EViews計(jì)量經(jīng)濟(jì)學(xué)試驗(yàn)報(bào)告-異方差的診斷及修正模板

1、姓名 學(xué)號(hào)實(shí)驗(yàn)題目異方差的診斷與修正一、實(shí)驗(yàn)?zāi)康呐c要求：要求目的：1用圖示法初步判斷是否存在異方差，再用White檢驗(yàn)異方差；2、用加權(quán)最小二乘法修正異方差。二、實(shí)驗(yàn)內(nèi)容根據(jù)1998年我國重要制造業(yè)的銷售利潤與銷售收入數(shù)據(jù)，運(yùn)用EV軟件，做回歸分析，用圖示法，White檢驗(yàn)?zāi)Ｐ褪欠翊嬖诋惙讲?，如果存在異方差，運(yùn)用加權(quán)最小二乘法修正異方差。三、實(shí)驗(yàn)過程：（實(shí)踐過程、實(shí)踐所有參數(shù)與指標(biāo)、理論依據(jù)說明等）（一）模型設(shè)定為了研究我國重要制造業(yè)的銷售利潤與銷售收入是否有關(guān)，假定銷售利潤與銷售收入之間滿足線性約束，則理論模型設(shè)定為：Yi= + 'Xi + 叫其中，Y表示銷售利潤，Xi表示銷售收入。

2、由1998年我國重要制造業(yè)的銷售收入與銷售利潤的數(shù)據(jù)，如圖1 :1988年我國重要制造業(yè)銷售收入與銷售利潤的數(shù)據(jù)（單位：億元）行業(yè)名稱銷售利潤Y銷售收入X食品加工業(yè)187.253180.44食品制造業(yè)111.421119.88飲料制造業(yè)205.421489.89煙草加工業(yè)183.871328.59紡織業(yè)316.793862.9服裝制造業(yè)157.71779.1皮革羽絨制品81.731081.77木材加工業(yè)35.67443.74家具制造業(yè)31.06226.78造紙及紙制品134.41124.94印刷業(yè)90.12499.83文教體育用品54.4504.44石油加工業(yè)194.452363.8化學(xué)原料制

3、品502.614195.22醫(yī)約制造業(yè)238.711264.1化學(xué)纖維制造81.57779.46橡膠制品業(yè)77.84692.08塑料制品業(yè)144.341345非金屬礦制業(yè)339.262866.14黑色金屬冶煉367.473868.28有色金屬冶煉144.291535.16金屬制品業(yè)201.421948.12普通機(jī)械制造354.692351.68專用設(shè)備制造238.161714.73交通運(yùn)輸設(shè)備511.944011.53電子機(jī)械制造409.833286.15電子通信設(shè)備508.154499.19儀器儀表設(shè)備72.46663.68(二)參數(shù)估計(jì)Depe ndent Variable: Y Meth

4、od: Least SquaresDate: 10/19/05 Time: 15:27Sample: 1 28In cluded observati ons: 28VariableCoefficie ntStd. Errort-StatisticProb.C12.0356419.517790.6166500.5428X0.1043930.00844112.366700.0000R-squared0.854696Mean depe ndent var213.4650Adjusted R-squared0.849107S.D.dependent var146.4895S.E. of regress

5、i on56.90368Akaike info criteri on10.98935Sum squared resid84188.74Schwarz criteri on11.08450Log likelihood-151.8508F-statistic152.9353Durb in -Watson stat1.212795Prob(F-statistic)0.000000估計(jì)結(jié)果為： Y? = 12.03564 + 0.104393 Xi(19.51779 )(0.008441)t= ( 0.616650 )( 12.36670 )2 2R =0.854696 R =0.849107 S.E

6、.=56.89947DW=1.212859F=152.9353這說明在其他因素不變的情況下，銷售收入每增長1元，銷售利潤平均增長 0.104393元。R =0.854696 ,擬合程度較好。在給定=0.0 時(shí)，t=12.36670 > 軸曲(26) =2.056 ,拒絕原假設(shè)，說明銷售收入對銷售利潤有顯著性影響。F=152.9353 > F0.O5 （1,26） = 4.23 ,表明方程整體顯著。（三）檢驗(yàn)?zāi)Ｐ偷漠惙讲睿ㄒ唬﹫D形法600500*.* 400.tY 300,.200''100: *0010002000300040005000X2500020000150

