《计量经济学》课程实验报告
实验序号 2 实验名称 Eviews的异方差检验与校正 实验组别 12 模拟角色 实验地点 2教602 指导老师 刘冬萍 实验日期 11月29日 实验时间 16:05——17:45 一、实验目的及要求 学会使用计量学分析软件Eviews的异方差检验与校正功能。 二、实验环境 2教602,经管学院电脑实验室 三、实验内容与步骤 DATA Y X SORT X 1.生成相关图 SCAT X Y 1086Y420050100150200X 根据相关图随着X的增大Y的取值范围不断增大,所以方程存在异方差. 2.方程的异方差检验
（1）WHITE 检验 建立回归模型 LS Y C X
Dependent Variable: Y Method: Least Squares Date: 11/22/12 Time: 17:06 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 0.859469 0.709057 1.212130 0.2411 X
0.036340
0.009633
3.772393
0.0014 R-squared
0.441531 Mean dependent var 3.100000 Adjusted R-squared 0.410504 S.D. dependent var 2.255986 S.E. of regression 1.732115 Akaike info criterion 4.031203 Sum squared resid 54.00399 Schwarz criterion 4.130776 Log likelihood -38.31203 F-statistic 14.23095 Durbin-Watson stat
2.111232 Prob(F-statistic)
0.001395
进行WHITE 检验
White Heteroskedasticity Test: F-statistic 6.172459 Probability 0.009656 Obs*R-squared
8.413667 Probability
0.014893
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 11/22/12 Time: 17:07 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C -0.840162 3.268547 -0.257045 0.8002 X 0.034691 0.096616 0.359062 0.7240 X^2 0.000259 0.000550 0.470375 0.6441 R-squared
0.420683 Mean dependent var 2.700200 Adjusted R-squared 0.352528 S.D. dependent var 5.061699 S.E. of regression 4.072927 Akaike info criterion 5.784082 Sum squared resid 282.0085 Schwarz criterion 5.933442 Log likelihood -54.84082 F-statistic 6.172459 Durbin-Watson stat 2.196613 Prob(F-statistic) 0.009656 Nr^2=8.413677 因为检验的P=0.014893小于0.05,所以存在异方差. (2) PARK检验
LS Y C X
Dependent Variable: Y Method: Least Squares Date: 11/22/12 Time: 17:13 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 0.859469 0.709057 1.212130 0.2411 X
0.036340
0.009633
3.772393
0.0014 R-squared
0.441531 Mean dependent var 3.100000 Adjusted R-squared 0.410504 S.D. dependent var 2.255986 S.E. of regression 1.732115 Akaike info criterion 4.031203 Sum squared resid 54.00399 Schwarz criterion 4.130776 Log likelihood -38.31203 F-statistic 14.23095 Durbin-Watson stat
2.111232 Prob(F-statistic)
0.001395
GENR E2=LOG(RESID2) GENR LNX=LOG(X) LS LNE2 C LNX
Dependent Variable: LNE2 Method: Least Squares Date: 11/22/12 Time: 17:16 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C -7.692798 2.272023 -3.385881 0.0033 LNX
1.839358
0.571316
3.219514
0.0048 R-squared
0.365421 Mean dependent var -0.465580 Adjusted R-squared 0.330167 S.D. dependent var 1.915506 S.E. of regression 1.567714 Akaike info criterion 3.831754 Sum squared resid 44.23911 Schwarz criterion 3.931327 Log likelihood -36.31754 F-statistic 10.36527 Durbin-Watson stat
1.937606 Prob(F-statistic)
0.004754
由上图可看出P分别为0.0033 ,0.0048,0.004754都是小概率事件,所以方程是显著的,表明随机误差项的方差随着解释变量的取值不同而不断变化,即存在异方差性.
