EViews計量經(jīng)濟學試驗報告-異方差的診斷及修正模板

1、姓名 學號實驗題目異方差的診斷與修正一、實驗目的與要求：要求目的：1用圖示法初步判斷是否存在異方差，再用White檢驗異方差；2、用加權(quán)最小二乘法修正異方差。二、實驗內(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)，運用EV軟件，做回歸分析，用圖示法，White檢驗模型是否存在異方差，如果存在異方差，運用加權(quán)最小二乘法修正異方差。三、實驗過程：（實踐過程、實踐所有參數(shù)與指標、理論依據(jù)說明等）（一）模型設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，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化學原料制

3、品502.614195.22醫(yī)約制造業(yè)238.711264.1化學纖維制造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普通機械制造354.692351.68專用設備制造238.161714.73交通運輸設備511.944011.53電子機械制造409.833286.15電子通信設備508.154499.19儀器儀表設備72.46663.68(二)參數(shù)估計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，t=12.36670 > 軸曲(26) =2.056 ,拒絕原假設，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）檢驗模型的異方差（一）圖形法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的變動呈增大趨勢因此，模型很可能存在異方差但是否確實存在異方差還應該通過更近一步的檢驗。探(二)White檢驗White檢驗結(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、因為本例為一元函數(shù)，沒有交叉乘積項，則輔助函數(shù)為從上表可以看出，n R 2 =6.270612 ,有White檢驗知，在：=0,05下，查2分布表，得臨界值20.05 (2) =5.99147 。比較計算的2統(tǒng)計量與臨界值，因為 n R2= 6.270612 >2q.q5(2) =5.99147 ,所以拒絕原假設，不拒絕備擇假設，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)異方差的修正在運用加權(quán)最小二乘法估計過程中,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)估計檢驗，發(fā)現(xiàn)用權(quán)數(shù)t , -, 3t的結(jié)果，其可決系數(shù)反而減小；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的估計結(jié)果為：Y?= 6.496703 + 0.106892 Xi(1.863374)( 9.725260 )2R =0.922715DW=1.905670 F= 94.58068括號中的數(shù)據(jù)為t統(tǒng)計量值。由上可以看出，運用加權(quán)最小二乘法消除了異方差后，參數(shù)'-2的t檢驗顯著，可決系數(shù)提高了不少，F(xiàn)檢驗也顯著，并說明銷售收入每增長1元，銷售利潤平均增長0.106892元。四、實踐結(jié)果報告：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的變動呈增大趨勢。因此，模型很可能存在異方差。但是否確實存在異方差還應該通過更近一步的檢驗。再用White檢驗異方差：因為n R2 = 6.270612 >E 2o.o5 (2)=5.99147 ,所以拒絕原假設，不拒絕備擇假設，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括號中的數(shù)據(jù)為t統(tǒng)計量值。2由上可以看出，R =0.922715,擬合程度較好。在給定=0.0時，t= 9.725260>t0.025 (26)=2.056 ,拒絕原假設，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。運用加權(quán)最小二乘法后，參數(shù) 七的t檢驗顯著，可決系數(shù)提高了不少，F(xiàn)檢驗也顯著，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檢驗修正后的模型是否還存在異方差：White檢驗結(jié)果White Heteroskedasticity Test:F-statistic3.144597Probability0.