實(shí)驗(yàn)五異方差模型的檢驗(yàn)

1、實(shí)驗(yàn)報(bào)告課程名稱：計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)項(xiàng)目：實(shí)驗(yàn)五異方差模型的檢驗(yàn)和處理實(shí)驗(yàn)類型：綜合性口設(shè)計(jì)性口驗(yàn)證性專業(yè)班別： 123姓 名：學(xué) 號(hào)：412實(shí)驗(yàn)課室：厚德樓 A404指導(dǎo)教師：實(shí)驗(yàn)日期：2015年5月28日廣東商學(xué)院華商學(xué)院教務(wù)處 制、實(shí)驗(yàn)項(xiàng)目訓(xùn)練方案小組合作：是否小組成員：無實(shí)驗(yàn)?zāi)康模赫莆债惙讲钅Ｐ偷臋z驗(yàn)和處理方法實(shí)驗(yàn)場(chǎng)地及儀器、設(shè)備和材料實(shí)驗(yàn)室：普通配置的計(jì)算機(jī)，Eviews軟件及常用辦公軟件。實(shí)驗(yàn)訓(xùn)練內(nèi)容（包括實(shí)驗(yàn)原理和操作步驟）：【實(shí)驗(yàn)原理】異方差的檢驗(yàn)：圖形檢驗(yàn)法、Goldfeld-Quanadt檢驗(yàn)法、White檢驗(yàn)法、Glejser檢 驗(yàn)法；異方差的處理：模型變換法、加權(quán)最小二乘法

2、 （WLS）?！緦?shí)驗(yàn)步驟】本實(shí)驗(yàn)考慮三個(gè)模型：【1】廣東省財(cái)政支出CZ對(duì)財(cái)政收入CS勺回歸模型；（數(shù)據(jù)見附表1：附表1-廣東 省數(shù)據(jù)）【2】廣東省固定資產(chǎn)折舊ZJ對(duì)國(guó)內(nèi)生產(chǎn)總值GDP和時(shí)間T的二元回歸模型；（數(shù) 據(jù)見附表1:附表1-廣東省數(shù)據(jù)）【3】廣東省各市城鎮(zhèn)居民消費(fèi)支出Y對(duì)人均收入X的回歸模型。（數(shù)據(jù)見附表2： 附表2-廣東省2005年數(shù)據(jù)）（一）異方差的檢驗(yàn)1. 圖形檢驗(yàn)法分別用相關(guān)分析圖和殘差散點(diǎn)圖檢驗(yàn)?zāi)Ｐ汀?】、模型【2】和模型【3】是否存 在異方差。注：相關(guān)分析圖是作應(yīng)變量對(duì)自變量的散點(diǎn)圖（亦可作模型殘差對(duì)自變量的散點(diǎn)圖）； 殘差散點(diǎn)圖是作殘差的平方對(duì)自變量的散點(diǎn)圖。 模型【2】

3、中作圖取自變量為 GDPS來作圖。模型【1】相關(guān)分析圖殘差散點(diǎn)圖模型【2】相關(guān)分析圖殘差散點(diǎn)圖模型【3】相關(guān)分析圖殘差散點(diǎn)圖【思考】 相關(guān)分析圖和殘差散點(diǎn)圖的不同點(diǎn)是什么？*在模型【2】中，自變量有兩個(gè)，有無其他處理方法？嘗試做岀來。（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi) ）2. Goldfeld-Qua nadt檢驗(yàn)法用Goldfeld-Quanadt檢驗(yàn)法檢驗(yàn)?zāi)Ｐ汀?】是否存在異方差。注：Goldfeld-Quanadt檢驗(yàn)法的步驟為：排序：刪除觀察值中間的約1/4的，并將剩下的數(shù)據(jù)分為兩個(gè)部分。構(gòu)造 F統(tǒng)計(jì)量：分別對(duì)上述兩個(gè)部分的觀察值求回歸模型，由此得到的兩個(gè)部2分的殘差平方為1i和e

