计量经济学精要第四版课后习题答案

5.14

(1)Y对X,即匕=5+h2Xt

DependentVariable:Y

Method:LeastSquares

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

Sample:19711987

Includedobservations:17

VariableCoefficientStdErrort-StatisticProb.

X0.2608780.01666415.654900.0000

C38.969073.85635110.105170.0000

R-squared0.942325Meandependentvar96.41176

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

S.E.ofregression4.891751Akaikeinfccriterion6/23109

Sumsquaredresid358.9385Schwarzcriterion6.221134

Loglikelihood-50.04642Hannan-Quinncriter.6/32853

F-statistic245.0760Durbin-Watsonstat0.629301

Prob(F-statistic)0.000000

v=38.9690+0.2609

/=(10.105)(15.655)

J=0.9423

(2)丫对InX,即In=，+bJnXi

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

=1.4041+0.5890Inx，

i=(8.954)(20.090)

2

r=0.9642

(3)丫对X,即InYi=仇+b2Xi

DependentVariable:LNY

Method:LeastSquares

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

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticP，ob.

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

Inj=3.93164-0.0028

r=(84.678)(13.950)

r2=0.9284

(4)丫对InX,即Yi=b^b2InXj

DependentVariable:Y

Method:LeastSquares

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

Sample:19711987

Includedobservations:17

VariableCoefficientStd.Errort-StatisticProb.

C-192.966116.38000-11.78059O.COOO

LNX54,212573.06227817.70335O.COOO

R-squared0.954325Meandependentvar96.41176

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

S.E.ofregression4.353186Akaikeinfocriterion5.88S824

Sumsquaredresid284.2535Schwarzcriterion5.987849

Loglikelihood-48.06350Hannan-Quinncriter.5.89S568

F-statistic313.4086Durbin-Watsonstat0.61C822

Prob(F-statistic)0.000000

y=-192.9661+54.21261nX,

r=(-11.781)(17.703)

J=0.9542

A

38.96900.2609X,R2=0.9424

1

t=(10.105)(15.655)

In/=1.40410.5890InR2=0.9642

2

t=(8.954)(20.090)

1ng=3.93160.0028X,=0.9284

3

t=(84.678)(13.950)

A

-192.966154.2126%,R2=0.9543

4yf=

t=(-11.781)(17.703)

B解释个回归结果

A/\r

解：1.舟二一斜率说明X每变动一个单位，丫的绝对变动量；

人ZAZ/I

24二菽市《斜率便是弹性系数；

人\Y/Y

3.P\=『斜率表示X每变动一个单位，Y的均值的瞬时增长率；

4,.A=▽斜率表示x的相对变化对Y的绝对量的影响。

W/X.

C对每一个模型求丫对X的变化率

〜Ay\Y%YY

解：1.4=一=0.2609;2.----=fitx—=0.5890—;

kX1XX

AX4

3.­=8.xY=0.0028K；4.—=fl,/X=54.2\26/X.

NX八bX

D对每一个模型求丫对X的弹性,对其中的一些模型，求丫对X的均值弹性。

解j£=^77=AX7=0-26097:

v29()1Q

均值弹性二0.2609x==0.2609x------：—=0.5959

Y96.41176

AY/Y*

2,E=---------=%=0.5890；

\X/XQ

\Y/Y

3.E==JxX=0.0028X；

△XIX'

均值弹性=0.0028xX=0.0028x220.19=0.6165

AK/y、

"EM/—*//.

均值弹性=0.2609xl=54.2126x——!一=0.5623.

Y96.41176

E根据这些回归结果，你将选择那个模型？为什么？

解：无法判断，因为只有当模型的解释变量的类型相同时，才可比较拟合优度检验数R2,

对模型的选择还取决于模型的用途。

5.15

a.解释B的含义

DependentVariable:W

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.Eofregression0.001576Akaikeinfocriterion-9.890749

Sumsquaredresid1.99E-05Schwarzcriterion-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Y对X的变化率

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

当X取均值X=38.9时,该导数为-0.3146

c.求Y对X的弹性

弹性二dy/dx*(X/Y)X=38.9Y=63.9均值弹性为-0.1915

d.用相同的数据，估计回归模型

DependentVariable:Y

Method:LeastSquares

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

Sample:110

Includedobservatio