計量經(jīng)濟學多元線性回歸多重共線性異方差實驗報告材料

實用標準文案實用標準文案精彩文檔精彩文檔實用標準文案精彩文檔計量經(jīng)濟學實驗報告多元線性回歸、多重共線性、異方差實驗報告一、研究目的和要求：隨著經(jīng)濟的發(fā)展，人們生活水平的提高，旅游業(yè)已經(jīng)成為中國社會新的經(jīng)濟增長點。旅游產(chǎn)業(yè)是一個關聯(lián)性很強的綜合產(chǎn)業(yè)，一次完整的旅游活動包括吃、住、行、游、購、娛六大要素，旅游產(chǎn)業(yè)的發(fā)展可以直接或者間接推動第三產(chǎn)業(yè)、第二產(chǎn)業(yè)和第一產(chǎn)業(yè)的發(fā)展。尤其是假日旅游，有力刺激了居民消費而拉動內(nèi)需。2012年，我國全年國內(nèi)旅游人數(shù)達到30.0億人次，同比增長13.6%，國內(nèi)旅游收入2.3萬億元，同比增長19.1%。旅游業(yè)的發(fā)展不僅對增加就業(yè)和擴大內(nèi)需起到重要的推動作用，優(yōu)化產(chǎn)業(yè)結構，而且可以增加國家外匯收入，促進國際收支平衡，加強國家、地區(qū)間的文化交流。為了研究影響旅游景區(qū)收入增長的主要原因，分析旅游收入增長規(guī)律，需要建立計量經(jīng)濟模型。影響旅游業(yè)發(fā)展的因素很多，但據(jù)分析主要因素可能有國內(nèi)和國際兩個方面，因此在進行旅游景區(qū)收入分析模型設定時，引入城鎮(zhèn)居民可支配收入和旅游外匯收入為解釋變量。旅游業(yè)很大程度上受其產(chǎn)業(yè)本身的發(fā)展水平和從業(yè)人數(shù)影響，固定資產(chǎn)和從業(yè)人數(shù)體現(xiàn)了旅游產(chǎn)業(yè)發(fā)展規(guī)模的內(nèi)在影響因素，因此引入旅游景區(qū)固定資產(chǎn)和旅游業(yè)從業(yè)人數(shù)作為解釋變量。因此選取我國31個省市地區(qū)的旅游業(yè)相關數(shù)據(jù)進行定量分析我國旅游業(yè)發(fā)展的影響因素。模型設定根據(jù)以上的分析，建立以下模型Y=β+βX+βX+βX+βX+Ut 1 2 0 1 2 3 3 4 4參數(shù)說明：Y——旅游景區(qū)營業(yè)收入/萬元X——旅游業(yè)從業(yè)人員/人1X——旅游景區(qū)固定資產(chǎn)/萬元2X——旅游外匯收入/萬美元3X——城鎮(zhèn)居民可支配收入/元4收集到的數(shù)據(jù)如下（見表2.1）：表2.12011年全國旅游景區(qū)營業(yè)收入及相關數(shù)據(jù)（按地區(qū)分）地地區(qū)營業(yè)收入從業(yè)人數(shù)固定資產(chǎn)外匯收入可支配收入北京145249.01145466694252.3054160032903.03天津48712.372478793529.6717555326920.86河北182226.8779643420342.744476518292.23山西29465.0357719121809.745671918123.87內(nèi)蒙古70313.0736264206819.126709720407.57遼寧25665.306481646573.2727131420466.84吉林20389.302906687827.163852817796.57黑龍江38367.8130341137426.279176215696.18上海194762.391106563007.4457511836230.48江蘇316051.651401541195000.6056529726340.73浙江385976.921324591110975.2045417330970.68安安徽79562.7555840139769.0211791818606.13福建155378.9580303151897.6936344424907.40江西54961.664179185528.054150017494.87山東116995.67143026327733.2925507622791.84河南222108.3370164482005.325490318194.80湖北104565.5862767243794.629401818373.87湖南118180.8780615257226.710143418844.05廣東476345.502265391160675.4139061926897.48廣西66195.5549876143982.0310518818854.06海南29081.603075970386.553761518368.95重慶86713.6750160230124.009680620249.70四川218624.0370756464763.525938317899.12貴貴州42214.142768362415.211350716495.01云南135897.9762679348426.0416086118575.62西藏30406.736023462971.031296316195.56陜西48692.1757077154529.1912950518245.23甘肅30949.003128056684.68174014988.68青海638.4387419851.28265915603.31寧夏49509.861219623149.9062017578.92新疆28993.114045152280.364651915513.62數(shù)據(jù)來源：1.中國統(tǒng)計年鑒2012，2.中國旅游年鑒2012。