的T检验没有通过，所以X1，X2，X3之间可能存在多重共线性。对X1 X2 X3 进行简单的系数相关检验，结果如下：
X1 X2 X3
X1 1.000000 0.995207 0.986669
X2 0.995207 1.000000 0.994043
X3 0.986669 0.994043 1.000000
由各相关系数值可知，解释变量之间都高度相关，模型存在严重的多重共线性。 （二）消除多重共线性
采用逐步回归的方法，来检验和解决多重多重共线性的问题
(1)
Dependent Variable: Y Method: Least Squares Date: 03/27/14 Time: 00:14 Sample: 1981 2012 Included observations: 32
Variable Coefficient Std. Error t-Statistic Prob. C 174.4242 41.59460 4.193433 0.0002 X1
0.445220
0.010305
43.20225
0.0000 R-squared
0.984181 Mean dependent var 1106.618 Adjusted R-squared 0.983654 S.D. dependent var 1573.355 S.E. of regression 201.1586 Akaike info criterion 13.50653 Sum squared resid 1213944. Schwarz criterion 13.59813 Log likelihood -214.1044 F-statistic 1866.435 Durbin-Watson stat
0.361008 Prob(F-statistic)
0.000000
则Y=174.4242+0.445220X1 (4.193433) (43.20225)
R^2=0.983654 F=1866.435 DW=0.361008
(2)
Dependent Variable: Y Method: Least Squares Date: 03/27/14 Time: 00:15 Sample: 1981 2012 Included observations: 32
Variable Coefficient Std. Error t-Statistic Prob. C 38.51608 21.93535 1.755891 0.0893 X2
2.288614
0.026723
85.64288
0.0000
7
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.995927 Mean dependent var 1106.618 0.995791 S.D. dependent var 102.0775 Akaike info criterion 312594.4 Schwarz criterion -192.3968 F-statistic 0.636747 Prob(F-statistic)
1573.355 12.14980 12.24141 7334.703 0.000000
则Y=38.51608+2.288614X2 (1.755891) (85.64288)
R^2=0.995791 F=7334.703 DW=0.636747
(3)
Dependent Variable: Y Method: Least Squares Date: 03/27/14 Time: 00:16 Sample: 1981 2012 Included observations: 32
Variable C X3
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -233.2828 1.589506
Std. Error 31.80022 0.024735
t-Statistic -7.335888 64.26238
Prob. 0.0000 0.0000 1573.355 12.72107 12.81268 4129.654 0.000000
0.992788 Mean dependent var 1106.618 0.992547 S.D. dependent var 135.8248 Akaike info criterion 553451.1 Schwarz criterion -201.5371 F-statistic 0.269861 Prob(F-statistic)
Y=-233.2828+1.589506X3 (-7.335888) (64.26238)
R^2=0.992547 F=4129.654 DW=0.269861
由以上三个检验可以综合比较X1，X2，X3的各项检验，X2的R^2最大,F检验，以及常数检验通过。所以以X2为基础，依次加入X1，X3来逐步回归。
(4)
Dependent Variable: Y Method: Least Squares Date: 03/27/14 Time: 00:17 Sample: 1981 2012 Included observations: 32
Variable C
Coefficient 23.83751
Std. Error 26.56408
t-Statistic 0.897359
Prob. 0.3769
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X2 X1
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
2.555557 -0.052491
0.273424 0.053507
9.346510 -0.981002
0.0000 0.3347 1573.355 12.17966 12.31707 3663.232 0.000000
0.996057 Mean dependent var 1106.618 0.995785 S.D. dependent var 102.1416 Akaike info criterion 302554.1 Schwarz criterion -191.8745 F-statistic 0.751807 Prob(F-statistic)
Y=23.83751+2.555557X2-0.052491X1 t=(0.897359)(9.346510)( -0.981002) R^2=0.995785 F=3663.232 DW=0.751807
(5)
Dependent Variable: Y Method: Least Squares Date: 03/27/14 Time: 00:18 Sample: 1981 2012 Included observations: 32
Variable C X2 X3 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient -64.83494 1.449728 0.587047 Std. Error 29.41969 0.193978 0.134936 t-Statistic -2.203794 7.473676 4.350560 Prob. 0.0356 0.0000 0.0002 1573.355 11.70991 11.84732 5868.348 0.000000