（3）GLEISER检验
LS Y C X
GENR E=ABS(RESID) ○1GENR X1=X^0.5 LS E C X1
Dependent Variable: E1 Method: Least Squares Date: 11/28/12 Time: 13:14 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C -1.250444 0.637839 -1.960437 0.0656 X1
0.326534
0.081232
4.019775
0.0008 R-squared
0.473046 Mean dependent var 1.192860 Adjusted R-squared 0.443771 S.D. dependent var 1.159531 S.E. of regression 0.864787 Akaike info criterion 2.641972 Sum squared resid 13.46141 Schwarz criterion 2.741545 Log likelihood -24.41972 F-statistic 16.15859 Durbin-Watson stat
2.047999 Prob(F-statistic)
0.000804
|e1|=-1.250444+0.326534X1^0.5
R^2=0.473046 F=16.15859 P=0.000804 ○2GENR X2=X^-2 LS E C X2 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:27 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 1.665123 0.342774 4.857786 0.0001 X2
-657.9505
338.0359
-1.946392
0.0674
R-squared
0.173874 Mean dependent var 1.192860 Adjusted R-squared 0.127978 S.D. dependent var 1.159531 S.E. of regression 1.082794 Akaike info criterion 3.091607 Sum squared resid 21.10398 Schwarz criterion 3.191180 Log likelihood -28.91607 F-statistic 3.788442 Durbin-Watson stat
1.454864 Prob(F-statistic)
0.067388
|e2|=1.665123-657.9505X^-2
R^2=0.173874 F=3.788442 P=0.067388 ○3GENR X3=X^2 LS E C X3 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:32 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 0.580535 0.237632 2.443001 0.0251 X3
0.000113
2.67E-05
4.233931
0.0005 R-squared
0.498972 Mean dependent var 1.192860 Adjusted R-squared 0.471138 S.D. dependent var 1.159531 S.E. of regression 0.843245 Akaike info criterion 2.591520 Sum squared resid 12.79911 Schwarz criterion 2.691093 Log likelihood -23.91520 F-statistic 17.92617 Durbin-Watson stat 2.064289 Prob(F-statistic)
0.000499
|e3|=0.580535+0.000113X4^2
R^2=0.498972 F=17.92617 P=0.000499
○4GENR X4=X^-0,5 LS E C X4 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:36 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 3.473060 0.761805 4.558987 0.0002 X4 -15.53960 4.981434 -3.119503 0.0059 R-squared
0.350914 Mean dependent var 1.192860 Adjusted R-squared 0.314854 S.D. dependent var 1.159531 S.E. of regression 0.959785 Akaike info criterion 2.850424 Sum squared resid 16.58137 Schwarz criterion 2.949998 Log likelihood -26.50424 F-statistic 9.731299 Durbin-Watson stat 1.759756 Prob(F-statistic) 0.005921 |e4|=3.473060-15.53960 X^-0.5
R^2=0.350914 F=9.731299 P=0.005921
○5GENR X5=X^-1 LS E C X5 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:45 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 2.265778 0.462875 4.895014 0.0001 X5
-45.87625
17.27699
-2.655339
0.0161 R-squared
0.281461 Mean dependent var 1.192860 Adjusted R-squared 0.241542 S.D. dependent var 1.159531 S.E. of regression 1.009829 Akaike info criterion 2.952079 Sum squared resid 18.35560 Schwarz criterion 3.051653 Log likelihood -27.52079 F-statistic 7.050824 Durbin-Watson stat
1.627325 Prob(F-statistic)
0.016106
|e5|=2.265778-45.87625X^-1
R^2=0.281461 F=7.050824 P=0.016106
由以上的五个方程表明，利润函数存在异方差性（只要取显著水平a大于
0.067388）
3.WLS方法估计利润函数
(1)利用最小二乘法估计模型 LS Y C X
Dependent Variable: Y Method: Least Squares Date: 11/28/12 Time: 12:40 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 0.859469 0.709057 1.212130 0.2411 X 0.036340 0.009633 3.772393 0.0014 R-squared
0.441531 Mean dependent var 3.100000 Adjusted R-squared 0.410504 S.D. dependent var 2.255986 S.E. of regression 1.732115 Akaike info criterion 4.031203 Sum squared resid
54.00399 Schwarz criterion
4.130776
Log likelihood -38.31203 F-statistic 14.23095 Durbin-Watson stat
2.111232 Prob(F-statistic)
0.001395
