多重共線性的檢驗(yàn)與修正

1、附件二：實(shí)驗(yàn)報(bào)告格式（首頁(yè)） 山東輕工業(yè)學(xué)院實(shí)驗(yàn)報(bào)告 成績(jī) 課程名稱 計(jì)量經(jīng)濟(jì)學(xué) 指導(dǎo)教師 實(shí)驗(yàn)日期 2013-5-25 院（系） 商學(xué)院 專業(yè)班級(jí) 實(shí)驗(yàn)地點(diǎn) 二機(jī)房 學(xué)生姓名 學(xué)號(hào) 同組人 無(wú) 實(shí)驗(yàn)項(xiàng)目名稱 多重共線性的檢驗(yàn)與修正 一、 實(shí)驗(yàn)?zāi)康暮鸵?掌握Eviews軟件的操作和多重共線性的檢驗(yàn)與修正二、 實(shí)驗(yàn)原理 Eviews軟件的操作和多重共線性的檢驗(yàn)修正方法三、 主要儀器設(shè)備、試劑或材料 Eviews軟件，計(jì)算機(jī)四、 實(shí)驗(yàn)方法與步驟 （1）準(zhǔn)備工作：建立工作文件，并輸入數(shù)據(jù)： CREATE EX-7-1 A 1974 1981; TATA Y X1 X2 X3 X4 X5 ; (2)

2、OLS估計(jì)： LS Y C X1 X2 X3 X4 X5; (3)計(jì)算簡(jiǎn)單相關(guān)系數(shù) COR X1 X2 X3 X4 X5 ; (4)多重共線性的解決 LS Y C X1; LS Y C X2;LS Y C X3;LS Y C X4;LS Y C X5;LS Y C X1 X3;LS Y C X1 X3 X2;LS Y C X1 X3 X4;LS Y C X1 X3 X5; 五、 實(shí)驗(yàn)數(shù)據(jù)記錄、處理及結(jié)果分析 （1）建立工作組，輸入以下數(shù)據(jù)： 98.45560.20 153.20 6.53 1.23 1.89 100.70 603.11 190.00 9.12 1.30 2.03 102.80

3、668.05 240.30 8.10 1.80 2.71 133.95 715.47 301.12 10.10 2.09 3.00 140.13 724.27 361.00 10.93 2.39 3.29 143.11 736.13 420.00 11.85 3.90 5.24 146.15 748.91 491.76 12.28 5.13 6.83 144.60 760.32 501.00 13.50 5.47 8.36 148.94 774.92 529.20 15.29 6.09 10.07 158.55 785.30 552.72 18.10 7.97 12.57 169.68 795

4、.50 771.16 19.61 10.18 15.12 162.14 804.80 811.80 17.22 11.79 18.25 170.09 814.94 988.43 18.60 11.54 20.59 178.69 828.73 1094.65 23.53 11.68 23.37 （2）OLS估計(jì) Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:10Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-Sta

5、tisticProb.C-3.30.00659-0.0.9101X.0669X.0877X.0658X.1965X5-4.2.-2.0.0771R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression5.Akaike info criterion6.Sum squared resid261.7185Schwarz criterion6.Log likelihood-40.36262F-s

6、tatistic52.53086Durbin-Watson stat1.Prob(F-statistic)0. 用Eviews進(jìn)行最小二乘估計(jì)得，=-3.497+0.125X1+0.074X2+2.678X3+3.453X4-4.491X5(-0.1) (2.1) (1.9) (2.1) (1.4) (-2.0)R=0.970, =0.952, DW=1.97, F=52.53其中括號(hào)內(nèi)的數(shù)字是t值。給定顯著水平=0.05，回歸系數(shù)估計(jì)值都沒(méi)有顯著性。查F分布表，得臨界值為F0.05（5,8）=3.69，故F=52.533.69，回歸方程顯著。(3)計(jì)算簡(jiǎn)單相關(guān)系數(shù) COR X1 X2 X3

7、X4 X5 ; X1X2X3X4X5X110.9170.64990.93940.8646X20.91710.00270.21920.193X30.64990.002710.39960.5427X40.93940.21920.399610.363X50.86460.1930.54270.3631 r12=0.867， r13=0.882， r14=0.852， r15=0.821，r23=0.946， r24=0.965,r25=0.983， r34=0.941，r35=0.948， r45=0.982可見(jiàn)解釋變量之間是高度相關(guān)的。(4)多重共線性的解決, 采用Frisch法。&1.對(duì)Y關(guān)于X1

8、，X2，X3，X4，X5作最小二乘回歸: 1) LS Y C X1Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:12Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-90.9207419.32929-4.0.0005X51610.0000R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dep

9、endent var26.09805S.E. of regression7.Akaike info criterion6.Sum squared resid665.4873Schwarz criterion7.Log likelihood-46.89537F-statistic147.6617Durbin-Watson stat1.Prob(F-statistic)0. 得回歸方程為：=-90.921+0.317X1（-4.7） （12.2)R=0.925, =0.919, DW=1.537, F=147.6192) LS Y C X2Dependent Variable: YMethod:

10、Least SquaresDate: 05/25/13 Time: 11:14Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C99.613496.15.489000.0000X.0000R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression11.28200Akaike info criterion7.Sum