4、l,。£為較大的殘差平方和，el,為較小的殘差平方和。算統(tǒng)2計(jì)量F*°：F(n_C)k,(n _C)k)。判斷：給定顯著性水平0.05，查F分布表得臨e2i22界值F (n c) (n c)()。如果F* F (n c) (n c)()，則認(rèn)為模型中的隨機(jī)誤差存在異方差。(k, k)( k, k)2 2 2 2(詳見課本135頁)將實(shí)驗(yàn)中重要的結(jié)果摘錄下來，附在本頁。obsXY17021.9427220.446317.0337299.256463.3746350.3858842.846757.0269214.67294.9379867.367669.84810097.274

5、76.65910908.368113.641011944.0818296.4311229.179505.661215762.7712651.951317680.114485.611418287.2414468.241518907.7314323.661621015.0318550.561722881.821767.781828665.2521188.84Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time: 11:18Sample: 1 7Included observations: 7VariableCoefficientS

6、td. Errort-StatisticProb.?X0.7230770.2183863.3110030.0212C536.88741814.2540.2959270.7792R-squared0.686771 ?Mean dependent var6497.894Adjusted R-squared0.624125 ?S.D. dependent var966.9988S.E. of regression592.8541 ?Akaike info criterion15.84273Sum squared resid1757380. ?Schwarz criterion15.82728Log

7、likelihood-53.44956 ?Hannan-Quinn criter.15.65172F-statisticProb(F-statistic)10.96274 ?Durbin-Watson stat0.0212171.761325Dependent Variable: YMethod: Least SquaresDate: 06/07/15Time:11:20Sample: 12 18Included observations: 7VariableCoefficientStd. Errort-StatisticProb.?X0.7592910.1778984.2681250.008

8、0C1243.7433707.2380.3354900.7509R-squared0.784640?Mean dependent var16776.66Adjusted R-squared0.741567?S.D. dependent var3677.261S.E. of regression1869.382?Akaike info criterion18.13956Sum squared resid?Schwarz criterion18.12411Log likelihood-61.48846?Hannan-Quinn criter.17.94855F-statistic18.21689?

9、Durbin-Watson stat2.037081Prob(F-statistic)0.007953有上圖可知el2 ,e；i =1757380?F=? & / &i在 0.05下，上式中分子、分母的自由度均為5,查F分布表得臨界值F0.05 (5,5) =5.05，因?yàn)镕=?F0.05 (5,5) =5.05，所以拒接 原假設(shè)，說明模型存在異方差。？(請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi))3.White檢驗(yàn)法分別用White檢驗(yàn)法檢驗(yàn)?zāi)Ｐ汀?】、模型【2】和模型【3】是否存在異方差。Eviews操作：先做模型，選 view/Residual Tests/ Heteroske

10、dasticity Tests/White/勾 選cross terms).摘錄主要結(jié)果附在本頁內(nèi)。模型【1】Heteroskedasticity Test: White4.F-statistic40866?Prob.F(2,25)0.0156Obs*R-squared7.932189?Prob.Chi-Square(2)0.0189Scaled explained SS14.57723?Prob.Chi-Square(2)0.0007Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15 Tim

11、e: 12:44Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?C-879.85131125.376-0.7818290.4417CS12.937204.6513282.7813980.0101CSA2-0.0066200.002964-2.2335610.0347R-squared0.283292?Mean dependent var1940.891Adjusted R-squared0.225956?S.D. dependent var4080.739S.E. o

12、f regression3590.225?Akaike info criterion19.31077Sum squared resid3.22E+08?Schwarz criterion19.45351Log likelihood-267.3508?Hannan-Quinn criter.19.35441F-statistic4.940866?Durbin-Watson stat2.144291Prob(F-statistic)0.015552模型【2】Heteroskedasticity Test: WhiteF-statistic1.993171?Prob. F(5,22)0.1195Ob

13、s*R-squared8.729438?Prob. Chi-Square(5)0.1204Scaled explained SS14.67857?Prob. Chi-Square(5)0.0118Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time: 12:47Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?C1837.8986243.7010.2943600.

