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Y?9.347522?0.637069X

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t?2.569104??32.00881?

R2?0.946423 F=1024.564

??Goldfeld-Quandt?:

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?1??????

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??9.347522+0.637069XYiit=(2.569104)(32.00881)

R22=0.945500 F=1024.564 DW=1.790431

?2??????

1?Goldfeld-Quandt???

a.???X????????????1/4????????????????

n1?n2?22?

b.????????????????????????????????

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?F????

2122

?603.0148?2495.840

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c.??????F??????F=4.1390>F0.05(20,20)?2.12?????????????????? 2?White??

Heteroskedasticity Test: White F-statistic

6.301373 Prob. F(2,57) 10.86401 Prob. Chi-Square(2) 9.912825 Prob. Chi-Square(2)

0.0034 0.0044 0.0070

eF?

e

Obs*R-squared Scaled explained SS

2??5.9915? ??0.05????????2?????????

22

nR?10.8640???5.9915????????????????????????

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?3????????

?????????WLS??????W1=1/x?W2=1/x^2?W3=1/sqr(x)??????????????1/e? 1/e^2?1/|e|???????????? ???????????White????????????

1/x 1/x^2 1/sqr(x) 1/e 1/|e| 1/e^2 ??

n*R^2 12.0169 44.56705 7.449289 48.87603 40.27676 13.86993

7.137548 82.30189 2.64608 82.01679 38.11912 5.612508 F?

???????W3????????????

Dependent Variable: Y Method: Least Squares Date: 11/19/10Time: 16:16 Sample: 1 60

Included observations: 60 Weighting series: 1/SQR(X)

X C

R-squared Adjusted R-squared S.E. of regression Sum squared resid

Coefficient 0.632671 10.10908

Std. Error 0.018379 2.980789

t-Statistic 34.42341 3.391409

Prob. 0.0000 0.0013 112.9123 18.33568 7.086817 7.156628

Weighted Statistics

0.953338 Mean dependent var 0.952533 S.D. dependent var 8.232480 Akaike info criterion 3930.877 Schwarz criterion

Log likelihood F-statistic Prob(F-statistic)

-210.6045 Hannan-Quinn criter. 1184.971 Durbin-Watson stat 0.000000

7.114124 1.874009

???5.3????

1????????Yt??0??1Xt?ut???Yt??????????Xt????????????????

Dependent Variable: Y Method: Least Squares Date: 11/19/10Time: 14:46 Sample: 1 31

Included observations: 31

X C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 0.719500 179.1916

Std. Error 0.045700 221.5775

t-Statistic 15.74411 0.808709

Prob. 0.0000 0.4253 3376.309 1499.612 15.30377 15.39628 15.33392 2.119816

0.895260 Mean dependent var 0.891649 S.D. dependent var 493.6240 Akaike info criterion 7066274. Schwarz criterion -235.2084 Hannan-Quinn criter. 247.8769 Durbin-Watson stat 0.000000

??179.1916?0.719500X Ytt

t=0.808709 15.74411

R2?0.895260 F?247.8769 DW?2.119816

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c.??????F??????F=12.1978>F0.05(12,12)?2.69?????????????????? ?3?White??

Heteroskedasticity Test: White F-statistic

7.194463 Prob. F(2,28) 10.52295 Prob. Chi-Square(2) 30.08105 Prob. Chi-Square(2)

0.0030 0.0052 0.0000

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Obs*R-squared Scaled explained SS

2

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n*R^2 F?

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13.68524

3.914182 5.205198 4.223407 7.113422

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1/|e| 16.01765 6.259783

1/e^2 10.07829 4.33543

1? ?????????Yt??0??1Xt?ut???Y?????X????? ???????

Dependent Variable: Y Method: Least Squares Date: 11/19/10Time: 11:38 Sample: 1978 2008 Included observations: 31

X C

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)

Coefficient 0.084665 -648.1236

Std. Error 0.004882 118.1625

t-Statistic 17.34164 -5.485018

Prob. 0.0000 0.0000 1250.323 820.9407 13.92404 14.01655 13.95419 0.911579

0.912050 Mean dependent var 0.909017 S.D. dependent var 247.6234 Akaike info criterion 1778203. Schwarz criterion -213.8226 Hannan-Quinn criter. 300.7324 Durbin-Watson stat 0.000000

???648.1236?0.084665X Ytt

t=-5.485018 17.34164

R2?0.912050 F?300.7324 DW?0.911579

??????????????????????????????????????

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Heteroskedasticity Test: White F-statistic

7.840687 Prob. F(2,28) 11.12883 Prob. Chi-Square(2) 6.682351 Prob. Chi-Square(2)

0.0020 0.0038 0.0354 Obs*R-squared Scaled explained SS

???????? ?? ???????

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2.1

?1? ????????????GDP???????Eviews???

Dependent Variable: Y

Method: Least Squares

Date: 12/27/14Time: 21:00

Sample: 1 22

Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 56.64794 1.960820 28.88992 0.0000

X1 0.128360 0.027242 4.711834 0.0001R-squared 0.526082 Mean dependent var 62.50000

Adjusted R-squared 0.502386 S.D. dependent var 10.08889

S.E. of regression 7.116881 Akaike info criterion 6.849324

Sum squared resid 1013.000 Schwarz criterion 6.948510

Log likelihood -73.34257 Hannan-Quinn criter. 6.872689

F-statistic 22.20138 Durbin-Watson stat 0.629074

Prob(F-statistic) 0.000134?????????y=56.64794+0.128360x1

??????????????????Eviews?????