7、00 -10000 -.#5000* 多 . 0 一 一一亶 J L* I100020003000400050006、判斷由圖3可以看出，被解釋變量 Y隨著解釋變量X的增大而逐漸分散，離散程度越來越大；2同樣，由圖4可以看出，殘差平方 e對解釋變量X的散點(diǎn)圖主要分布在圖形中的下三角部2分，大致看出殘差平方 e隨X的變動(dòng)呈增大趨勢因此，模型很可能存在異方差但是否確實(shí)存在異方差還應(yīng)該通過更近一步的檢驗(yàn)。探(二)White檢驗(yàn)White檢驗(yàn)結(jié)果White Heteroskedasticity Test:F-statistic3.607218Probability0.042036Obs*R-squar

8、ed6.270612Probability0.043486Test Equati on:Depe ndent Variable: RESIDEMethod: Least SquaresDate: 10/19/05 Time: 15:29Sample: 1 28In cluded observati ons: 28VariableCoefficie ntStd. Errort-StatisticProb.C-3279.7792857.117-1.1479330.2619X5.6706343.1093631.8237280.0802Xa2-0.0008710.000653-1.3340000.19

9、42R-squared0.223950Mean depe ndent var3006.741Adjusted R-squared0.161866S.D.dependent var5144.470S.E. of regressi on4709.744Akaike info criteri on19.85361Sum squared resid5.55E+08Schwarz criteri on19.99635Log likelihood-274.9506F-statistic3.607218Durb in -Watson stat1.479908Prob(F-statistic)0.042036

10、2、因?yàn)楸纠秊橐辉瘮?shù)，沒有交叉乘積項(xiàng)，則輔助函數(shù)為從上表可以看出，n R 2 =6.270612 ,有White檢驗(yàn)知，在：=0,05下，查2分布表，得臨界值20.05 (2) =5.99147 。比較計(jì)算的2統(tǒng)計(jì)量與臨界值，因?yàn)?n R2= 6.270612 >2q.q5(2) =5.99147 ,所以拒絕原假設(shè)，不拒絕備擇假設(shè)，這表明模型存在異方差。分別選用了權(quán)數(shù)'1t =1/ Xt,'2t = 1/ Xt2, '3t = 1/ X t(四)異方差的修正在運(yùn)用加權(quán)最小二乘法估計(jì)過程中,Depe ndent Variable: YR-squaredAdjust

11、ed R-squaredS.E. of regressi onSum squared resid Log likelihood0.032543 Mean depe ndent var-0.004667 S.D. dependent var32.07117 Akaike info criteri on26742.56 Schwarz criteri on-135.7956F-statistic123.406031.996599.8425419.937699177.3515Durb in -Watson stat1.465148 Prob(F-statistic)0.000000Un weight

12、ed StatisticsR-squared0.853095 Mean depe ndent varAdjusted R-squared0.847445 S.D. dependent var213.4650146.4895S.E. of regressi on Durb in -Watson stat57.21632 Sum squared resid85116.401.261469Method: Least SquaresDate: 10/22/10Time: 00:13Sample: 1 28In cluded observati ons: 28Weight ing series: W1V

13、ariableCoefficie ntStd. Errort-StatisticProb.C5.9883516.4033920.9351840.3583X0.1086060.00815513.317340.0000Weighted Statistics用權(quán)數(shù)''2t的結(jié)果Depe ndent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:16Sample: 1 28In cluded observati ons: 28Weighti ng series: W2VariableCoefficie ntStd. Er

14、rort-StatisticProb.C6.4967033.4865261.8633740.0737X0.1068920.0109919.7252600.0000Weighted StatisticsR-squared0.922715Mean depe ndent var67.92129Adjusted R-squared0.919743S.D.dependent var75.51929S.E. of regressi on21.39439Akaike info criteri on9.032884Sum squared resid11900.72Schwarz criteri on9.128

15、041Log likelihood-124.4604F-statistic94.58068Durb in -Watson stat1.905670Prob(F-statistic)0.000000Un weighted StatisticsR-squared0.854182Mean depe ndent var213.4650Adjusted R-squared0.848573S.D.dependent var146.4895S.E. of regressi on57.00434Sum squared resid84486.88Durb in -Watson stat1.242212用權(quán)數(shù)-&

16、#39;3t的結(jié)果Depe ndent Variable: Y Method: Least Squares Date: 10/22/10 Time: 00:17 Sample: 1 28In cluded observati ons: 28Weighti ng series: W3VariableCoefficie ntStd. Errort-StatisticProb.X0.1061530.00774613.704730.0000Weighted StatisticsR-squared0.611552Mean depe ndent var165.8420Adjusted R-squared0

