計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)課單元多重共線性練習(xí)

1、7716895611.583956811.3534634.4162663 # 實(shí)驗(yàn)課單元（六）多重共線性練習(xí)實(shí)驗(yàn)?zāi)康摹空莆斩嘀毓簿€性及相關(guān)內(nèi)容的軟件操作實(shí)驗(yàn)內(nèi)容】用OLS方法估計(jì)模型的參數(shù)，檢驗(yàn)多重共線性，修正多重共線性【實(shí)驗(yàn)步驟】計(jì)算機(jī)操作：（1）運(yùn)用OLS法對(duì)方程估計(jì)參數(shù)。從EViews主窗口，點(diǎn)擊Quick點(diǎn)擊EstimateEquation功能。（2）做F檢驗(yàn)，由方程得到F統(tǒng)計(jì)量，在給定顯著性水平0.05下，查Foe（k,n-k-1）,這里k為變量出個(gè)數(shù)，n為樣本點(diǎn)數(shù)。如果F005（k，n-k-1）F統(tǒng)計(jì)量。則表明從整體上看,被解釋變量和解釋變量之間線性關(guān)系顯著。（3）檢驗(yàn)。先計(jì)算被解

2、釋變量和解釋變量之間的相關(guān)系數(shù)，EViews操作如下：在主窗口點(diǎn)擊QuickGroupStatisticsCorrelationSeriesLine（輸入被解釋變量和解釋變量）一OK，判斷解釋變量之間的相關(guān)程度。（4）多重共線性的修正（逐步回歸法）。運(yùn)用OLS方法逐一求Y（被解釋變量）對(duì)各個(gè)解釋變量的回歸，結(jié)合經(jīng)濟(jì)意義和統(tǒng)計(jì)檢驗(yàn)選出擬合效果最好的雙變量回歸方程為基礎(chǔ)，在此基礎(chǔ)上，再添加其他解釋變量，直到選出最佳的回歸模型?！纠课覈?guó)（19781997年）鋼材供應(yīng)量資料年份鋼材供應(yīng)量（萬(wàn)噸）生鐵產(chǎn)量（萬(wàn)噸）原煤產(chǎn)量（萬(wàn)噸）電力產(chǎn)量（億千瓦小時(shí)）固定資產(chǎn)投資（億元）國(guó)內(nèi)生產(chǎn)總值（億元）鐵路運(yùn)輸量（

3、萬(wàn)噸）1978y2208x1x2x3x4x5x619792497198027161981267019822920198330721984337219853693198640581987438619884689198948591990515319915638199266973479367338023417355137384001438450645503594361596635676580946.186.356.26.226.667.157.898.728.949.289.810.5410.810.8711.162566282030063093327735143770410744954773545

4、25848621267757539668.72699.36746.9638.2805.9885.261052.431523.511795.322101.692554.862340.5225343139.034473.763624.14038.24517.84862.45294.75934.571718964.410202.211962.514928.316909.218547.921617.826638.111011911189311127910767311353211878412407413070813563614065314494815148915068115289315762777168

5、95611.583956811.3534634.4162663 199319941995199619978428926112.492819355.3546759.41630938979.89535.9913.6110070.310702.9758478.11658559338.029978.9310124.0610894.1713.9713.7310813.111355.5312185.7913838.9667884.674772.4168803169734一、建立模型的多元線性回建立被解釋變量關(guān)于個(gè)解釋變量歸模型：Y=B+BX+BX+BX+BX+BX+BX+Di0112233445566i樣

6、本回歸模型如下：Y=人D+B1X1+B2X2+B3X3+B4X4+B5X5+B6+二、最小二乘估計(jì)利用表中的數(shù)據(jù)，做最小二乘估計(jì)，如下表DependentVariable:YMethod:LeastSquaresDate:05/29/07Time:14:28Sample:19781997Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C463.1035850.74750.5443490.5954X10.0682880.1387330.4922280.6308X299.71201147.82200.674541