得到:y^=0.859469+0.036340X R^2=0.441531
(0.2411)
(0.0014)
T=(1.212130) (3.772393 )
(2)生成权数变量： 根据帕克检验得到： Ls y c x
Genr lne2=log(resid^2) Genr lnx=log(x) Ls lne2 c lnx
Dependent Variable: LNE2 Method: Least Squares Date: 11/28/12 Time: 12:56 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C -7.692798 2.272023 -3.385881 0.0033 LNX
1.839358
0.571316
3.219514
0.0048
R-squared
0.365421 Mean dependent var -0.465580 Adjusted R-squared 0.330167 S.D. dependent var 1.915506 S.E. of regression 1.567714 Akaike info criterion 3.831754 Sum squared resid 44.23911 Schwarz criterion 3.931327 Log likelihood -36.31754 F-statistic 10.36527 Durbin-Watson stat
1.937606 Prob(F-statistic)
0.004754
LNEi^2=--7.692798+1.839358LNX R^2=0.365421 进行戈里瑟检验 LS Y C X
GENR E=ABS(RESID) ○1GENR X1=X^0.5 LS E C X1
Dependent Variable: E1 Method: Least Squares Date: 11/28/12 Time: 13:14 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C -1.250444 0.637839 -1.960437 0.0656 X1 0.326534 0.081232 4.019775 0.0008 R-squared
0.473046 Mean dependent var 1.192860 Adjusted R-squared 0.443771 S.D. dependent var 1.159531 S.E. of regression 0.864787 Akaike info criterion 2.641972 Sum squared resid 13.46141 Schwarz criterion 2.741545 Log likelihood -24.41972 F-statistic 16.15859 Durbin-Watson stat
2.047999 Prob(F-statistic)
0.000804
|e1|=-1.250444+0.326534X1^0.5
R^2=0.473046 F=16.15859 P=0.000804 ○2GENR X2=X^-2 LS E C X2 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:27 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 1.665123 0.342774 4.857786 0.0001 X2 -657.9505 338.0359 -1.946392 0.0674 R-squared
0.173874 Mean dependent var 1.192860 Adjusted R-squared 0.127978 S.D. dependent var 1.159531 S.E. of regression 1.082794 Akaike info criterion 3.091607 Sum squared resid 21.10398 Schwarz criterion 3.191180 Log likelihood -28.91607 F-statistic 3.788442 Durbin-Watson stat 1.454864 Prob(F-statistic) 0.067388 |e2|=1.665123-657.9505X^-2
R^2=0.173874 F=3.788442 P=0.067388 ○3GENR X3=X^2 LS E C X3 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:32 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 0.580535 0.237632 2.443001 0.0251 X3 0.000113 2.67E-05 4.233931 0.0005 R-squared
0.498972 Mean dependent var 1.192860 Adjusted R-squared 0.471138 S.D. dependent var 1.159531 S.E. of regression 0.843245 Akaike info criterion 2.591520 Sum squared resid 12.79911 Schwarz criterion 2.691093 Log likelihood -23.91520 F-statistic 17.92617 Durbin-Watson stat 2.064289 Prob(F-statistic)
0.000499
|e3|=0.580535+0.000113X4^2
R^2=0.498972 F=17.92617 P=0.000499
○4GENR X4=X^-0,5 LS E C X4 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:36 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 3.473060 0.761805 4.558987 0.0002 X4
-15.53960
4.981434
-3.119503
0.0059 R-squared
0.350914 Mean dependent var 1.192860 Adjusted R-squared 0.314854 S.D. dependent var 1.159531 S.E. of regression 0.959785 Akaike info criterion 2.850424 Sum squared resid 16.58137 Schwarz criterion 2.949998 Log likelihood -26.50424 F-statistic 9.731299 Durbin-Watson stat
1.759756 Prob(F-statistic)
0.005921
|e4|=3.473060-15.53960 X^-0.5 R^2=0.350914 F=9.731299 P=0.005921
○5GENR X5=X^-1 LS E C X5 Dependent Variable: E Method: Least Squares Date: 11/28/12 Time: 13:45 Sample: 1 20
Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob. C 2.265778 0.462875 4.895014 0.0001 X5 -45.87625 17.27699 -2.655339 0.0161 R-squared
0.281461 Mean dependent var 1.192860 Adjusted R-squared 0.241542 S.D. dependent var 1.159531 S.E. of regression 1.009829 Akaike info criterion 2.952079 Sum squared resid 18.35560 Schwarz criterion 3.051653 Log likelihood -27.52079 F-statistic 7.050824 Durbin-Watson stat 1.627325 Prob(F-statistic) 0.016106 |e5|=2.265778-45.87625X^-1
