5.14

(1)丫對(duì)X,即Yj=bx+b2Xi

DependentVariable:Y

Method:LeastSquares

Date:11/13/17Time:20:58

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

X0.2608780.01666415.654900.0000

C38.969073.85635110.105170.0000

R-squared0.942325Meandependentvar96.41176

AdjustedR-squared0.938480S.D.dependentvar19.72216

S.E.ofregression4.891751Akaikeinfocriterion6.123109

Sumsquaredresid358.9385Schwarzcriterion6.221134

Loglikelihood-50.04642Hannan-Quinncriter.6.132853

F-statistic245.0760Durbin-Watsonstat0.629301

Prob(F-statistic)0.000000

；=38.9690+0.2609a

r=(10.105)(15.655)

J=0.9423

(2)/〃丫對(duì)InX,即InYi=b、+b21nxi

DependentVariable:LNY

Method:LeastSquares

Date:11/13/17Time:21:40

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C1.4040510.1568138.9536490.0000

LNX0.5889650.02931720.089810.0000

R-squared0.964166Meandependentvar4.547848

AdjustedR-squared0.961777S.D.dependentvar0.213165

S.E.ofregression0.041675Akaikeinfocriterion-3.407698

Sumsquaredresid0.026052Schwarzcriterion-3.309673

Loglikelihood30.96543Hannan-Quinncriter.-3.397954

F-statistic403.6007Durbin-Watsonstat0.734161

Prob(F-statistic)0.000000

lnj/=1.4041+0.5890In

t=(8.954)(20.090)

2

r=0.9642

⑶y對(duì)X,即InYi="+b?xi

DependentVariable:LNY

Method:LeastSquares

Date:11/13/17Time:21:42

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C3.9315780.04643084.677640.0000

X0.0027990.00020113.949720.0000

R-squared0.928433Meandependentvar4.547848

AdjustedR-squared0.923662S.D.dependentvar0.213165

S.E.ofregression0.058896Akaikeinfocriterion-2.715956

Sumsquaredresid0.052031Schwarzcriterion-2.617930

Loglikelihood25.08562Hannan-Quinncriter.-2.706212

F-statistic194.5946Durbin-Watsonstat0.529132

Prob(F-statistic)0.000000

=3.9316+0.0028%

/=(84.678)(13.950)

2

r=0.9284

(4)y對(duì)InX,即Yi=b^b2InXi

DependentVariable:Y

Method:LeastSquares

Date:11/13/17Time:21:43

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C-192.966116.38000-11.780590.0000

LNX54.212573.06227817.703350.0000

R-squared0.954325Meandependentvar96.41176

AdjustedR-squared0.951280S.D.dependentvar19.72216

S.E.ofregression4.353186Akaikeinfocriterion5.889824

Sumsquaredresid284.2535Schwarzcriterion5.987849

Loglikelihood-48.06350Hannan-Quinncriter.5.899568

F-statistic313.4086Durbin-Watsonstat0.610822

Prob(F-statistic)0.000000

r=-192.9661+54.2126InXt

/=(-11.781)(17.703)

2

r=0.9542

%=38.96900.2609X,7?2=0.9424

1

t=(10.105)(15.655)

In/=1.40410.5890InX,R2=0.9642

2

t=(8.954)(20.090)

InY=3.93160.0028%,收=0.9284

3t

t=(84.678)(13.950)

-192.966154.2126X,

4X=A?=0.9543

t=(-11.781)(17.703)

B解釋個(gè)回歸結(jié)果

人ZAZ

解：=—；；斜率說明x每變動(dòng)一個(gè)單位，丫的絕對(duì)變動(dòng)量；

人LX1/I

2"=-斜率便是彈性系數(shù)；

人Ay/y

3.⑸=7□斜率表示X每變動(dòng)一個(gè)單位，丫的均值的瞬時(shí)增長率；

八Ay

4,.A二不77”斜率表示X的相對(duì)變化對(duì)Y的絕對(duì)量的影響。

AX/A

C對(duì)每一個(gè)模型求丫對(duì)X的變化率

八\YAr>YY

解：1.四=—=0.2609;2.j=/31X—=0.5890—;

Ay'XX

AKAZ

3.—=3,Xy=0.00287；4.——=自/X=54.2126/X.

AT?\X1

D對(duì)每一個(gè)模型求丫對(duì)X的彈性，對(duì)其中的一些模型，求丫對(duì)X的均值彈性。

解"八A*"哼=°26。冷

v22019

均值彈性二0.2609x==0.2609x------------=0.5959

Y96.41176

Ay/y-

2.E=——=0=0.5890；

AA7X]

\Y/Y-

3.E==回xX=0.0028X；

△X/X'

均值彈性=0.0028xj=0.0028x220.19=0.6165

Ar/y-

4.八赤T”=54.2"

均值彈性=0.2609xi=54.2126x——-——=0.5623.

Y96.41176

E根據(jù)這些回歸結(jié)果，你將選擇那個(gè)模型？為什么？

解：無法判斷，因?yàn)橹挥挟?dāng)模型的解釋變量的類型相同時(shí)，才可比較擬合優(yōu)度檢驗(yàn)數(shù)&2,

對(duì)模型的選擇還取決于模型的用途。

5.15

a.解釋B的含義

DependentVariable:Iff

Method:LeastSquares

Date11/13/17Time2249

Sample:110

Includedobservations:10

VariableCoefficientStd.Errort-StatisticProb.

C0.0130320.00075717.205860.0000

X8.33E-051.47E-055.6830600.0005

R-squared0.801475Meandependentvar0.016273

AdjustedR-squared0.776659S.D.dependentvar0.003335

S.E.ofregression0.001576Akaikeinfocriterion-9.890749

Sumsquaredresid1.99E-05Sctiwarzcriterion-9.830232

Loglikelihood51.45374Hannan-Quinncriter.-9.957136

F-statistic32,29717Durbin-Watsonstat0.853162

Prob(F-statistic)0.000463

1/Y=0.013031987405+8.33170838469e-05*X

b.求丫對(duì)X的變化率

dy/dx=-B2/(B1+B2X1)

當(dāng)X取均值X=38.9時(shí)，該導(dǎo)數(shù)為-0.3146

c.求丫對(duì)X的彈性

彈性=dy/dx*(X/Y)X=38.9Y=63.9均值彈性為-0.1915

d.用相同的數(shù)據(jù)，估計(jì)回歸模型

DependentVariable:Y

Method:LeastSquares

Date:11/12/17Time:22:19

Sample:110

Includedob