7、0.5118X30.8922810.1427356.2512990.0000X40.4459750.0748695.9567230.0000X5-0.0936030.0189304.9447630.0003X6-0.0112930.0176020.6415810.5323R-squared0.998997Meandependentvar5153.438AdjustedR-squared0.998533S.D.dependentvar2512.110S.E.ofregression96.20118Akaikeinfocriterion12.23998Sumsquaredresid120310.7

8、Schwarzcriterion12.58848Loglikelihood-115.3998F-statistic2157.162Durbin-Watsonstat2.197329Prob(F-statistic)0.000000Y=463.1035+0.068288Xi+99.71201X2+0.892281X3+0.445975X4-0.093603X5(0.544349)(0.492228)(0.674541)(6.251299)(5.956723)(-4.944763)-0.011293X66(-0.641581)R2=0.988997R2=0.998533DW=2.197F=2157

9、.162在給定顯著性水平=0.05，查F分布表，得臨界值F=2.91v2157.162,故0.05(7,12)該模型存在多重共線性。三、分別計(jì)算Y、X1、X2、X3、X4、X5、X6的兩兩相關(guān)系數(shù)，如下表從上表可以看出，變量之間是高度相關(guān)的。四、用逐步回歸法修正多重共線性1、對(duì)Y分別關(guān)于X、X2、X3、X4、x5、x6作最小二乘回歸得：Y=-955.1385+0.9934X(-5.6)(36.94)R2=0.9870R2=0.9863DW=0.5404F=1364.78丫=-3614.403+913.45X2(-6.35)(15.97)R2=0.9340R2=0.9304DW=0.4143F=

10、254.88 (3)Y=-18.200+0.8828x3(-0.19)(60.43)R2=0.9948DW=0.8937F=3652.205R2=0.99514)y=2896.27+0.5725X4(13.72)(15.48)R2=0.9301R2=0.9263DW=0.1818F=239.68(5)Y=2720.57+0.1087X5(13.25)(16.55)R2=0.9383R2=0.9349DW=0.2600F=273.86(6)Y=-9762.81+0.1068X6(-7.41)(11.46)R2=0.8794R2=0.8727DW=0.1834F=131.24根據(jù)經(jīng)濟(jì)理論分析和回歸

11、結(jié)果，比較各個(gè)回歸結(jié)果的R2的值，其中方程(3)中R2的值最大，易知我國(guó)電力產(chǎn)量X3是最重要的解釋變量，所以選取第三個(gè)回歸方程為基本回歸方程。2、加入解釋變量X3,對(duì)y、X3分別關(guān)于、X2、X4、X5、X6作最小二乘回歸得：Y=-212.24+0.7121X3+0.1942X(-1.27)(5.77)(1.39)R2=0.995R2=0.9951DW=0.6672F=1922.33丫=399.17+0.9723X3+-98.09X2(1.33)(15.51)(-1.46)R2=0.9956R2=0.9951DW=0.9165F=1943.43Y=210.84+0.8090X3+0.0516X4

12、(1.20)(16.07)(1.53)R2=0.9957R2=0.9952DW=0.9322F=1962.52Y=43.72+0.8617X3+0.0028X5(0.21)(14.08)(0.36)R2=0.9951R2=0.9946DW=0.9128F=1737.58Y=385.60+0.9135X3+-0.0042X6(0.68)(20.35)(-0.72)R2=0.9952R2=0.9947DW=0.9469F=1777.92比較以上各組數(shù)據(jù)的R2和R2可知，加入固定資產(chǎn)投資X4的那組方程的R2和R2最大。加入X4后，擬合優(yōu)度R2和R2均有所增加，參數(shù)估計(jì)值的符號(hào)也正確，并且沒(méi)有影響X3

13、系數(shù)的顯著性，因此在模型中保留X4。3、加入解釋變量X3、X4后，對(duì)Y、X3、X4分別關(guān)于X、X2、X5、X6作最小二乘回歸得：Y=21.20+0.5139X+0.0756X+0.2964XTOC o 1-5 h z341(0.12)(3.72)(2.35)(2.26)R2=0.9967R2=0.9961DW=0.6482F=1625.56y=354.14+0.8841X+0.0330X53.094X HYPERLINK l bookmark22342(1.14)(6.20)(0.69)(-0.56)R2=0.9958R2=0.9950DW=0.9230F=1255.97Y=-35.90+0.