參數(shù)估計利用Eviews6.0做多元線性回歸分析步驟如下：創(chuàng)建工作文件雙擊Eviews6.0圖標，進入其主頁。在主菜單中依次點擊“File\New\Workfile”，出現(xiàn)對話框“WorkfileRange”。本例中是截面數(shù)據(jù)，在workfilestructuretype中選擇“Unstructured/Undated”,在Daterange中填入observations31,點擊ok鍵，完成工作文件的創(chuàng)建。輸入數(shù)據(jù)在命令框中輸入dataYX1X2X3X4,回車出現(xiàn)“Group”窗口數(shù)據(jù)編輯框，在對應的YX1X2X3X4下輸入相應數(shù)據(jù)，關閉對話框?qū)⑵涿麨間roup01,點擊ok,保存。對數(shù)據(jù)進行存盤，點擊“File/SaveAs”，出現(xiàn)“SaveAs”對話框，選擇存入路徑，并將文件命名，再點“ok”。參數(shù)估計在Eviews6.0命令框中鍵入“LSYCX1X2X3X4”,按回車鍵，即出現(xiàn)回歸結果。利用Eviews6.0估計模型參數(shù)，最小二乘法的回歸結果如下：表3.1回歸結果 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:14 Sample:131 Includedobservations:31 Coefficient Std.Errort-Statistic Prob.C32390.8339569.490.8185810.4205X10.6036240.3661121.6487410.1112X20.2342650.0412185.6835830.0000X30.0446320.0607550.7346200.4691X4-1.9140342.098257-0.9122020.3700R-squared 0.879720Meandependentvar114619.2AdjustedR-squared0.861215S.D.dependentvar112728.1S.E.ofregression41995.55Akaikeinfocriterion24.27520Sumsquaredresid4.59E+10Schwarzcriterion24.50649Loglikelihood-371.2657Hannan-Quinncriter.24.35060F-statistic47.54049Durbin-Watsonstat2.007191Prob(F-statistic)0.000000 根據(jù)表中的樣本數(shù)據(jù)，模型估計結果為 Y^=32390.83+0.603624X +0.234265X+0.044632X-1.914034X 1 2 3 4（39569.49）（0.366112）（0.041218）（0.060755）（2.098257）t=(0.818581)(1.648741)(5.683583)(0.734620)(-0.912202)R2=0.879720R2=0.861215F=47.54049DW=2.007191可以看出，可決系數(shù)R2=0.879720，修正的可決系數(shù)R2=0.861215。說明模型的擬合程度還可以。但是當α=0.05時，X、X、X系數(shù)均不能通過檢 1 2 4驗，且X的系數(shù)為負，與經(jīng)濟意義不符，表明模型很可能存在嚴重的多重共線4性。四、模型修正1．多重共線性的檢驗與修正檢驗選中X1X2X3X4數(shù)據(jù)，點擊右鍵，選擇“Open/asGroup”,在出現(xiàn)的對話框中選擇“View/CovarianceAnalysis/correlation”,點擊ok,得到相關系數(shù)矩陣。計算各個解釋變量的相關系數(shù)，得到相關系數(shù)矩陣。表4.1相關系數(shù)矩陣變量X1X2X3X4X11.0000000.8097770.8720930.659239X20.8097771.0000000.7583220.641086X30.8720930.7583221.0000000.716374X40.6592390.6410860.7163741.000000由相關系數(shù)矩陣可以看出，解釋變量X2、X3之間存在較高的相關系數(shù)，證實確實存在嚴重的多重共線性。多重共線性修正采用逐步回歸的辦法，檢驗和回歸多重共線性問題。分別作Y對X1、X2、X3、X4的一元回歸，在命令窗口分別輸入LSYCX1，LSYCX2,LSYCX3，LSYCX4，并保存，整理結果如表4.2所示。表4.2一元回歸結果變量X1X2X3X4參數(shù)估計值1.9782240.3151200.31694612.54525t統(tǒng)計量8.63511112.474956.9224794.005547R20.7199830.8429240.6229880.356191R20.7103270.8375080.6099880.333991其中，X2的方程R2最大，以X2為基礎，順次加入其它變量逐步回歸。在命令窗口中依次輸入：LSYCX2X1，LSYCX2X3,LSYCX2X4,并保存結果，整理結果如表4.3所示。表4.3加入新變量的回歸結果（一）變量變量變量X1X2X3X42RX2，X10.711446(2.679575)0.230304(5.891959)0.866053X2，X30.258113(7.016265)0.087950(2.043471)0.853546X2X2，X40.312045(9.319239)0.293708（0.143226）0.831828經(jīng)比較，新加入X1的方程R=0.866053，改進最大，而且各個參數(shù)的t檢驗顯著，選擇保留X1，再加入其它新變量逐步回歸，在命令框中依次輸入：LSYCX2X1X3，LSYCX2X1X4，保存結果，整理結果如表4.4所示。