天津大學(xué)版經(jīng)濟(jì)計(jì)量學(xué)課后習(xí)題答案

1、4.61.進(jìn)行最小二乘估計(jì),結(jié)果為：Dependent Variable: YMethod： Least SquaresSample: 1 20Included observations: 20VariableCoefficientStd. Errort-StatisticProb.c29.0322747.260190.6143070. 5467X0.8061780. 01695147. 559560. 0000R-SQuared0.992105Mean dependent var2188.500Adjusted R-squared0.991666S. D. dependent var642.

2、 2246S. E. of regression58.62795Akaike info criterion11. 07494Sum squared resid61870.26Schwarz criterion11. 17451Log likelihood-108.7494F-statistic2261.912Durbin-Watson stat2.066630Prob (F-statistic)0. 000000Y = 29.03227493 + 0. 8061776361*X2.異方差檢驗(yàn)散點(diǎn)圖如下X與Y散點(diǎn)分布的相關(guān)圖顯示隨機(jī)項(xiàng)存在遞增的異方差3 .用Goldfeld-Quandt檢驗(yàn)分析

3、異方差性假設(shè)：H0：隨機(jī)項(xiàng)是同方差的H1：隨機(jī)項(xiàng)是遞增異方差的第一個(gè)子樣本數(shù)據(jù)為進(jìn)行最小二乘估計(jì)(010),Dependent Variable: YMethod: Least SquaresSample: 1 10Included observations: 10VariableCoefficientStd. Errort-StatisticProb.c-90.22196123. 2315-0.7321340. 4850X0.8698120. 05844214.883460. 0000R-SQuared0.965144Mean dependent var1735. 600Adjusted R

4、-squared0.960787S. D. dependent var186. 8839S E of regression37.00713Akaike info criterion10. 23695Sum squared resid10956. 22Schwarz criterion10. 29747Log likelihood-49.18477F-statistic221.5174Durbin-Watson stat2. 939370Prob (F-statistic)0. 000000Y = -90.22196172 + 0.8698118059*X表中的殘差平方和為10956. 22第二

5、個(gè)子樣本數(shù)據(jù)(1廣20),進(jìn)行最小二乘估計(jì)為Dependent Variable: YMethod： Least SquaresSample: 11 20Included observations: 10VariableCoefficientStd. Errort-StatisticProb.c-79.77156108. 5232-0.7350650. 4833X0.8351760. 03257325. 640250. 0000R-squared0.987978Mean dependent var2641.400Adjusted R-squared0.986475S. D. dependent

6、 var616. 4322S. E. of regression71.68987Akaike info criterion11.55943Sum squared resid41115. 50Schwarz criterion11.61995Log likelihood-55.79716F-statistic657. 4227Durbin-Watson stat1.971395Prob (F-statistic)0. 000000Y = -79. 77156004 + 0.8351763428*X表中的殘差平方和為41115. 50從而G-Q檢驗(yàn)的F統(tǒng)計(jì)量為F二ESS2/ESS1=3. 7527

7、08507,F0. 05 (10-1-1, 10-1-1) 40.05 (8, 8) =3. 44F> F0. 05 (8, 8)隨機(jī)項(xiàng)存 在遞增的異方差4 .異方差的修正變量代換后最小二乘估計(jì)的Eviews輸出表Dependent Variable： YMethod： Least SquaresSample: 1 20Included observations: 20Weighting series: 1/XVariableCoefficientStd. Errort-StatisticProb.c45.4633751.691340. 8795160. 3907X0. 7998340.

8、02126637. 610750. 0000Weighted StatisticsR-squared0. 041204Mean dependent var2044.832Adjusted R-squared-0. 012062S. D. dependent var55.15445S. E. of regression55.48609Akaike info criterion10. 96478Sum squared resid55416. 72Schwarz criterion11.06435Log likelihood-107. 6478F-statistic0. 773548Durbin-W

9、atson stat2. 090260Prob(F-statistic)0. 390713Unweighted StatisticsR-squared0. 992043Mean dependent var2188. 500Adjusted R-squared0. 991601S.D. dependent var642. 2246S. E. of regression58.85852Sum squared resid62357. 86Durbin-Watson stat2. 072106得到原模型對(duì)應(yīng)參數(shù)的加權(quán)對(duì)小二乘估計(jì)?；貧w方程為,Y=45. 4633662 +0. 7998344672*X

