计量作业第8章
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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