試驗(yàn)作業(yè)4異方差性的檢驗(yàn)和修正

1、實(shí)驗(yàn)作業(yè)4異方差性的檢驗(yàn)和修正表4所給出的是我國(guó)2005年31個(gè)打市或自治區(qū)城鎮(zhèn)居民家庭平均每人全年交通和 通訊支出fcuml人各地區(qū)城鎮(zhèn)居民平均每人全年家庭可支配收入（】旗）有關(guān)數(shù)據(jù).單位 為元，數(shù)據(jù)來源于中國(guó)統(tǒng)計(jì)年鑒一如婚年.北京*中國(guó)統(tǒng)計(jì)出版社，2006年.本實(shí)驗(yàn)表建國(guó)2005年城慎居民家庭人均交通，通訊支出與人均可支配收入觀測(cè)值cumtinc11943.4817652.952998.0112638.553772.349107.094604.358913.915755.519136.796744.029107.557733.58690.628596.978272.5191983.7218

2、645.03101050.8812318.57112097.4116293.7712676.868470.68131048.7112321.3114567.528619.6615902.3210744.7916636.578667.9717649.878785.9418801.279523.97192333.0514769.9420703.399286.721728.298123.9422929.9210243.4623827.668385.9624625.448151.1325930.599265.9261309.959431.1827630.168272.0228638.638086.82

3、29691.258057.8530705.698093.6431757.097990.15本實(shí)驗(yàn)利用表4J的數(shù)據(jù).先建立被解釋變僦為人均交通和通訊支用（cumt）i解釋變 量為人均可支配收入Snc）的消費(fèi)方程,設(shè)定消費(fèi)方程的形式為工cumt= cr + /? *inc4- （ 4.3 ）利用上述數(shù)據(jù)，對(duì)方程（4.3）進(jìn)行回歸，并分析回歸結(jié)果的經(jīng)濟(jì)意義。用Eviews錄入數(shù)據(jù)得View |pracObjectPrintMameFreezeEstimateForecastStats | Resids Equation： UNTILED Workfile: UNTITLED:UntitledDepe

4、ndent Variable: Y Method: Least Squares Date: 10/27/15 Time: 21:22Sample: 1 31Included observations: 31VariableCoefficientStd Error t-StatisticProb.C-563.5647134.5313-4.1890970.0002X01432100.01269711 67311oooooR-squared0.824521Mean dependentvar947.5619Adjusted R-squaredQ.81S469S D. dependent var478.

5、4392S.E of regression203.8457Akaike info criterion13,53494Sum squared resid1205039Schwarz criterion13.62746Log likelihood-207.7916Hannan-Quinn criter13.56610F-stati stic135.2615Durbin-VVatson stat1 890233ProbiF*statisti c；0.000000估計(jì)結(jié)果為:AY=-563.5647+0.148210Xi(134.5313) (0.012697)t = (-4.189097) (11.

6、67311)F=136.2615df=29R2=0.824521R2=0.818469經(jīng)濟(jì)意義： 人均可支配收入每增加一個(gè)單位，人均交通和通訊支出增加 0.148210個(gè)單位利用圖形法、Goldfeld-Quanadt檢驗(yàn)和 White異方差檢驗(yàn)，檢驗(yàn)方程(4.3)的異方差。圖形法:岷yJProcOhjed RrKt| Name Freeze | Default :SortTranspose | Edit+/-15npi +/-TobsXE2117652.9511947.97A212638.5597088.5539107 090192.130748913.91023476.3259136.79

7、01231.51769107.5501785.00378690,62091 4340288272.5104295 184136450346700.671012318.5744645.991116293.7760549.4112B470.6B0225.55581312321.3145741.26148619.5602U44.351510744.7916028 9216B667.9707148.526178785 9407873605189523.9702132.436V194 Z A A口 Group: UNTfTLED Workfile: UNTITLED:Untitled 國(guó)巨應(yīng)由散點(diǎn)圖可以

8、看出，殘差平方E2對(duì)解釋變量 X的散點(diǎn)圖主要分布在圖形中的下三角部分, 大致看出殘差平方 E2隨X的變動(dòng)呈增大的趨勢(shì)，因此，模型很可能存在異方差。但是否 確實(shí)存在異方差還應(yīng)通過更進(jìn)一步的檢驗(yàn)。Goldfeld-Quanadt 檢驗(yàn)O WdfHiIk UNTITLEDd喟ew|ProcObject Print Save Details+/-1 ShoTFEtdi StofgMete Genr|SampleRange: 1 311 - 31 obsDisplay Filter Sample 1 31 - 31 obs國(guó)c回gi Equation: UNTITLED Workfile! UNTITL