14、7712GDPS-3.3950935.407361-0.6278650.5366GDPSA2-9.08E-050.000185-0.4895370.6293GDPS*T0.1603000.3151760.5086040.6161T-491.56141982.891-0.2479010.8065TA249.08543152.98750.3208460.7514R-squared0.311766?Mean dependent var3461.910Adjusted R-squared0.155349?S.D. dependent var7240.935S.E. of regression6654.

15、775?Akaike info criterion20.63147Sum squared resid9.74E+08?Schwarz criterion20.91694Log likelihood-282.8405?Hannan-Quinn criter.20.71874F-statistic1.993171?Durbin-Watson stat1.971537Prob(F-statistic)0.119510模型【3】Heteroskedasticity Test: WhiteF-statistic7.670826?Prob. F(2,15)0.0051Obs*R-squared9.1013

16、41 ?Prob. Chi-Square(2)0.0106Scaled explained SS14.09286 ?Prob. Chi-Square(2)0.0009Test Equation:Dependent Variable: RESIDA2Method: Least SquaresDate: 06/07/15Time:12:51Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?C1865425.2810916.0.6636360.5170X-354.7917388.145

17、4-0.9140690.3751XA20.0188100.0116861.6095970.1283R-squared0.505630 ?Mean dependent var1232693.Adjusted R-squared0.439714 ?S.D. dependent var2511199.S.E. of regression1879689. ?Akaike info criterion31.88212Sum squared resid5.30E+13 ?Schwarz criterion32.03052Log likelihood-283.9391 ?Hannan-Quinn crite

18、r.31.90258F-statistic7.670826 ?Durbin-Watson stat2.010913Prob(F-statistic)0.005074（請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在一頁內(nèi)）4.Glejser檢驗(yàn)法用Glejser檢驗(yàn)法檢驗(yàn)?zāi)Ｐ汀?】是否存在異方差。分別用殘差的絕對(duì)值對(duì)自變量的一次項(xiàng) cs二次項(xiàng)CSi2，開根號(hào)項(xiàng)和倒數(shù)項(xiàng)1/CSi作回歸。檢驗(yàn)異方差是否存在，并選定異方差的最優(yōu)形式。摘錄主要結(jié)果附在本頁內(nèi)。一、一次項(xiàng)CSi回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time:13:17Samp

19、le: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CS0.0292360.0122792.3809470.0249C14.159918.2594921.7143800.0984R-squared0.179006 ?Mean dependent var27.30288Adjusted R-squared0.147429 ?S.D. dependent var35.20964S.E. of regression32.51074 ?Akaike info criterion9.869

20、767Sum squared resid27480.66?Schwarz criterion9.964925Log likelihood-136.1767?Hannan-Quinn criter.9.898858F-statistic5.668911?Durbin-Watson stat1.339465Prob(F-statistic)0.024881二、去掉常數(shù)項(xiàng)再回歸？Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time:13:22Sample: 1978 2005Included observations: 28Var

21、iableCoefficientStd. Errort-StatisticProb.?CS0.0433040.0094564.5794730.0001R-squared0.086198?Mean dependent var27.30288Adjusted R-squared0.086198?S.D. dependent var35.20964S.E. of regression33.65794?Akaike info criterion9.905436Sum squared resid30587.14?Schwarz criterion9.953015Log likelihood-137.67

22、61?Hannan-Quinn criter.9.919981Durbin-Watson stat1.209310三、二次項(xiàng)cs2回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time:13:19Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA21.11E-058.36E-061.3222070.1976C22.302367.5752862.9440940.0067R-squared0.06

23、3003?Mean dependent var27.30288Adjusted R-squared0.026965?S.D. dependent var35.20964S.E. of regression34.73168?Akaike info criterion10.00193Sum squared resid31363.53?Schwarz criterion10.09709Log likelihood-138.0270?Hannan-Quinn criter.10.03102F-statistic1.748231?Durbin-Watson stat1.203183Prob(F-stat

24、istic)0.197614四、開根號(hào)項(xiàng)'CST回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time:13:24Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(1/2)1.5372330.2690365.7138480.0000R-squared0.265081?Mean dependent var27.30288Adjusted R-squared0.265081?S.D. d