表4.4加入新變量的回歸結果（二）變量變量X1X2X3X42RX2，X1，X30.603269(1.652919)0.227087(5.630196)0.024860(0.439370)0.862078X2，X1，X40.773017(2.741794)0.237243(5.833838)-1.364110(-0.701920)0.863581當加入X3或X4時，R均沒有所增加，且其參數(shù)是t檢驗不顯著。從相關系數(shù)可以看出X3、X4與X1、X2之間相關系數(shù)較高，這說明X3、X4引起了多重共線性，予以剔除。當取α=0.05時，tα/2(n-k-1)=2.048，X1、X2的系數(shù)t檢驗均顯著，這是最后消除多重共線性的結果。修正多重共線性影響后的模型為Y^=0.711446X+0.230304X 1 2（0.265507）（0.039088）t=(2.679575)(5.891959) R2=0.874983 R2=0.866053 F=97.98460DW=1.893654在確定模型以后，進行參數(shù)估計表4.5消除多重共線性后的回歸結果 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:47 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-Statistic Prob.-4316.82C412795.42-0.3373730.7384X10.7114460.2655072.6795750.0122X20.2303040.0390885.8919590.0000R-squared0.874983Meandependentvar114619.2AdjustedR-squared0.866053S.D.dependentvar112728.1S.E.ofregression41257.10Akaikeinfocriterion24.18480Sumsquaredresid4.77E+10Schwarzcriterion24.32357Loglikelihood-371.8644Hannan-Quinncriter.24.23004F-statistic97.98460Durbin-Watsonstat1.893654 Prob(F-statistic) 0.000000 五、異方差檢驗在實際的經(jīng)濟問題中經(jīng)常會出現(xiàn)異方差這種現(xiàn)象，因此建立模型時，必須要注意異方差的檢驗，否則，在實際中會失去意義。（1）檢驗異方差由表4.5的結果，按路徑“View/ResidualTests/HeteroskedasticityTests”，在出現(xiàn)的對話框中選擇Specification:White，點擊ok.得到White檢驗結果如下。表5.1White檢驗結果 HeteroskedasticityTest:White F-statistic 3.676733Prob.F(5,25)0.0125Obs*R-squared 13.13613Prob.Chi-Square(5)0.0221ScaledexplainedSS15.97891Prob.Chi-Square(5)0.0069 TestEquation: DependentVariable:RESID^2 Method:LeastSquares Date:11/14/13Time:21:48 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb.C-1.10E+091.11E+09-0.9927790.3303X1-12789.3630151.30-0.4241730.6751X1^20.4207160.2943321.4293930.1653X1*X2-0.1018140.083576-1.2182160.2345X214604.525047.7012.8933010.0078X2^2-0.0024890.008030-0.3099720.7592R-squared0.423746Meandependentvar1.54E+09AdjustedR-squared0.308495S.D.dependentvar2.70E+09S.E.ofregression2.24E+09Akaikeinfocriterion46.07313Sumsquaredresid1.26E+20Schwarzcriterion 46.35068Loglikelihood-708.1335Hannan-Quinncriter.46.16360F-statistic3.676733Durbin-Watsonstat1.542170Prob(F-statistic)0.012464 從上表可以看出，nR2=13.13613，由White檢驗可知，在α=0.05下，查2分布表，得臨界值χ2(5)=11.0705,比較計算的2統(tǒng)計量與臨界值，因為0.05nR2=13.13613>χ2(5)=11.0705,所以拒絕原假設，表明模型存在異方差。0.05（2）異方差的修正①用WLS估計：選擇權重w=1/e1^2,其中e1=resid。在命令窗口中輸入genre1=resid,點回車鍵。