14、9256X+0.4369X0.0873X HYPERLINK l bookmark24345(-0.38)(30.55)(7.68)(-7.10)R2=0.9990R2=0.9988DW=2.2526F=5129.52Y=-583.81+0.6488X3+0.1081X4+0.0102X6(-0.74)(3.98)(1.68)(1.03)R2=0.9960R2=0.9952DW=0.8707F=1313.95比較以上各組數(shù)據(jù)的R2和R2可知,加入生鐵產(chǎn)量X的那組方程的R2和R2最大。加入生鐵產(chǎn)量X1后，擬合優(yōu)度R2和R2均有所增加，參數(shù)估計(jì)值的符號(hào)也正確，并且沒(méi)有影響X3、X4系數(shù)的顯著性，因

15、此在模型中保留X。4、加入解釋變量X3、X4、X后，對(duì)Y、X3、X4、X分別關(guān)于X2、X5、X6作最小二乘回歸得：y=65.3682+0.5403X+0.0699X+0.2916X-15.1855XTOC o 1-5 h z342(0.21)(2.59)(1.50)(2.11)(-0.17)R2=0.9967R2=0.9959DW=0.6520F=1145.29Y=-36.9837+0.9224X+0.4359X+0.0029X-0.0871X HYPERLINK l bookmark303415(-.35)(8.54)(6.59)(0.03)(-0.15)R2=0.9990R2=0.9987

16、DW=2.2303F=3606.93y=-252.51+0.4751X+0.0944X+0.2777X+0.0039X HYPERLINK l bookmark323416(-0.34)(2.71)(1.58)(1.93)(0.38)R2=0.9968R2=0.9959DW=0.6438F=1153.84比較以上各組數(shù)據(jù)的R2和R2可知，加入鐵路運(yùn)輸量X6的那組方程的R2和R2最大。加入X6后，擬合優(yōu)度R2和R2均有所增加，參數(shù)估計(jì)值的符號(hào)也正確，并且沒(méi)有影響X3、X4、X1系數(shù)的顯著性，因此在模型中保留X6。4、加入解釋變量X3、X4、X1、X6后，對(duì)Y、X3、X4、X1、X6分別關(guān)于X2、

17、X5、作最小二乘回歸得：(1)Y=-1529.63+06533X3+0.1341X4+0.0466X1+0.0332X6270.8884X2(-1.25)(2.97)(2.03)(0.21)(1.34) # #(-1.30)R2=0.9971R2=0.9961DW=0.8790F=965.85(2)y=-23.9746+0.9245X+0.4353X+0.0036X0.00019X34160.0871X5(-0.05)(7.01)(-5.45)(6.07)(0.04)(-0.03)R2=0.9990R2=0.9986DW=2.2404F=2696.35 #由以上數(shù)據(jù)的比較可知，在加入了變量原煤產(chǎn)量X2、國(guó)內(nèi)生產(chǎn)總值X5以后，擬合優(yōu)度R2和R2均有所增加，但是系數(shù)的符號(hào)與經(jīng)濟(jì)理論相悖。按經(jīng)濟(jì)理論，原煤產(chǎn)量應(yīng)與鋼鐵供應(yīng)量同方向變動(dòng)，且國(guó)內(nèi)生產(chǎn)總值也應(yīng)與鋼鐵供應(yīng)量同方向變動(dòng)，符號(hào)都應(yīng)為正，但上述結(jié)果與人們預(yù)期的不一致。所以，應(yīng)舍去變量X2、X5。綜上所述，得到Y(jié)關(guān)于X3