25、ependent var35.20964S.E. of regression30.18432?Akaike info criterion9.687583Sum squared resid24599.52?Schwarz criterion9.735162Log likelihood-134.6262?Hannan-Quinn criter.9.702128Durbin-Watson stat1.471849五、倒數(shù)項(xiàng)1/CSi作回歸Dependent Variable: E1Method: Least SquaresDate: 06/07/15Time: 13:26Sample: 1978 2

26、005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?CSA(-1)-2029.779607.7392-3.3398840.0025C46.202298.0122115.7664840.0000R-squared0.300226?Mean dependent var27.30288Adjusted R-squared0.273311?S.D. dependent var35.20964S.E. of regression30.01483?Akaike info criterion9.710009Sum

27、 squared resid23423.14?Schwarz criterion9.805167Log likelihood-133.9401?Hannan-Quinn criter.9.739100F-statistic11.15483?Durbin-Watson stat1.566457Prob(F-statistic)0.002542從四個(gè)回歸的結(jié)果看，第二個(gè)不顯著，其他三個(gè)顯著，比較這三個(gè)回歸，還是選擇第三個(gè)，方程為即異方差的形式為:(T 2 =(1.537233*(CSA(1 /2) ) 2=2.36085CS也即異方差的形式為:可2=(T 2CSi就把這個(gè)形式確定為異方差的形式。對(duì)

28、ZJ與GDPS和T回歸的Glejser 檢驗(yàn)可以類似進(jìn)行檢驗(yàn)，消費(fèi)支出與可支配收入回歸的Glejser檢驗(yàn)可以類似進(jìn)行檢驗(yàn)。通過前面實(shí)驗(yàn)的異方差模型的檢驗(yàn)，發(fā)現(xiàn)根據(jù)廣東數(shù)據(jù)CZ對(duì)CS的回歸，ZJ對(duì)GDPS和T的回歸，消費(fèi)支出與可支配收入回歸都存在異萬差，現(xiàn)在分別對(duì)它們進(jìn)行處理。加權(quán)最小二乘法已經(jīng)成為處理異方差模型的標(biāo)準(zhǔn)方法,再Eviews中使用WLS來消除異方差，關(guān)鍵是權(quán)數(shù)的選取。(請(qǐng)對(duì)得到的冬表進(jìn)行處理，以上在一頁內(nèi))(二)異方差的處理1模型【1】中CZ對(duì)CS回歸異方差的處理已知CZ對(duì)CS回歸異方差的形式為：i22CSi，選取權(quán)數(shù)，使用加權(quán)最小二乘法處理異方差。并檢驗(yàn)處理異方差之后模型是否仍

29、存在異方差，若仍然存在異方差，請(qǐng)繼續(xù)處理 異方差。摘錄主要結(jié)果附在本頁內(nèi)。Dependent Variable: CZMethod: Least SquaresDate: 06/07/15 Time: 13:32Sample: 1978 2005Included observations: 28Weighting series: 1/(CSA(1/2)VariableCoefficientStd. Errort-StatisticProb.?CS1.2756770.01940665.736280.0000C-21.243654.264097-4.9819800.0000Weighted Sta

30、tisticsR-squared0.994019 ?Mean dependent var254.4606Adjusted R-squared0.993789 ?S.D. dependent var189.1988S.E. of regression22.86683 ?Akaike info criterion9.166001Sum squared resid13595.19 ?Schwarz criterion9.261159Log likelihood-126.3240 ?Hannan-Quinn criter.9.195092F-statistic4321.259 ?Durbin-Wats

31、on stat1.550317Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.995276 ?Mean dependent var552.2429Adjusted R-squared0.995095 ?S.D. dependent var653.1881S.E. of regression45.74872 ?Sum squared resid54416.57Durbin-Watson stat1.545575回歸方程為它與存在異方差的如下方程估計(jì)有所不同。至于經(jīng)過加權(quán)最小二乘法估計(jì)的殘差項(xiàng)是否存在異方差，同樣可以用本實(shí)驗(yàn)的異方差