17、.596612S.D.dependent var67.13044S.E. of regressi on42.63646Akaike info criteri on10.41205Sum squared resid47264.56Schwarz criteri on10.50720Log likelihood-143.7686F-statistic187.8197Durb in -Watson stat1.275429Prob(F-statistic)0.000000Un weighted StatisticsR-squared0.854453Mean depe ndent var213.465

18、0Adjusted R-squared0.848855S.D.dependent var146.4895S.E. of regressi on56.95121Sum squared resid84329.44Durb in -Watson stat1.233545C8.64034111.187330.7723330.4469經(jīng)估計(jì)檢驗(yàn)，發(fā)現(xiàn)用權(quán)數(shù)t , -, 3t的結(jié)果，其可決系數(shù)反而減??；只有用權(quán)數(shù) 2t的效果 最好，可決系數(shù)增大。用權(quán)數(shù)？，2t的結(jié)果Depe ndent Variable: YMethod: Least SquaresDate: 10/22/10 Time: 00:16Sa

19、mple: 1 28In cluded observati ons: 28Weighti ng series: W2VariableCoefficie ntStd. Errort-StatisticProb.C6.4967033.4865261.8633740.0737X0.1068920.0109919.7252600.0000Weighted StatisticsR-squared0.922715Mean depe ndent var67.92129Adjusted R-squared0.919743S.D.dependent var75.51929S.E. of regressi on2

20、1.39439Akaike info criteri on9.032884Sum squared resid11900.72Schwarz criteri on9.128041Log likelihood-124.4604F-statistic94.58068Durb in -Watson stat1.905670Prob(F-statistic)0.000000Un weighted StatisticsR-squared0.854182Mean depe ndent var213.4650Adjusted R-squared0.848573S.D.dependent var146.4895

21、S.E. of regressi on57.00434Sum squared resid84486.88Durb in -Watson stat1.242212用權(quán)數(shù)'-2t的估計(jì)結(jié)果為：Y?= 6.496703 + 0.106892 Xi(1.863374)( 9.725260 )2R =0.922715DW=1.905670 F= 94.58068括號(hào)中的數(shù)據(jù)為t統(tǒng)計(jì)量值。由上可以看出，運(yùn)用加權(quán)最小二乘法消除了異方差后，參數(shù)'-2的t檢驗(yàn)顯著，可決系數(shù)提高了不少，F(xiàn)檢驗(yàn)也顯著，并說明銷售收入每增長1元，銷售利潤平均增長0.106892元。四、實(shí)踐結(jié)果報(bào)告：1用圖示法初步判斷

22、是否存在異方差：被解釋變量Y隨著解釋變量X的增大而逐漸分散，一一 2離散程度越來越大；同樣的，殘差平方ei對解釋變量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 ei隨Xi的變動(dòng)呈增大趨勢。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)該通過更近一步的檢驗(yàn)。再用White檢驗(yàn)異方差：因?yàn)閚 R2 = 6.270612 >E 2o.o5 (2)=5.99147 ,所以拒絕原假設(shè)，不拒絕備擇假設(shè)，這表明模型存在異方差。2、用加權(quán)最小二乘法修正異方差：發(fā)現(xiàn)用權(quán)數(shù)-.2t的效果最好，則估計(jì)結(jié)果為：Y?= 6.496703+0.106892 Xi(1.863374 )( 9.72

23、5260 )2R =0.922715DW=1.905670 F=94.58068括號(hào)中的數(shù)據(jù)為t統(tǒng)計(jì)量值。2由上可以看出，R =0.922715,擬合程度較好。在給定=0.0時(shí)，t= 9.725260>t0.025 (26)=2.056 ,拒絕原假設(shè)，說明銷售收入對銷售利潤有顯著性影響。F=94.58068 > F0.05(1,26) = 4.23 ,表明方程整體顯著。運(yùn)用加權(quán)最小二乘法后，參數(shù) 七的t檢驗(yàn)顯著，可決系數(shù)提高了不少，F(xiàn)檢驗(yàn)也顯著，并說明銷售收入每增長1元，銷售利潤平均增長 0.106892元。3、再用 White檢驗(yàn)修正后的模型是否還存在異方差：White檢驗(yàn)結(jié)果White Heteroskedasticity Test:F-statistic3.144597Probability0.