在消除多重共線性后的回歸結果（表4.5的回歸結果）對話框中點擊Estimate/Options/WeithtedLS/TSLS,并在Weight中輸入1/e1^2,點確定，得到如下回歸結果。表5.2用權數(shù)1/e1^2的回歸結果 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:49 Sample:131 Includedobservations:31 Weightingseries:1/E1^2 Coefficie ntStd.Errort-StatisticProb.-7074.87 C 3389.4944-18.16425 0.0000 X1 0.788277 0.01369257.57099 0.0000 X2 0.235806 0.000968 243.6786 0.0000 WeightedStatistics R-squared0.999848Meandependentvar31056.56AdjustedR-squared0.999837S.D.dependentvar171821.4S.E.ofregression4.259384Akaikeinfocriterion5.827892Sumsquaredresid507.9857Schwarzcriterion5.966665Loglikelihood-87.33232Hannan-Quinncriter.5.873128F-statistic92014.78Durbin-Watsonstat1.663366Prob(F-statistic)0.000000 UnweightedStatistics R-squared0.871469Meandependentvar114619.2AdjustedR-squared0.862288S.D.dependentvar112728.1S.E.ofregression41832.86Sumsquaredresid4.90E+10Durbin-Watsonstat1.853343 ②修正后的White檢驗為在表5.2的回歸結果中，按路徑“View/ResidualTests/HeteroskedasticityTests”，在出現(xiàn)的對話框中選擇Specification:White，點擊ok.得到White檢驗結果如下。表5.3修正后的White檢驗結果 HeteroskedasticityTest:White F-statistic 0.210748Prob.F(2,28) 0.8113 Obs*R-squared 0.459736Prob.Chi-Square(2) 0.7946 ScaledexplainedSS0.595955Prob.Chi-Square(2) 0.7423 TestEquation: DependentVariable:WGT_RESID^2 Method:LeastSquares Date:11/15/13Time:20:29 Sample:131 Includedobservations:31 CollineartestregressorsdroppedfromspecificationCoefficie ntStd.Errort-StatisticProb.C17.639915.9225942.9784100.0059WGT-256.0052728.8280-0.3512560.7280WGT^28.26192623.571550.3505040.7286 R-squared 0.014830Meandependentvar16.38664-0.05553 AdjustedR-squared 9S.D.dependentvar29.69485S.E.ofregression30.50832Akaikeinfocriterion9.765641 Sumsquaredresid 26061.21Schwarzcriterion9.904414-148.367 Loglikelihood 4Hannan-Quinncriter.9.810878 F-statistic 0.210748Durbin-Watsonstat2.081320 Prob(F-statistic) 0.811251 從上表可知nR2==0.459736<χ2(5)=11.0705，證明模型中的異方差已0.05經(jīng)被消除了。異方差修正后的模型為Y^=-7074.873+0.788277X1*+0.235806X2*389.49440.0136920.000968t=(-18.16425)(57.57099)(243.6786) R2=0.999848 R2=0.999837 F=92014.78DW=1.663366其中X*=1/e1^2*X,X*=1/e1^2*X,e1=resid。 1 1 2 2六、自相關檢驗與修正DW檢驗在顯著性水平α=0.05，查DW表，當n=31，k=2時，得上臨界值d=1.27，u下臨界值d=1.15，DW=1.663365。因為d<DW<4-d ，所以模型不存在l u u序列自相關。由圖示法也可以看出隨機誤差項μ不存在自相關。下圖是殘差及一階滯后殘i差相關圖。實用標準文案實用標準文案精彩文檔精彩文檔實用標準文案精彩文檔圖6.1殘差與其滯后一階殘差圖LM檢驗在表5.2的回歸結果中，按路徑“View/ResidualTests/SerialCorrelationLMTests”，在出現(xiàn)的對話框中選擇Lagstoinclude:1，點擊ok.得到LM檢驗結果如下。