10、4.7 證明：Yi=bXi+ £ i Var( £ i) = o 2Xi2線性：因?yàn)閰?shù)的最小二乘估計(jì)量的表達(dá)式只依賴于殘差平方和最小這一原則，與隨機(jī)項(xiàng)t i的古典假設(shè)無關(guān)，因此線性特征任成立。.»涓2*坦/1=.，=二 ,令，則爐爐SV Zm=XxN滅=。 /if一 W 2 工Xjil根據(jù)經(jīng)典假設(shè)8,因?yàn)閤i不全為零，所以Ki不全為零，故線性關(guān)系成立。無偏性：參數(shù)的最小二乘估計(jì)量的無偏性依賴于解釋變量的非隨機(jī)變量和隨 機(jī)項(xiàng)的零均值假定，與同方差假定無關(guān)，因此隨機(jī)項(xiàng)存在異方差時(shí)，并不影響到無 偏性的成立。夙團(tuán)=EXr XY XrY = Xr XY XrE(XB +

11、 £)= /?最小方差性：在模型的所有線性無偏估計(jì)兩種，最小二乘估計(jì)量的方差最小 的前提條件是隨機(jī)項(xiàng)ei是同方差的，如果隨機(jī)項(xiàng)是異方差的，就不能保證最小 二乘估計(jì)量的方差最小。y。= Qg + 2 K 島)-其值隨Xi而變化，會(huì)夸大或縮小真實(shí)的方差和協(xié)/差，因此無法確定最小方差 性。5 . 7.1. 進(jìn)行最小二乘估計(jì)Dependent Variable: YMethod： Least SquaresSample: 1 20Included observations: 20VariableCoefficientStd. Errort-StatisticProb.c-1. 4547500

12、. 214146-6. 7932610. 0000X0. 1762830. 001445122.01700. 0000R-SQuared0. 998792Mean dependent var24.56900Adjusted R-squared0. 998725S. D. dependent var2. 410396S. E. of regression0. 086056Akaike info criterion-1. 972991Sum squared resid0. 133302Schwarz criterion-1.873418Log likelihood21. 72991Hannan-Q

13、uinn criter.-1.953553F-statistic14888. 14Durbin-Watson stat0.734726Prob (F-statistic)0. 000000回歸方程為,Y = -1. 454750 + 0. 17628*X2. D-W檢驗(yàn)分析隨機(jī)項(xiàng)的一階自相關(guān)性作散點(diǎn)圖如下相鄰2期殘差散點(diǎn)分布的自相關(guān)圖顯示隨機(jī)項(xiàng)存在一階的正自相關(guān)利用D-W方法檢驗(yàn)隨機(jī)項(xiàng)的自相關(guān)。在表中，D-W檢驗(yàn)的d統(tǒng)計(jì)量值為 0.734726,dL=l. 20 dU=L41（KddL,拒絕H0,故隨機(jī)項(xiàng)存在一階的正自相關(guān)。3. 用Durbin兩步法估計(jì)回歸模型的參數(shù)（1）估計(jì)一階自相關(guān)系數(shù)根

14、據(jù)Eviews軟件計(jì)算殘差關(guān)于其滯后項(xiàng)回歸的Eviews輸出表如下Dependent Variable： RMethod: Least SquaresSample (adjusted): 2 20Included observations: 19 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.R(-l)0. 6311640. 1832943.4434500. 0029R-SQuared0. 396971Mean dependent var0. 001371Adjusted R-squared0. 396971S.D.

15、 dependent var0. 085825S. E. of regression0. 066648Akaike info criterion-2.527598Sum squared resid0. 079954Schwarz criterion-2.477891Prob(F-statistic)0. 000000得到原模型對(duì)應(yīng)系數(shù)的廣義最小二乘估計(jì)值YY = -0. 3941168467 + 0. 173它*x,*XX（4）直接用差分法估計(jì)回歸模型參數(shù)Dependent Variable: YYMethod: Least SquaresDate: 11/22/14 Time: 22:57S

16、ample (adjusted): 2 20Included observations： 19 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.c0. 0405280. 0226421. 7899590. 0913XX0. 1587830. 00724821. 907560. 0000R-squared0. 965791Mean dependent var0.411579Adjusted R-squared0. 963778S. D. dependent var0.344146S. E. of regression0. 065498Akaike info criterion-2.514302Sum squared resid0. 072929Schwarz criterion-2.414888Log likelihood25. 88587Hannan-Quinn criter.-2.497477F-statistic479. 9410Durbin-Watson stat1. 748834Prob (F-statistic