0.997535 Mean dependent var 1106.618 0.997365 S.D. dependent var 80.76046 Akaike info criterion 189145.3 Schwarz criterion -184.3586 F-statistic 0.514925 Prob(F-statistic)
Y=-64.83494+1.449728X2+0.587047X3 t= (-2.203794) (7.473676) (4.350560) R^2=0.997365 F=5868.348 DW=0.514925
在分别加入X1，X3之后，我们可以比较它们的R^2,以及修正后的R^2，t检验，F检验。消除了多重共线性，由X2和X3构成的方程为：
Y=-64.83494+1.449728X2+0.587047X3
（三）异方差的检验及修正
1.怀特检验
White Heteroskedasticity Test:
9
F-statistic Obs*R-squared
Test Equation:
6.604920 Probability 15.82619 Probability
0.000767 0.003261
Dependent Variable: RESID^2 Method: Least Squares Date: 03/26/14 Time: 23:34 Sample: 1981 2012 Included observations: 32
Variable C X2 X2^2 X3 X3^2 R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 4507.472 128.5286 -0.084317 -64.73470 0.031944 Std. Error 5208.204 56.31768 0.024952 35.90995 0.010790 t-Statistic 0.865456 2.282207 -3.379086 -1.802696 2.960452 Prob. 0.3944 0.0306 0.0022 0.0826 0.0063 14518.96 21.60271 21.83173 6.604920 0.000767
0.494568 Mean dependent var 5910.790 0.419690 S.D. dependent var 11060.27 Akaike info criterion 3.30E+09 Schwarz criterion -340.6433 F-statistic 1.763555 Prob(F-statistic)
由上图可以看出，nR^2所对应的概率p值=0.003<0.05，说明拒绝原假设，模型存在着异方差。
2.异方差修正
用加权最小二乘法（WLS）修正，权数w=1/abs(resid^1/2)的结果如下：
Variable C X2 X3
Weighted Statistics R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat Unweighted Statistics R-squared
Adjusted R-squared S.E. of regression
Coefficient -51.30430 1.660986 0.457609
Std. Error 1.861219 0.033228 0.020142 t-Statistic -27.56489 49.98784 22.71899 Prob. 0.0000 0.0000 0.0000 5130.023 -7.693815 -7.556403 2.00E+12 0.000000 1573.355 205524.2
10
1.000000 Mean dependent var 937.2386 1.000000 S.D. dependent var 0.004940 Akaike info criterion 0.000708 Schwarz criterion 126.1010 F-statistic 0.246164 Prob(F-statistic)
0.997322 Mean dependent var 1106.618 0.997137 S.D. dependent var 84.18458 Sum squared resid
Durbin-Watson stat 0.563326
再次用怀特检验是否还存在异方差，结果如下：
White Heteroskedasticity Test: F-statistic Obs*R-squared Test Equation:
Dependent Variable: STD_RESID^2 Method: Least Squares Date: 03/27/14 Time: 00:30 Sample: 1981 2012 Included observations: 32
Variable C X2 X2^2 X3 X3^2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
Coefficient 2.01E-05 -3.97E-08 9.97E-12 2.19E-08 -2.78E-12
Std. Error 2.89E-06 3.13E-08 1.39E-11 2.00E-08 6.00E-12
t-Statistic 6.946782 -1.269658 0.719377 1.095886 -0.463876
Prob. 0.0000 0.2150 0.4781 0.2828 0.6465 2.21E-05 5.98E-06 -21.01912 -20.79010 0.586055 0.675461
0.586055 Probability 2.556383 Probability
0.675461 0.634569
0.079887 Mean dependent var -0.056426 S.D. dependent var 6.15E-06 Akaike info criterion 1.02E-09 Schwarz criterion 341.3060 F-statistic 2.160271 Prob(F-statistic)
由上图检验可以看出，从上面的结果看出，运用加权最小二乘法估计的结果不论拟合度，残差，还是各参数的t统计量的值都有了显著的改善。且nR^2所对应的P值=0.63>0.05说明模型修正成功，不存在异方差，所以得到最后最佳模型为：
Y= -51.30430+1.660986X2+0.457609X3 T=(-27.56489)(49.98784)(22.71899) R^2=1.000000 F=0.586055 DW =2.160271
五、对第三产业发展的预测
根据最后最佳的回归模型Y= -51.30+1.66X2+0.46X3，把1990年—2012年的政府消费（X2）和居民消费（X3）分别带入此模型中，来检验和预测由于政府消费拉动第三产业的增值和由于居民消费拉动第三产业的增值分别有多大。在带入X2的时候，令X3为零；在带入X3的时候，令X2为零。预测的数据如表6：
11