表6.1LM檢驗結果 Breusch-GodfreySerialCorrelationLMTest: F-statistic 0.809839Prob.F(1,27) 0.3761 Obs*R-squared 0.902738Prob.Chi-Square(1) 0.3420 TestEquation: DependentVariable:RESID Method:LeastSquares Date:11/14/13Time:21:50 Sample:131 Includedobservations:31 Presamplemissingvaluelaggedresidualssettozero. Weightseries:1/E1^2 Coefficie ntStd.Errort-StatisticProb.C-766.3965937.0314-0.8178980.4206X10.0209900.0270700.7753900.4448X2-0.0012730.001716-0.7420020.4645RESID(-1)-0.0070920.007881-0.8999100.3761WeightedStatistics-0.56451 R-squared 0.029121Meandependentvar 3AdjustedR-squared-0.07875S.D.dependentvar4.0747475S.E.ofregression4.273921Akaikeinfocriterion5.862855 Sumsquaredresid 493.1929Schwarzcriterion6.047885-86.8742 Loglikelihood 5Hannan-Quinncriter.5.923170 F-statistic 0.269946Durbin-Watsonstat1.683210 Prob(F-statistic) 0.846488 UnweightedStatistics R-squared-0.01456 -4021.72 9Meandependentvar 2AdjustedR-squared-0.127299S.D.dependentvar40207.07S.E.ofregression42689.59Sumsquaredresid4.92E+10Durbin-Watsonstat1.69E-08 從上表可以看出，nR2=0.902738，由LM檢驗可知，在α=0.05下，查2分布表，得臨界值χ2(5)=11.0705,比較計算的2統(tǒng)計量與臨界值，因為0.05nR2=0.902738<χ2(5)=11.0705,所以接受原假設，表明模型不存在自相關。0.05七、模型檢驗經(jīng)濟意義檢驗模型估計結果表明，在假定其他變量不變的情況下，當景區(qū)固定資產(chǎn)每增長1元時，旅游收入增加0.788277元；在假定其他變量不變的情況下，當景區(qū)從業(yè)人員每增加1人時，旅游收入增加0.235806萬元。這與理論分析判斷相一致。統(tǒng)計檢驗（1）擬合優(yōu)度：由表中數(shù)據(jù)可得：R2=0.999848，修正的可決系數(shù)為R=0.999837，這說明模型對樣本的擬合很好。（2）F檢驗：針對H0：β1=β2=0，給定顯著性水平α=0.05，在F分布表中查出自由度為k=2和n-k-1=28的臨界值F(2，28)=3.34。由表中得到αF=92014.78，由于F=92014.78>F(2，28)=3.34，應拒絕原假設，說明回歸α方程顯著，即“旅游景區(qū)固定資產(chǎn)”、“旅游從業(yè)人員”等變量聯(lián)合起來確實對“旅游景區(qū)營業(yè)收入”有顯著影響。（3）t檢驗：分別對H0：βj=0(j=1,2),給定顯著性水平α=0.05，查t分布表得自由度為n-k-1=28臨界值tα/2(n-k-1)=2.048。由表中數(shù)據(jù)可得，^1、^2對應的t統(tǒng)計量分別為57.57099、243.6786，其絕對值均大于tα/2(n-k-1)=2.048，這說明應該分別拒絕H0：βj=0(j=1,2),也就是說，當在其他解釋變量不變的情況下，解釋變量“旅游景區(qū)固定資產(chǎn)”（X1）、“旅游從業(yè)人數(shù)”（X2）分別對被解釋變量“旅游景區(qū)營業(yè)收入”(Y)影響顯著。八、附錄以下是多重共線性參數(shù)估計備表1對X回歸分析1 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:14 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb.C-15595.6 118604.86-0.838255 0.4087X11.978224 0.229091 8.635111 0.0000R-squared0.719983Meandependentvar114619.2AdjustedR-squared0.710327S.D.dependentvar112728.1S.E.ofregression60671.69Akaikeinfocriterion24.92668Sumsquaredresid1.07E+11Schwarzcriterion 25.01920Loglikelihood-384.3636Hannan-Quinncriter.24.95684F-statistic74.56515Durbin-Watsonstat2.090544Prob(F-statistic)0.000000 備表2對X回歸分析2 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb.C15958.73 11364.71 1.404236 0.1709X20.315120 0.025260 12.47495 