9、EDUrvtitledC3View| Proc Objeet| Print Name Freeze Estimate Forecast Stats ResidDependent Variable. YMetfiod： Least SquaresDate: 10/27/15 Time: 22:01Sample： 1 11Included observatjons: 11 Untitled k Hew FjgVariableCoefficientStd. Error (-StatisticProbC1S69 93610125041 6493130 1335X-0.1206720.123002-0

10、9S105403522R-squared0 09660gMean d&pendentvar5758591蚓 U0tMRqii3ea-0.0037S7S.D. dependentvar75S1877S.E. of regression75 g6145Akaike info criterian11 66129Sum squ3r&d r&sid51931.29Schwarz criterion11 73364Log likelihood-62 13712Hannan-Quinn criter.11.61569F-statistic0.902457Durbin-Wats on stat2123027P

11、ro b(.F-stati stic)0 352201圖1-1r口 Equation： UNTITLEDWorkfile： UNTITLED:Untitled | o 1 B |Proc | ObjectPrint| Name | FreezeBriEate | Fareagt| SteM RE# Dependent Variable: Y M ethod: Least Squares Date: 10/27/15 Time: 22:03 Sample: 19 29 Included observations: 11VariableCoefficientStd. Error卜 Statisti

12、cProb.C X-921.73160.183261501.&029-1.8368400 04270142917050099400020R-squaredAdjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F*statis1icl0.6717570.635286321.04789276453-77 99213 1841873 0.002015Mean dependent var S.D. dependentvar Akaike info criterion Schwarz

13、criterion Hannan-Quinn criter. Durbin-Watson stat1191.409531.610314.5440214.6163714498422014766圖1-2卜面求F統(tǒng)計(jì)量值?；趫D1-1 和圖1-2中殘差平方和的數(shù)據(jù)，即 Sumsquared resid的值。由圖1-1計(jì)算得到的殘差平方和為51931.29 ,由圖1-2計(jì)算得到的殘差平方和為 927645.3,根據(jù) Goldfeld-Quanadt 檢驗(yàn)，F(xiàn)統(tǒng)計(jì)量為927645.3/51931.29=17.8629判斷：在 a =0.05下，在式中分子、分母的自由度均為9,查F分布表得臨界值為F0.0

14、5(9,9) =3.18 ,因?yàn)镕=17.86293.18 ,所以拒絕原假設(shè),表明模型確實(shí)存在異方差White異方差檢驗(yàn)rWle: UNTITLEDPrint | Sar 131 - 311005值 131 - 31ObS.id根據(jù)White統(tǒng)計(jì)量的分析：從圖可以看出，nRA2= 7.583705 ,由 White檢驗(yàn)知，在a =0.05下，查x2分布表，得臨界值 xA2 0.05(2)= 5.9915比較計(jì)算的 x2統(tǒng)計(jì)量與臨界值，因?yàn)?nRA2= 7.5837055.9915所以拒絕原假設(shè)，接受備擇假設(shè)，表明模型存在異方差。根據(jù)White統(tǒng)計(jì)量所對(duì)應(yīng) p值的分析：給定顯著性水平 a =0.

15、05 ,因?yàn)?Probability (White) =0.01970.05所以拒絕原假設(shè)，表明模型存在異方差。(3)修正異方差。O Equation： UNTITLED Workfile: UNTITLED：rUntitl&d肥胃| Prod Object| PrtitNdEe Freeze Estimate Forecast1 5tats ResidsDependent Variable: YM&thod: Least SquaresDate 10/26/15 Time. 00:5SSample; 1 31Included obseivatons: 31Weighting series:

16、W2VariableCoefficientStd.3阿b StatisticProb一C聞56 3893iai 46M-Z51&0ia0.0177X0.13B68B0.0203626.7130300.0000Weighted StatisticsR-squared0.609451Mean dependent var8083763Adjusted RTquaE0594949S.D. dependent var169.4S28S,E. of regression145.0533Akaike infti criterion12 85442Sum squared resid&1Q173.4Schwarz criterion1294694Log likelihood-197 2435Hannan-Quinn enter.12.3S458Fatalistic45,0647BDurbin-Walson stat2.026116Prob(F-statlstic)0.000000Unweighied StatisticsR-squared0.S1905SMean dependent var947.5619Adjusted R號(hào)quz(J0 上 12819S.D. dependentvar473.4392S.E. of regression206 9941Sum squ