(1.667662) (1.393956) (-0.958254)
R2?0.784228 R2 DW?0.83292 0 F?23.6243 4?0.75103 222可以看出，在加入X3后，拟优优度R增加不显著，R有所减少，并且X3系数不显著，说明存在严重的多重共线性。所以在模型中去除X3。
3.加入X1，对Y关于X1,X2作最小二乘回归，得：
????Dependent Variable: Y Method: Least Squares Date: 12/14/11 Time: 10:11 Sample: 1994 2009 Included observations: 16
C X1 X2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
Coefficient -15.11043 -0.004651 0.167123
Std. Error 146.1315 0.001670 0.047199
t-Statistic -0.103403 -2.785603 3.540778
Prob. 0.9192 0.0154 0.0036 677.4095 133.3843 11.00147 11.14633 11.00889 1.489029
0.855336 Mean dependent var 0.833079 S.D. dependent var 54.49538 Akaike info criterion 38606.70 Schwarz criterion -85.01176 Hannan-Quinn criter. 38.43156 Durbin-Watson stat 0.000003
??-15.11043?-0.004651X1?0.167123X2Y (-0.103403) (-2.785603) (3.540778)
R?0.855336 R22?0.83307 9 DW?1.48902 9 F?38.4315 6 加入X1后，拟合优度增加，但参数估计值的符号不正确，所以在模型中是否保留X1待定。
从上述尝试中发现，由于严重的共线性，无法将多个解释变量同时放入同个模型中。因此只能保留变量X2，相应的回归结果是：
??377.5253?0.036205X2Y（6.826606） （8.03980）
R?0.768987 R22?0.75248 6 DW?0.71590 2 F?46.6025 5 上述回归结果基本上消除了多重共线性，并且在其他因素不变的情况下城镇居民消费水平每增加1元，城镇旅游消费将增加0.036205元。 1.3.3异方差检验和克服 1.消除异方差
确定了模型的基本方程后，对模型的异方差进行检验和处理，从残差图中得出：
12080400-40-80-120-16004,0008,000X212,00016,000RESID残差随着X2的增加，离散程度增加。下面用怀特检验，对方程进行异方差检验：
????Heteroskedasticity Test: White F-statistic Obs*R-squared Scaled explained SS
Test Equation:
Dependent Variable: RESID^2 Method: Least Squares Date: 12/14/11 Time: 11:19 Sample: 1994 2009 Included observations: 16
C X2 X2^2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
Coefficient 25079.84 -5.350023 0.000295
Std. Error 7951.210 1.833508 9.55E-05
5.061640 Prob. F(2,13) 7.004736 Prob. Chi-Square(2) 3.618408 Prob. Chi-Square(2)
t-Statistic 3.154216 -2.917916 3.085096
Prob. 0.0076 0.0120 0.0087 3853.169 4622.769 19.44995 19.59481 19.45736 2.006298
0.0237 0.0301 0.1638
0.437796 Mean dependent var 0.351303 S.D. dependent var 3723.258 Akaike info criterion 1.80E+08 Schwarz criterion -152.5996 Hannan-Quinn criter. 5.061640 Durbin-Watson stat 0.023676
TR2?16?0.437796?7.004736
2且Prob.
Chi-Square(2)=0.0301<0.05,说明模型不存在显著的异方差。但于此同时， F-statistic=5.061640>F(2,13)=3.81 Prob. F(2,13)=Prob. F(2,13)<0.05，说明显著性较高。
2.克服异方差
假设异方差与X相关，以1/X为为权作加权最小二乘估计，估计结果如下：
????Dependent Variable: Y Method: Least Squares Date: 12/17/11 Time: 09:05 Sample: 1994 2009 Included observations: 16 Weighting series: 1/X2
Coefficien
C X2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
t
264.1975 0.050890
Std. Error 43.40243 0.006367
t-Statistic 6.087159 7.992201
Prob. 0.0000 0.0000 632.9339 115.4731 11.22760 11.32417 11.23254 0.494374
677.4095 133.3843 96520.65
Weighted Statistics
0.820225 Mean dependent var 0.807384 S.D. dependent var 62.59127 Akaike info criterion 54847.34 Schwarz criterion -87.82078 Hannan-Quinn criter. 63.87527 Durbin-Watson stat 0.000001
Unweighted Statistics
0.638324 Mean dependent var 0.612490 S.D. dependent var 83.03211 Sum squared resid 0.523153
?/X?264.1975/XY22?0.050890
(6.087159) (7.992201) 还原变量，得：
??264.1975?0.050890XY2
(6.087159) (7.992201)
R?0.820225 2 R2?0.807384 DW?0.494374 F?63.87527
对新产生的回归方程进行White检验，检验新产生的方程是否存在异方差。得出：
TR2?16?0.173106?2.769699
2Obs*R-squared=2.76969，说明模型已经克服了显著的异方差。 1.3.4 自相关性分析
1. 从回归结果中可以直接得出DW检验的结果： 当??0.05 K
从Q检验也可以明显看出残差的自相关性显示正弦衰竭。
?1 T?15时，dL?1.08 dU?1.54
方程中DW?0.494374，DW取值在（0，dL）之间，认为存在一阶正自相关：
2. 再通过LM检验对方程的残差自相关性进行检验。
????Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared
Test Equation:
Dependent Variable: RESID Method: Least Squares Date: 12/17/11 Time: 09:27 Sample: 1994 2009 Included observations: 16
Presample missing value lagged residuals set to zero. Weight series: 1/X2
C X2
Coefficien
t
6.833571 -0.001851
Std. Error 33.73237 0.004973
t-Statistic 0.202582 -0.372216
Prob. 0.8426 0.7157
10.27027 Prob. F(1,13) 7.061555 Prob. Chi-Square(1)
0.0069 0.0079
RESID(-1) 0.841426 0.262558 3.204726 0.0069
R-squared
Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
R-squared
Adjusted R-squared S.E. of regression Durbin-Watson stat
Weighted Statistics 2.13E-14 60.46891 10.77037 10.91523 10.77779 1.391563
-8.311730 79.75600 45898.58
0.441347 Mean dependent var 0.355401 S.D. dependent var 48.54864 Akaike info criterion 30640.62 Schwarz criterion -83.16296 Hannan-Quinn criter. 5.135134 Durbin-Watson stat 0.022721
Unweighted Statistics
0.518960 Mean dependent var 0.444954 S.D. dependent var 59.41936 Sum squared resid 0.928969
TR2?16?0.441347?7.061552??????(1)?3.84，所以LM检验结果也说明了误差项
?存在一阶正自相关。
3.用广义最小二乘法估计回归参数
?。 首先估计自相关系数p??1??DW2?1?0.494374/2?0.752813
对原变量做广义差分变换，令
Yt?Y?0.752813Yt?1 Xt?X?0.752813Xt?1
以t,
YXt为样本再次回归，得：
t-Statistic 5.751418 2.035675
Prob. 0.0001 0.0627 265.2897 51.25115 10.63233 10.72674
????Dependent Variable: YT Method: Least Squares Date: 12/15/11 Time: 10:34 Sample (adjusted): 1995 2009
Included observations: 15 after adjustments
Coefficien
C XT2
R-squared
Adjusted R-squared S.E. of regression Sum squared resid
t
199.1419 0.018639
Std. Error 34.62483 0.009156
0.241716 Mean dependent var 0.183386 S.D. dependent var 46.31395 Akaike info criterion 27884.77 Schwarz criterion