R^2=0.281461 F=7.050824 P=0.016106
由上可得在戈里瑟检验里最显著的是：|e3|=0.580535+0.000113X4^2 R^2=0.498972 F=17.92617 P=0.000499 所以取权数变量为 : GENR W1=1/X^1.839358
GENR W2=X^2
另外取： GENR W3=1/ABS(RESID) GENR W4=1/RESID^2 （3）利用最小二乘法估计模型：
模型一LS(W=W1) Y C X
Dependent Variable: Y Method: Least Squares Date: 11/28/12 Time: 14:00 Sample: 1 20
Included observations: 20 Weighting series: W1
Variable Coefficient Std. Error t-Statistic Prob. C -0.625981 0.318225 -1.967103 0.0648 X
0.071060
0.011649 6.100161 0.0000 Weighted Statistics R-squared
0.573253 Mean dependent var 1.734420 Adjusted R-squared 0.549545 S.D. dependent var 0.940124 S.E. of regression 0.630973 Akaike info criterion 2.011533 Sum squared resid 7.166292 Schwarz criterion 2.111106 Log likelihood -18.11533 F-statistic 24.17958 Durbin-Watson stat 1.896786 Prob(F-statistic) 0.000111 Unweighted Statistics R-squared
-0.050320 Mean dependent var 3.100000
Adjusted R-squared -0.108671 S.D. dependent var 2.255986 S.E. of regression 2.375406 Sum squared resid 101.5659
Durbin-Watson stat 1.104724
怀特检验的结果是
White Heteroskedasticity Test: F-statistic 0.986667 Probability 0.393183 Obs*R-squared 2.080114 Probability 0.353435
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 11/28/12 Time: 14:36 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 0.899486 0.438002 2.053611 0.0557 X -0.014613 0.012947 -1.128698 0.2747 X^2
6.64E-05
7.37E-05
0.901174
0.3801 R-squared
0.104006 Mean dependent var 0.358315 Adjusted R-squared -0.001405 S.D. dependent var 0.545410 S.E. of regression 0.545793 Akaike info criterion 1.764328 Sum squared resid 5.064137 Schwarz criterion 1.913688 Log likelihood -14.64328 F-statistic 0.986667 Durbin-Watson stat
2.743143 Prob(F-statistic)
0.393183
得到估计结果Y^=-0.625981+0.071060X
(0.318225) (6.100161) R^2=0.573253 NR^2=2.080114 P=0.393183
模型二LS(W=W2) Y C X
Dependent Variable: Y Method: Least Squares Date: 11/28/12 Time: 14:12 Sample: 1 20
Included observations: 20 Weighting series: W2
Variable Coefficient Std. Error t-Statistic Prob. C 4.378943 3.255974 1.344895 0.1954 X
0.006014
0.022701 0.264907 0.7941 Weighted Statistics
R-squared
0.702288 Mean dependent var 4.737844 Adjusted R-squared 0.685748 S.D. dependent var 8.767922 S.E. of regression 4.915135 Akaike info criterion 6.117155 Sum squared resid 434.8540 Schwarz criterion 6.216728 Log likelihood -59.17155 F-statistic 42.46109 Durbin-Watson stat 2.705915 Prob(F-statistic) 0.000004 Unweighted Statistics
R-squared
-0.428848 Mean dependent var 3.100000 Adjusted R-squared -0.508229 S.D. dependent var 2.255986 S.E. of regression 2.770576 Sum squared resid 138.1696
Durbin-Watson stat
0.878203
进行怀特检验的结果是
White Heteroskedasticity Test: F-statistic 46.95441 Probability 0.000000 Obs*R-squared
16.93442 Probability
0.000210
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 11/28/12 Time: 14:39 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 36.17065 19.84812 1.822372 0.0860 X -1.694246 0.586696 -2.887774 0.0102 X^2 0.016617 0.003339 4.976024 0.0001 R-squared
0.846721 Mean dependent var 21.74270 Adjusted R-squared 0.828688 S.D. dependent var 59.75546 S.E. of regression 24.73269 Akaike info criterion 9.391610 Sum squared resid 10399.00 Schwarz criterion 9.540970 Log likelihood -90.91610 F-statistic 46.95441 Durbin-Watson stat 2.837461 Prob(F-statistic) 0.000000 得到结果是：Y^=4.378943+0.006014X
(3.255974) (0.022701)
R^2=0.702288 NR^2=16.93442 P=0.00000
模型三LS(W=W3) Y C X
Dependent Variable: Y Method: Least Squares Date: 11/28/12 Time: 14:19
Sample: 1 20
