089841

18、0.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R-squared0.993624    Mean dependent var10049.04Adjusted R-squared0.993152    S.D. dependent var12585.51S.E. of regression1041.474    Akaike info criterion16.82930Sum sq

19、uared resid29286057    Schwarz criterion16.96942Log likelihood-249.4395    F-statistic2103.946Durbin-Watson stat1.662637    Prob(F-statistic)0.000000依照上面，在順次加入X4、X5、X6、X7，進行逐步回歸。綜合結(jié)果如下圖5：圖5.加入新變量的回歸結(jié)果（一）變量X2X3X4X5X6X7X3,X2-1.1053390.7219890

20、.993152（-10.50486）（25.00056）X3,X41.65227-9.2557480.990547（11.46367）（-8.514941）X3,X50.514796-0.2619970.98301（26.29703）（-5.325453）X3,X60.910503-0.3864590.985025（11.18199）（-5.984236）X3,X70.430639-0.1255790.970053（30.62427）（-2.099504）經(jīng)比較，新加入的方程= 0.993152 ，改進最大， 但是得系數(shù)為負，這顯然不符題意。在的基礎(chǔ)上分別加入其他變量后發(fā)現(xiàn)，的系數(shù)都為負，與預

21、期估計違背。因此這些變量都會引起嚴重的多重共線性，全部剔除，只保留。修正的回歸結(jié)果為：Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567 &#

22、160;  Mean dependent var10049.04Adjusted R-squared0.966408    S.D. dependent var12585.51S.E. of regression2306.678    Akaike info criterion18.38935Sum squared resid1.49E+08    Schwarz criterion18.48276Log likelihood-273.8402 

23、   F-statistic835.3074Durbin-Watson stat0.292531    Prob(F-statistic)0.000000= -1075.289 + 0.426817（-1.884708） （28.90168）= 0.967567 =0.966408 F=835.3074這說明在其他因素不變的情況下，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)19782007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

24、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。最后修正的回歸結(jié)果為：= -1075.289 + 0.426817（-1.884708） （28.90168）= 0.967567 =0.966408 F=835.3074這說明在其他因素不變的情況下，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

25、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：ls y c x2Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:49Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-4086.5441463.091-2.7930900.0093X21.4541860.1172

26、3512.403980.0000R-squared0.846034    Mean dependent var10049.04Adjusted R-squared0.840536    S.D. dependent var12585.51S.E. of regression5025.770    Akaike info criterion19.94689Sum squared resid7.07E+08    Schwarz crite

27、rion20.04030Log likelihood-297.2033    F-statistic153.8588Durbin-Watson stat0.166951    Prob(F-statistic)0.000000ls y c x3Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Erro

28、rt-StatisticProb.  C-1075.289570.5337-1.8847080.0699X30.4268170.01476828.901680.0000R-squared0.967567    Mean dependent var10049.04Adjusted R-squared0.966408    S.D. dependent var12585.51S.E. of regression2306.678    Akaike info c

29、riterion18.38935Sum squared resid1.49E+08    Schwarz criterion18.48276Log likelihood-273.8402    F-statistic835.3074Durbin-Watson stat0.292531    Prob(F-statistic)0.000000ls y c x4Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Tim

30、e: 17:50Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-1235.177727.9896-1.6966950.1008X43.1868510.14053022.677330.0000R-squared0.948364    Mean dependent var10049.04Adjusted R-squared0.946520    S.D. depend

31、ent var12585.51S.E. of regression2910.486    Akaike info criterion18.85437Sum squared resid2.37E+08    Schwarz criterion18.94778Log likelihood-280.8155    F-statistic514.2614Durbin-Watson stat0.215531    Prob(F-statistic

32、)0.000000ls y c x5 Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-86420.4215618.35-5.5332600.0000X50.8297890.1337076.2060250.0000R-squared0.579041    Mean dep

33、endent var10049.04Adjusted R-squared0.564006    S.D. dependent var12585.51S.E. of regression8310.188    Akaike info criterion20.95269Sum squared resid1.93E+09    Schwarz criterion21.04611Log likelihood-312.2904    F-stat

34、istic38.51474Durbin-Watson stat0.132458    Prob(F-statistic)0.000001ls y c x6Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 17:51Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-2026.867934.3495-2.1692810.0387X60

35、.3303540.01822218.128950.0000R-squared0.921494    Mean dependent var10049.04Adjusted R-squared0.918690    S.D. dependent var12585.51S.E. of regression3588.750    Akaike info criterion19.27334Sum squared resid3.61E+08    

36、Schwarz criterion19.36675Log likelihood-287.1000    F-statistic328.6589Durbin-Watson stat0.189127    Prob(F-statistic)0.000000ls y c x7Dependent Variable: YMethod: Least SquaresDate: 10/12/10 Time: 18:36Sample: 1978 2007Included observations: 30VariableCoeffic

37、ientStd. Errort-StatisticProb.  C4934.61616135.440.3058250.7620X70.1115300.3481620.3203380.7511R-squared0.003651    Mean dependent var10049.04Adjusted R-squared-0.031932    S.D. dependent var12585.51S.E. of regression12784.87    A

38、kaike info criterion21.81425Sum squared resid4.58E+09    Schwarz criterion21.90767Log likelihood-325.2138    F-statistic0.102616Durbin-Watson stat0.065981    Prob(F-statistic)0.7510912、 以為基礎(chǔ)，順次加入其他變量逐步回歸。X3、X2:Dependent Variable: YMethod: L

39、east SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C1976.086388.24135.0898410.0000X2-1.1053390.105222-10.504860.0000X30.7219890.02887925.000560.0000R-squared0.993624    Mean dependent var10049.0

40、4Adjusted R-squared0.993152    S.D. dependent var12585.51S.E. of regression1041.474    Akaike info criterion16.82930Sum squared resid29286057    Schwarz criterion16.96942Log likelihood-249.4395    F-statistic2103.946Durb

41、in-Watson stat1.662637    Prob(F-statistic)0.000000X3、X4:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:27Sample: 1978 2007Included observations: 30VariableCoefficientStd. Errort-StatisticProb.  C-241.4297318.0985-0.7589780.4544X31.6522700.14413111.46

42、3670.0000X4-9.2557481.087001-8.5149410.0000R-squared0.991199    Mean dependent var10049.04Adjusted R-squared0.990547    S.D. dependent var12585.51S.E. of regression1223.617    Akaike info criterion17.15165Sum squared resid40425409 

43、0;  Schwarz criterion17.29177Log likelihood-254.2747    F-statistic1520.477Durbin-Watson stat1.669559    Prob(F-statistic)0.000000X3、X5:Dependent Variable: YMethod: Least SquaresDate: 10/13/10 Time: 01:28Sample: 1978 2007Included observations: 30Vari

44、ableCoefficientStd. Errort-StatisticProb.  C27090.895304.5145.1071380.0000X30.5147960.01957626.297030.0000X5-0.2619970.049197-5.3254530.0000R-squared0.984182    Mean dependent var10049.04Adjusted R-squared0.983010    S.D. dependent var12585.51S.E. of regression1640.462    Akaike info criterion17.73798Sum squared resid72660152    Schwarz criterion17.87810Log likelihood-263.0698    F-statistic839.9479Durbin