计量作业第8章

  • 格式:doc
  • 大小:109.00 KB
  • 文档页数:3

第八章

8、如果一个定性变量有k个类别,为什么不能设k个虚拟变量?

答:如果一个定性变量有k个类别,设k个虚拟变量的话,当模型中存在截距项时就会产生完全多重共线性,无法估计回归参数。

9、1982年—1986年按季节全国酒销售量Yi(万吨)数据如下表。试建立酒销售量Yi对时间t的季节销售模型。(表略)

回归模型

Dependent Variable: YI

Method: Least Squares

Date: 11/29/13 Time: 22:12

Sample: 1982Q1 1986Q4

Included observations: 20

Variable Coefficient Std. Error t-Statistic Prob.

C 76.66750 2.873219 26.68349 0.0000

@TREND(1982Q1) 1.677500 0.182083 9.212839 0.0000

D1 16.19250 2.964094 5.462883 0.0001

D2 3.815000 2.935998 1.299388 0.2134

D3 3.557500 2.919010 1.218735 0.2418

R-squared 0.874341 Mean dependent var 98.49500

Adjusted R-squared 0.840832 S.D. dependent var 11.54599

S.E. of regression 4.606372 Akaike info criterion 6.105076

Sum squared resid 318.2800 Schwarz criterion 6.354009

Log likelihood -56.05076 Hannan-Quinn criter. 6.153671

F-statistic 26.09270 Durbin-Watson stat 0.846159

Prob(F-statistic) 0.000001

由于D2、D3的回归参数没有显著性,说明没有必要把第二季度、第三季度单独分类。从模型中删除虚拟变量D2、D3。

Dependent Variable: YI

Method: Least Squares

Date: 11/29/13 Time: 22:21

Sample: 1982Q1 1986Q4

Included observations: 20

Variable Coefficient Std. Error t-Statistic Prob.

C 79.41846 2.170471 36.59044 0.0000

@TREND(1982Q1) 1.648154 0.181293 9.091121 0.0000

D1 13.67631 2.414212 5.664915 0.0000

R-squared 0.856614 Mean dependent var 98.49500

Adjusted R-squared 0.839745 S.D. dependent var 11.54599

S.E. of regression 4.622075 Akaike info criterion 6.037046

Sum squared resid 363.1808 Schwarz criterion 6.186405

Log likelihood -57.37046 Hannan-Quinn criter. 6.066202

F-statistic 50.78056 Durbin-Watson stat 1.047418

Prob(F-statistic) 0.000000

YI = 79.4184615385 + 1.64815384615*t + 13.6763076923*D1

(36.59044) (9.091121) (5.564915)

R2=0.856614 ad-R2=0.839745 F=50.78056

令D1=0,

YI = 79.4184615385 + 1.64815384615*t

令D1=1,

YI = 79.4184615385 + 1.64815384615*t + 13.6763076923*D1

10、1996:1—2004:4中国季度GDP(万亿元人民币)数据如下表。试建立中国季度GDP对时间t的回归模型。(表略)

回归模型

Dependent Variable: GDP

Method: Least Squares

Date: 11/29/13 Time: 22:45

Sample: 1996Q1 2000Q4

Included observations: 20

Variable Coefficient Std. Error t-Statistic Prob.

C 1.916178 0.158852 12.06267 0.0000

@TREND(1996Q1) 0.036276 0.010067 3.603501 0.0026

D1 -0.478013 0.163876 -2.916914 0.0106

D2 -0.349679 0.162323 -2.154219 0.0479

D3 -0.342148 0.161384 -2.120093 0.0511

R-squared 0.644673 Mean dependent var 1.968338

Adjusted R-squared 0.549919 S.D. dependent var 0.379610

S.E. of regression 0.254673 Akaike info criterion 0.314644

Sum squared resid 0.972874 Schwarz criterion 0.563577

Log likelihood 1.853560 Hannan-Quinn criter. 0.363238

F-statistic 6.803663 Durbin-Watson stat 2.881829

Prob(F-statistic) 0.002487

GDP = 1.916177925 + 0.036275825*t - 0.478012525*D1 - 0.34967875*D2 -

0.342148175*D3

(12.06267) (3.603501) (-2.916914)

(-2.154219)

(-2.120093)

R2=0.644673 ad-R2=0.549919

令D1=0,

GDP = 1.916177925 + 0.036275825*t - 0.34967875*D2 - 0.342148175*D3

令D2=0,

GDP = 1.916177925 + 0.036275825*t - 0.478012525*D1- 0.342148175*D3

令D3=0,

GDP = 1.916177925 + 0.036275825*t - 0.478012525*D1 - 0.34967875*D2