Included observations: 20 Weighting series: W3
Variable Coefficient Std. Error t-Statistic Prob. C 0.707659 0.208266 3.397867 0.0032 X
0.038792
0.005388 7.200169 0.0000 Weighted Statistics R-squared
0.945796 Mean dependent var 2.344549 Adjusted R-squared 0.942785 S.D. dependent var 2.209824 S.E. of regression 0.528582 Akaike info criterion 1.657402 Sum squared resid 5.029181 Schwarz criterion 1.756975 Log likelihood -14.57402 F-statistic 314.0812 Durbin-Watson stat 1.849162 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared
0.439521 Mean dependent var 3.100000 Adjusted R-squared 0.408383 S.D. dependent var 2.255986 S.E. of regression 1.735229 Sum squared resid 54.19836
Durbin-Watson stat 2.097049 进行怀特检验得
White Heteroskedasticity Test: F-statistic 0.494755 Probability 0.618232 Obs*R-squared 1.100097 Probability 0.576922
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 11/28/12 Time: 14:40 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 0.181965 0.082153 2.214961 0.0407 X 0.001835 0.002428 0.755834 0.4601 X^2
-8.06E-06
1.38E-05
-0.583150
0.5674 R-squared
0.055005 Mean dependent var 0.251459 Adjusted R-squared -0.056171 S.D. dependent var 0.099611 S.E. of regression 0.102370 Akaike info criterion -1.582959 Sum squared resid 0.178155 Schwarz criterion -1.433599 Log likelihood 18.82959 F-statistic 0.494755 Durbin-Watson stat
2.096222 Prob(F-statistic)
0.618232
Y^=0.707659+0.038792X (0.208266) (0.005388)
R^2=0.945796 NR^2=1.100097 P=0.618232
模型四 LS(W=W4) Y C X
Dependent Variable: Y Method: Least Squares Date: 11/28/12 Time: 14:24 Sample: 1 20
Included observations: 20 Weighting series: W4 Variable Coefficient Std. Error t-Statistic Prob. C 0.591893 0.128353 4.611440 0.0002 X 0.042939 0.004093 10.49056 0.0000 Weighted Statistics R-squared
0.994979 Mean dependent var 2.087552 Adjusted R-squared 0.994700 S.D. dependent var 4.277070 S.E. of regression 0.311364 Akaike info criterion 0.598931 Sum squared resid 1.745056 Schwarz criterion 0.698505 Log likelihood -3.989313 F-statistic 3567.168 Durbin-Watson stat 2.173306 Prob(F-statistic) 0.000000 Unweighted Statistics
R-squared
0.422958 Mean dependent var 3.100000 Adjusted R-squared 0.390900 S.D. dependent var 2.255986 S.E. of regression 1.760681 Sum squared resid 55.79997
Durbin-Watson stat
2.027424
进行怀特检验的结果是
White Heteroskedasticity Test: F-statistic 0.851707 Probability 0.444108 Obs*R-squared
1.821500 Probability
0.402222
Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 11/28/12 Time: 14:42 Sample: 1 20
Included observations: 20 Variable Coefficient Std. Error t-Statistic Prob. C 0.275073 0.176282 1.560417 0.1371 X
-0.004839
0.005211
-0.928584
0.3661
X^2 2.04E-05 2.97E-05 0.687681 0.5009 R-squared
0.091075 Mean dependent var 0.087253 Adjusted R-squared -0.015857 S.D. dependent var 0.217943 S.E. of regression 0.219664 Akaike info criterion -0.055951 Sum squared resid 0.820291 Schwarz criterion 0.093409 Log likelihood 3.559512 F-statistic 0.851707 Durbin-Watson stat
2.356883 Prob(F-statistic)
0.444108
得到结果 ：Y^=0.591893+0.042939X
(0.128353) (0.004093)
R^2=0.994979 NR^2=1.821500 P=0.444108
分析.：模型二的拟合优度下降不多，但P=0.00000，模型任然存在异方差性，故排除。模型一的P=0.393183可以认为已经消除了异方差性，但是其判定系数R^2=0.573253，模型的拟合优度相对较低。模型三和四的P分别为0.618232和0.444108可以认为已经不存在异方差性，但是模型四的拟合优度为0.994979相对较高，故排除模型三。则最终选择模型四。 四、实验体会与建议
体会与建议:今天我们小组4人在2教602实验室进行了使用计量学分析软件Eviews的异方差检验与校正功能的实验学习.具体学习了如何使用软件进行数据异方差性检验,以及异方差性的校正与模型的确定选择.经过一系列的复杂检验校正得出了一个消除异方差性的统计模型,然后利用该模型去分析1995年北京市规模最大的20家百货零售商的利润函数情况以及其他情况..经过这个实验我们小组体会并懂得了如何利用软件进行数据的检验和校正并确定模型.这对以后我们的进一步学习有很大的帮助。
指导老师： 日期： 成绩：
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