0.0000R-squared0.842924Meandependentvar114619.2AdjustedR-squared0.837508S.D.dependentvar112728.1S.E.ofregression45441.05Akaikeinfocriterion24.34856Sumsquaredresid5.99E+10Schwarzcriterion 24.44108Loglikelihood-375.4027Hannan-Quinncriter.24.37872F-statistic155.6243Durbin-Watsonstat1.665119Prob(F-statistic)0.000000 備表3對X回歸分析3 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb. C 53599.95 15413.41 3.477488 0.0016 X3 0.316946 0.045785 6.922479 0.0000R-squared0.622988Meandependentvar114619.2AdjustedR-squared0.609988S.D.dependentvar112728.1S.E.ofregression70399.77Akaikeinfocriterion25.22411Sumsquaredresid1.44E+11Schwarzcriterion 25.31662Loglikelihood-388.9737Hannan-Quinncriter.25.25427F-statistic47.92072Durbin-Watsonstat1.724195Prob(F-statistic)0.000000 備表4對X回歸分析4 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb.-143904. C 966622.99-2.159989 0.0392 X4 12.54525 3.131970 4.005547 0.0004 R-squared 0.356191Meandependentvar114619.2AdjustedR-squared0.333991S.D.dependentvar112728.1S.E.ofregression91996.75Akaikeinfocriterion25.75923 Sumsquaredresid2.45E+11Schwarzcriterion 25.85175-397.268 Loglikelihood 1Hannan-Quinncriter.25.78939 F-statistic 16.04440Durbin-Watsonstat1.829839 Prob(F-statistic) 0.000394 備表5對X、X回歸分析 2 1 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb.-4316.82 C 412795.42-0.337373 0.7384 X2 0.230304 0.039088 5.891959 0.0000 X1 0.711446 0.265507 2.679575 0.0122 R-squared 0.874983Meandependentvar114619.2AdjustedR-squared0.866053S.D.dependentvar112728.1S.E.ofregression41257.10Akaikeinfocriterion24.18480 Sumsquaredresid4.77E+10Schwarzcriterion 24.32357-371.864 Loglikelihood 4Hannan-Quinncriter.24.23004 F-statistic 97.98460Durbin-Watsonstat1.893654 Prob(F-statistic) 0.000000 備表6對X、X回歸分析 2 3 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb. C 16874.53 10798.59 1.562660 0.1294 X2 0.258113 0.036788 7.016265 0.0000 X3 0.087950 0.043040 2.043471 0.0505 R-squared 0.863310Meandependentvar114619.2AdjustedR-squared0.853546S.D.dependentvar112728.1S.E.ofregression43140.27Akaikeinfocriterion24.27407 Sumsquaredresid5.21E+10Schwarzcriterion 24.41284-373.248 Loglikelihood 0Hannan-Quinncriter.24.31930 F-statistic 88.42123Durbin-Watsonstat1.600090 Prob(F-statistic) 0.000000 備表7對X、X回歸分析 2 4 DependentVariable:Y Method:LeastSquares Date:11/14/13Time:21:15 Sample:131 Includedobservations:31 Coefficie ntStd.Errort-StatisticProb. C 10868.79 37371.23 0.290833 0.7733 X2 0.312045 0.033484 9.319239 0.0000 X4 0.293708