32、模型的檢驗(yàn)去檢驗(yàn)，但是若在eviews中使用wls命令估計(jì)的序列resed不能用倆檢驗(yàn)，因?yàn)楫a(chǎn)生的序列resid是非加權(quán)方 式的殘差。要想檢驗(yàn)只能自己進(jìn)行同方差變換，然后回歸以后再檢驗(yàn)了。進(jìn)行同方差行變換，然后回歸實(shí)際上就是 CZ/(CSA(1/2)對(duì)1/(CSA(1/2) 和CS/(CSA(1/2)回歸，結(jié)果如 下：Dependent Variable: CZ/(CSA(1/2)Method: Least SquaresDate: 06/07/15 Time: 13:39Sample: 1978 2005Included observations: 28VariableCoefficient

33、Std. Errort-StatisticProb.?1/(CSA(1/2)-21.243654.264097-4.9819800.0000CS/(CS/2)1.2756770.01940665.736280.0000R-squared0.985934?Mean dependent var21.13688Adjusted R-squared0.985393?S.D. dependent var15.71588S.E. of regression1.899444?Akaike info criterion4.189748Sum squared resid93.80503?Schwarz crit

34、erion4.284906Log likelihood-56.65647?Hannan-Quinn criter.4.218839Durbin-Watson stat1.550317觀察其殘差趨勢(shì)圖還是存在異方差，再改為 CZ/CS對(duì)1/CS和回歸，如果如下Dependent Variable: CZ/CSMethod: Least SquaresDate: 06/07/15 Time: 13:42Sample: 1978 2005Included observations: 28VariableCoefficientStd. Errort-StatisticProb.?1/CS-19.828

35、602.064540-9.6043680.0000C1.2625010.02721846.384560.0000R-squared0.780115?Mean dependent var1.077876Adjusted R-squared0.771658?S.D. dependent var0.213378S.E. of regression0.101963?Akaike info criterion-1.659667Sum squared resid0.270307?Schwarz criterion-1.564510Log likelihood25.23534?Hannan-Quinn cr

36、iter.-1.630577F-statistic92.24388?Durbin-Watson stat1.613436Prob(F-statistic)0.000000觀察其殘差趨勢(shì)圖（請(qǐng)對(duì)得至U的圖表講行處理，以上在兩頁內(nèi) ） 2模型【2】中ZJ對(duì)GDPS和T回歸異方差的處理3已知ZJ對(duì)GDPS和T回歸異方差的形式為：i22 GDPSi 4，選取權(quán)數(shù)，使用加權(quán)最小二乘法處理異方差。并檢驗(yàn)處理異方差之后模型是否仍存在異方差，若仍然存在異方差，請(qǐng)繼續(xù)處理 異方差。摘錄主要結(jié)果附在本頁內(nèi)。Dependent Variable: ZJMethod: Least SquaresDate: 06/07

37、/15 Time: 13:46Sample: 1978 2005Included observations: 28Weighting series: 1/(GDPSA(3/8)VariableCoefficientStd. Errort-StatisticProb.?GDPS0.1669950.00256565.100680.0000T-4.3536850.881296-4.9400930.0000Weighted StatisticsR-squared0.997009?Mean dependent var418.9342Adjusted R-squared0.996894?S.D. depe

38、ndent var382.1762S.E. of regression29.59878?Akaike info criterion9.682092Sum squared resid22778.28?Schwarz criterion9.777250Log likelihood-133.5493?Hannan-Quinn criter.9.711183Durbin-Watson stat0.668750Unweighted StatisticsR-squared0.996289?Mean dependent var846.0661Adjusted R-squared0.996146?S.D. d

39、ependent var1014.824S.E. of regression63.00261?Sum squared resid103202.6Durbin-Watson stat0.754208它與存在異方差時(shí)的如下方程估計(jì)也有所不同。進(jìn)行同方差性變換，然后回歸實(shí)際上就是 ZJ/(GDPSA(8/3) 對(duì)GDPS/(GDPSA(8/3)和T/(GDPSA(8/3)回歸，結(jié)果如下：Dependent Variable: ZJ/(GDPSA(3/8)Method: Least SquaresDate: 06/07/15Time: 13:50Sample: 1978 2005Included ob

