试验作业4异方差性的检验和修正

1、实验作业4异方差性的检验和修正表4所给出的是我国2005年31个打市或自治区城镇居民家庭平均每人全年交通和 通讯支出fcuml人各地区城镇居民平均每人全年家庭可支配收入（】旗）有关数据.单位 为元，数据来源于中国统计年鉴一如婚年.北京*中国统计出版社，2006年.本实验表建国2005年城慎居民家庭人均交通，通讯支出与人均可支配收入观测值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本实验利用表4J的数据.先建立被解释变僦为人均交通和通讯支用（cumt）i解释变 量为人均可支配收入Snc）的消费方程,设定消费方程的形式为工cumt= cr + /? *inc4- （ 4.3 ）利用上述数据，对方程（4.3）进行回归，并分析回归结果的经济意义。用Eviews录入数据得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估计结果为:AY=-563.5647+0.148210Xi(134.5313) (0.012697)t = (-4.189097) (11.

6、67311)F=136.2615df=29R2=0.824521R2=0.818469经济意义： 人均可支配收入每增加一个单位，人均交通和通讯支出增加 0.148210个单位利用图形法、Goldfeld-Quanadt检验和 White异方差检验，检验方程(4.3)的异方差。图形法: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 国巨应由散点图可以

8、看出，残差平方E2对解释变量 X的散点图主要分布在图形中的下三角部分, 大致看出残差平方 E2随X的变动呈增大的趋势，因此，模型很可能存在异方差。但是否 确实存在异方差还应通过更进一步的检验。Goldfeld-Quanadt 检验O WdfHiIk UNTITLEDd喟ew|ProcObject Print Save Details+/-1 ShoTFEtdi StofgMete Genr|SampleRange: 1 311 - 31 obsDisplay Filter Sample 1 31 - 31 obs国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图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图1-2卜面求F统计量值。基于图1-1 和图1-2中残差平方和的数据，即 Sumsquared resid的值。由图1-1计算得到的残差平方和为51931.29 ,由图1-2计算得到的残差平方和为 927645.3,根据 Goldfeld-Quanadt 检验，F统计量为927645.3/51931.29=17.8629判断：在 a =0.05下，在式中分子、分母的自由度均为9,查F分布表得临界值为F0.0

14、5(9,9) =3.18 ,因为F=17.86293.18 ,所以拒绝原假设,表明模型确实存在异方差White异方差检验rWle: UNTITLEDPrint | Sar 131 - 311005值 131 - 31ObS.id根据White统计量的分析：从图可以看出，nRA2= 7.583705 ,由 White检验知，在a =0.05下，查x2分布表，得临界值 xA2 0.05(2)= 5.9915比较计算的 x2统计量与临界值，因为 nRA2= 7.5837055.9915所以拒绝原假设，接受备择假设，表明模型存在异方差。根据White统计量所对应 p值的分析：给定显著性水平 a =0.

15、05 ,因为 Probability (White) =0.01970.05所以拒绝原假设，表明模型存在异方差。(3)修正异方差。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闻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号quz(J0 上 12819S.D. dependentvar473.4392S.E. of regression206 9941Sum squ