Dependent Variable: Y

Method: Least Squares

Date: 11/26/14Time: 21:10

Sample: 1 22

Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C 38.79424 3.532079 10.98340 0.0000

X2 0.331971 0.046656 7.115308 0.0000R-squared 0.716825 Mean dependent var 62.50000

Adjusted R-squared 0.702666 S.D. dependent var 10.08889

S.E. of regression 5.501306 Akaike info criterion 6.334356

Sum squared resid 605.2873 Schwarz criterion 6.433542

Log likelihood -67.67792 Hannan-Quinn criter. 6.357721

F-statistic 50.62761 Durbin-Watson stat 1.846406

Prob(F-statistic) 0.000001?????????y=38.79424+0.331971x2

??????????????????????Eviews?????

Dependent Variable: Y

Method: Least Squares

Date: 11/26/14Time: 21:14

Sample: 1 22

Included observations: 22 Variable Coefficient Std. Error t-Statistic Prob. C 31.79956 6.536434 4.864971 0.0001

X3 0.387276 0.080260 4.825285 0.0001R-squared 0.537929 Mean dependent var 62.50000

Adjusted R-squared 0.514825 S.D. dependent var 10.08889

S.E. of regression 7.027364 Akaike info criterion 6.824009

Sum squared resid 987.6770 Schwarz criterion 6.923194

Log likelihood -73.06409 Hannan-Quinn criter. 6.847374

F-statistic 23.28338 Durbin-Watson stat 0.952555

Prob(F-statistic) 0.000103 ?????????y=31.79956+0.387276x3

?2???????????GDP?????????????0.526082????????????????????

???????t???t??1?=4.711834>t0.025(20)=2.086?????????????????GDP???????????

??????????????????????????0.716825????????????????????

???????t???t??2?=7.115308>t0.025(20)=2.086???????????????????????????????

????????????????????????????0.537929????????????????????

???????t???t??3?=4.825285>t0.025(20)=2.086???????????????????????????????????

2.2

?1?

??????????????????????Eviews??????? Dependent Variable: Y

Method: Least Squares

Date: 12/03/14Time: 17:00

Sample (adjusted): 1 33

Included observations: 33 after adjustments Variable Coefficient Std. Error t-Statistic Prob. X 0.176124 0.004072 43.25639 0.0000

C -154.3063 39.08196 -3.948274 0.0004R-squared 0.983702 Mean dependent var 902.5148

Adjusted R-squared 0.983177 S.D. dependent var 1351.009

S.E. of regression 175.2325 Akaike info criterion 13.22880

Sum squared resid 951899.7 Schwarz criterion 13.31949

Log likelihood -216.2751 Hannan-Quinn criter. 13.25931

F-statistic 1871.115 Durbin-Watson stat 0.100021

Prob(F-statistic) 0.000000

????????????????0.176124????�154.3063

????????????????????????????????

1??????0.983702????????????????????

2????????t???t??2?=43.25639>t0.025(31)=2.0395???????????????????????????????????

???????????????

Y=0.176124X�154.3063

(0.004072) (39.08196)

t= (43.25639) ?-3.948274?

R2=0.983702 F=1871.115 n=33

????????????????1????????????0.176124???

?2??x=32000??

???????????Y=0.176124X�154.3063??????

Y= Y=0.176124*32000�154.3063=5481.6617

????????

??Eviews???

??????

?x2=??Xi�X?2=?2x(n�1)= 7608.0212 x (33�1)=1852223.473

(Xf�X)2=(32000� 6000.441)2=675977068.2

?Xf=32000??????????????

5481.6617�2.0395x175.2325x?1/33+1852223.473/675977068.2?

Yf?5481.6617+2.0395x175.2325x?1/33+1852223.473/675977068.2

?Yf???????5481.6617�64.9649, 5481.6617+64.9649?

(3) ?????????????????????????Eviews??????? Dependent Variable: LNY

Method: Least Squares

Date: 12/03/14Time: 18:00

Sample (adjusted): 1 33

Included observations: 33 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

LNX 0.980275 0.034296 28.58268 0.0000

C -1.918289 0.268213 -7.152121 0.0000

R-squared 0.963442 Mean dependent var 5.573120

Adjusted R-squared 0.962263 S.D. dependent var 1.684189

S.E. of regression 0.327172 Akaike info criterion 0.662028

Sum squared resid 3.318281 Schwarz criterion 0.752726

Log likelihood -8.923468 Hannan-Quinn criter. 0.692545

F-statistic 816.9699 Durbin-Watson stat 0.096208

Prob(F-statistic) 0.000000

???????lnY=0.980275lnX-1.918289

?????????????????0.980275????-1.918289

??????????????????????????????

1??????0.963442????????????????????

2????????t???t??2?=28.58268>t0.025(31)=2.0395???????????????????????????????????

???????????????1%??????????0.980275%


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