40、servations: 28VariableCoefficientStd. Errort-StatisticProb.?GDPS/(GDPSA(3/8)0.1669950.00256565.100680.0000T/(GDPSA(3/8)-4.3536850.881296-4.9400930.0000R-squared0.994224?Mean dependent var27.59529Adjusted R-squared0.994002?S.D. dependent var25.17403S.E. of regression1.949678?Akaike info criterion4.24

41、1955Sum squared resid98.83235?Schwarz criterion4.337112Log likelihood-57.38737?Hannan-Quinn criter.4.271045Durbin-Watson stat0.668750觀測(cè)其殘差趨勢(shì)圖可能還存在異方差，再改為ZJ/GDPS對(duì)C和T/GDPS回歸，結(jié)果如下:Dependent Variable: ZJ/GDPSMethod: Least SquaresDate: 06/07/15 Time: 13:52Sample: 1978 2005Included observations: 28Variabl

42、eCoefficientStd. Errort-StatisticProb.?C0.1619500.00346146.793580.0000T/GDPS-3.7265040.399838-9.3200440.0000R-squared0.769633?Mean dependent var0.135596Adjusted R-squared0.760772?S.D. dependent var0.021590S.E. of regression0.010560?Akaike info criterion-6.194729Sum squared resid0.002899?Schwarz crit

43、erion-6.099572Log likelihood88.72621?Hannan-Quinn criter.-6.165638F-statistic86.86322?Durbin-Watson stat0.439676Prob(F-statistic)0.000000觀測(cè)其殘差趨勢(shì)圖應(yīng)該不存在異方差了，其方程為變換為原方程(請(qǐng)對(duì)得到的圖表進(jìn)行處理，以上在兩頁內(nèi))3. 模型【3】中消費(fèi)支出Y對(duì)可支配收入X回歸異方差的處理-4已知丫對(duì)X回歸異方差的形式為：i22 Xi 3，選取權(quán)數(shù)，使用加權(quán)最小二乘法處理異方差。并檢驗(yàn)處理異方差之后模型是否仍存在異方差，若仍然存在異方差，請(qǐng)繼續(xù)處理 異方差。

44、摘錄主要結(jié)果附在本頁內(nèi)。Dependent Variable: YMethod: Least SquaresDate: 06/07/15 Time: 13:56Sample: 1 18Included observations: 18Weighting series: 1/XA(2/3)VariableCoefficientStd. Errort-StatisticProb.?X0.7951570.01725246.090120.0000Weighted StatisticsR-squared0.954867 ?Mean dependent var9599.510Adjusted R-squa

45、red0.954867 ?S.D. dependent var1867.615S.E. of regression895.7229 ?Akaike info criterion16.48709Sum squared resid?Schwarz criterion16.53656Log likelihood-147.3838 ?Hannan-Quinn criter.16.49391Durbin-Watson stat1.472431Unweighted StatisticsR-squared0.952547 ?Mean dependent var10906.35Adjusted R-squar

46、ed0.952547 ?S.D. dependent var5381.587S.E. of regression1172.315 ?Sum squared residDurbin-Watson stat1.419465它與存在異方差時(shí)如下方程估計(jì)明顯不同進(jìn)行同方差性變換，然后回歸實(shí)際上就是丫/伍人(2/3)和X/(XA(2/3)回歸，結(jié)果如下：Dependent Variable: Y/(XA(2/3)Method: Least SquaresDate: 06/07/15Time:13:59Sample: 1 18Included observations: 18VariableCoefficientStd. Errort-StatisticProb.?1/(XA(2/3)-495.5562520.4173-0.9522280.3551X/(XA(2/3)0.8337080.04402618.936730.0000R-squared0.782313 ?Mean dependent var18.56257Adjusted R-squared0.768707 ?S.D. dependent var3.