11、 squared resid1527.403Schwarz criterion7.Log likelihood-52.71101F-statistic57.56437Durbin-Watson stat0.Prob(F-statistic)0. 得回歸方程為：=99.614+0.0815X2（15.5） （7.6）R=0.828, =0.813, DW=0.639，F(xiàn)=57.5643）LS Y C X3Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:14Sample: 1974 1987Included obs

12、ervations: 14VariableCoefficientStd. Errort-StatisticProb.C74.648000X.0000R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression10.06704Akaike info criterion7.Sum squared resid1216.144Schwarz criterion7.Log likelihood-51.11582F-statisti

13、c75.36868Durbin-Watson stat0.Prob(F-statistic)0.得回歸方程為：=74.648+4.893X3（9.0） （8.7）R=0.863, =0.851, DW=0.814，F(xiàn)=75.3694) LS Y C X4Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:15Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C108.86475.18.3449

14、00.0000X.0000R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression12.26828Akaike info criterion7.Sum squared resid1806.129Schwarz criterion8.Log likelihood-53.88433F-statistic46.82904Durbin-Watson stat0.Prob(F-statistic)0. 得回歸方程為：=108.865+5.740

15、X4（18.3） （6.8）R=0.796, =0.779, DW=0.769，F(xiàn)=46.8295) LS Y C X5Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:16Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C113.37476.18.655960.0000X.0001R-squared0.Mean dependent var142.7129Adjusted

16、R-squared0.S.D. dependent var26.09805S.E. of regression13.55865Akaike info criterion8.Sum squared resid2206.044Schwarz criterion8.Log likelihood-55.28443F-statistic36.16444Durbin-Watson stat0.Prob(F-statistic)0.得回歸方程為：=113.375+3.081X5（18.7） （6.0）R=0.75, =0.73, DW=0.59，F(xiàn)=36.16選第一個(gè)方程為基本回歸方程。&2. 加入肉銷(xiāo)售量

17、X3，對(duì)Y關(guān)于X1，X3作最小二乘回歸1) LS Y C X1 X3Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:17Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-39.7947925.01570-1.0.1400X.0007X.0231R-squared0.Mean dependent var142.7129Adjusted R-squared0

18、.S.D. dependent var26.09805S.E. of regression6.Akaike info criterion6.Sum squared resid407.7910Schwarz criterion6.Log likelihood-43.46702F-statistic113.9220Durbin-Watson stat1.Prob(F-statistic)0. 得回歸方程為：=-39.795+0.212X1+1.909X3（-1.6） （4.7）(2.6)R=0.954, =0.946, DW=1.656，F(xiàn)=113.922可以看出，加入X3后，擬合優(yōu)度R和均有所增

19、加，參數(shù)估計(jì)值的符號(hào)也正確，并且沒(méi)有影響X1系數(shù)的顯著性，所以在模型中保留X3.2)加入人均收入X2，對(duì)Y關(guān)于X1,X2,X3作最小二乘回歸 LS Y C X1 X3 X2Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:18Sample: 1974 1987Included observations: 14VariableCoefficientStd. Errort-StatisticProb.C-34.7768327.80679-1.0.2395X.0016X.2457X20.

20、292R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression6.Akaike info criterion6.Sum squared resid397.9210Schwarz criterion6.Log likelihood-43.29551F-statistic70.83889Durbin-Watson stat1.Prob(F-statistic)0. 得回歸方程為：=-34.777+0.207X1+0.009X2+1.456X

21、3(-1.3) (4.3) (0.5) (1.2)R=0.955, =0.942, DW=1.683, F=70.839可以看出，再加入X2后，擬合優(yōu)度R增加不顯著，有所減小，并且X2和X3系數(shù)均不顯著，說(shuō)明存在嚴(yán)重的共線性。比較X2和X3，肉銷(xiāo)售量比人均收入對(duì)糧食銷(xiāo)售量的影響大，所以在模型中保留X3，略去X2。3) 加入蛋銷(xiāo)售量X4，對(duì)Y關(guān)于X1,X3,X4作最小二乘估計(jì) LS Y C X1 X3 X4Dependent Variable: YMethod: Least SquaresDate: 05/25/13 Time: 11:19Sample: 1974 1987Included ob

22、servations: 14VariableCoefficientStd. Errort-StatisticProb.C-37.9988428.00654-1.0.2047X.0014X.1694X.8598R-squared0.Mean dependent var142.7129Adjusted R-squared0.S.D. dependent var26.09805S.E. of regression6.Akaike info criterion6.Sum squared resid406.4568Schwarz criterion6.Lo

23、g likelihood-43.44408F-statistic69.28123Durbin-Watson stat1.Prob(F-statistic)0.得回歸方程為：=-37.999+0.210X1+1.746X3+0.235X4 (-1.4) （4.4） （1.5） （0.2） R=0.954, =0.940, DW=1.674, F=69.281 可以看出，在加入X4后，擬合優(yōu)度R沒(méi)有增加， 有所減小，并且X3和X4系數(shù)均不顯著，說(shuō)明存在嚴(yán)重的多重共線性。比較X3和X4，肉銷(xiāo)售量比蛋銷(xiāo)售量對(duì)糧食銷(xiāo)售量的影響大，所以在模型中保留X3,略去X4。4) 加入魚(yú)蝦銷(xiāo)售量X5，對(duì)Y關(guān)于X1,X3,X5作最小二乘回歸 LS Y C X1 X3 X5Dependent Variable: YMethod: Least SquaresDate: 05/25/13