计量经济学多元线性回归、多重共线性、异方差实验报告概要(3)

图6.1 残差与其滞后一阶残差图

（2） LM检验

在表5.2的回归结果中，按路径“View/Residual Tests/Serial Correlation LM Tests”，在出现的对话框中选择Lags to include:1，点击ok.得到LM检验结果如下。

表6.1 LM检验结果

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 0.809839 Prob. F(1,27)

Obs*R-squared 0.902738 Prob. Chi-Square(1)

Test Equation: Dependent Variable: RESID Method: Least Squares Date: 11/14/13 Time: 21:50 Sample: 1 31 Included observations: 31 Presample missing value lagged residuals set to zero. Weight series: 1/E1^2

Coefficient Std. Error t-Statistic

0.3761 0.3420 Prob.

C X1 X2 RESID(-1)

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

-766.3965 937.0314 -0.817898 0.020990 0.027070 0.775390 -0.001273 0.001716 -0.742002 -0.007092 0.007881 -0.899910

Weighted Statistics 0.029121 Mean dependent var -0.078755 S.D. dependent var 4.273921 Akaike info criterion 493.1929 Schwarz criterion -86.87425 Hannan-Quinn criter. 0.269946 Durbin-Watson stat 0.846488 Unweighted Statistics -0.014569 Mean dependent var -0.127299 S.D. dependent var 42689.59 Sum squared resid

1.69E-08

0.4206 0.4448 0.4645 0.3761 -0.564513 4.074747 5.862855 6.047885 5.923170 1.683210 -4021.722 40207.07 4.92E+10

2从上表可以看出，nR2=0.902738，由LM检验可知，在α=0.05下，查?分

2?2统计量与临界值，因为布表，得临界值χ0 (5)=11.0705,比较计算的.052nR2=0.902738<χ0.05 (5)=11.0705,所以接受原假设，表明模型不存在自相关。

七、模型检验 1、经济意义检验

模型估计结果表明，在假定其他变量不变的情况下，当景区固定资产每增长1元时，旅游收入增加0.788277元；在假定其他变量不变的情况下，当景区从业人员每增加1人时，旅游收入增加0.235806万元。这与理论分析判断相一致。 2、统计检验

（1）拟合优度：由表中数据可得：R2=0.999848，修正的可决系数为

R2=0.999837，这说明模型对样本的拟合很好。

?（2）F检验：针对H0：β1=β2=0，给定显著性水平α=0.05，在F分布表中查出自由度为k=2和n-k-1=28的临界值Fα( 2，28)=3.34。由表中得到F=92014.78，

由于F=92014.78> Fα( 2，28)=3.34，应拒绝原假设，说明回归方程显著，即“旅游景区固定资产”、“旅游从业人员”等变量联合起来确实对“旅游景区营业收入”有显著影响。 （3）t检验：分别对H0：βj=0(j=1,2),给定显著性水平α=0.05，查t分布表得自由度为n-k-1=28临界值tα/2(n-k-1)=2.048。由表中数据可得，?1、?2对应的t统计量分别为57.57099、243.6786，其绝对值均大于tα/2(n-k-1)=2.048，这说明应该分别拒绝H0：βj =0(j=1,2),也就是说，当在其他解释变量不变的情况下，解释变量“旅游景区固定资产”（X1） 、“旅游从业人数”（X2）分别对被解释变量“旅游景区营业收入”(Y)影响显著。 八、附录

以下是多重共线性参数估计

备表1 对X1回归分析

Dependent Variable: Y Method: Least Squares Date: 11/14/13 Time: 21:14 Sample: 1 31 Included observations: 31

Coefficient Std. Error t-Statistic C -15595.61 18604.86 -0.838255 X1 1.978224 0.229091 8.635111 R-squared 0.719983 Mean dependent var

Adjusted R-squared 0.710327 S.D. dependent var S.E. of regression 60671.69 Akaike info criterion Sum squared resid 1.07E+11 Schwarz criterion Log likelihood -384.3636 Hannan-Quinn criter. F-statistic 74.56515 Durbin-Watson stat Prob(F-statistic) 0.000000

备表2 对X2回归分析 Dependent Variable: Y Method: Least Squares

Date: 11/14/13 Time: 21:15 Sample: 1 31

Prob. 0.4087 0.0000 114619.2 112728.1 24.92668 25.01920 24.95684 2.090544

^^

Included observations: 31

Coefficient Std. Error t-Statistic C 15958.73 11364.71 1.404236 X2 0.315120 0.025260 12.47495 R-squared 0.842924 Mean dependent var

Adjusted R-squared 0.837508 S.D. dependent var S.E. of regression 45441.05 Akaike info criterion Sum squared resid 5.99E+10 Schwarz criterion Log likelihood -375.4027 Hannan-Quinn criter. F-statistic 155.6243 Durbin-Watson stat Prob(F-statistic) 0.000000

备表3 对X3回归分析 Dependent Variable: Y Method: Least Squares Date: 11/14/13 Time: 21:15 Sample: 1 31 Included observations: 31

Coefficient Std. Error t-Statistic C 53599.95 15413.41 3.477488 X3 0.316946 0.045785 6.922479 R-squared 0.622988 Mean dependent var

Adjusted R-squared 0.609988 S.D. dependent var S.E. of regression 70399.77 Akaike info criterion Sum squared resid 1.44E+11 Schwarz criterion Log likelihood -388.9737 Hannan-Quinn criter. F-statistic 47.92072 Durbin-Watson stat Prob(F-statistic) 0.000000

备表4 对X4回归分析 Dependent Variable: Y Method: Least Squares

Date: 11/14/13 Time: 21:15 Sample: 1 31

Included observations: 31

Coefficient

t-Statistic

Prob. 0.1709 0.0000 114619.2 112728.1 24.34856 24.44108 24.37872 1.665119 Prob. 0.0016 0.0000 114619.2 112728.1 25.22411 25.31662 25.25427 1.724195 Prob.

Std. Error

C X4 R-squared

-143904.9 66622.99 -2.159989 12.54525 3.131970 4.005547 0.356191 Mean dependent var

Adjusted R-squared 0.333991 S.D. dependent var S.E. of regression 91996.75 Akaike info criterion Sum squared resid 2.45E+11 Schwarz criterion Log likelihood -397.2681 Hannan-Quinn criter. F-statistic 16.04440 Durbin-Watson stat Prob(F-statistic) 0.000394

备表5 对X2、X1回归分析 Dependent Variable: Y Method: Least Squares Date: 11/14/13 Time: 21:15 Sample: 1 31 Included observations: 31

Coefficient Std. Error t-Statistic C -4316.824 12795.42 -0.337373 X2 0.230304 0.039088 5.891959 X1 0.711446 0.265507 2.679575 R-squared 0.874983 Mean dependent var

Adjusted R-squared 0.866053 S.D. dependent var S.E. of regression 41257.10 Akaike info criterion Sum squared resid 4.77E+10 Schwarz criterion Log likelihood -371.8644 Hannan-Quinn criter. F-statistic 97.98460 Durbin-Watson stat Prob(F-statistic) 0.000000

备表6 对X2、X3回归分析 Dependent Variable: Y Method: Least Squares

Date: 11/14/13 Time: 21:15 Sample: 1 31

Included observations: 31

Coefficient C 16874.53 X2 0.258113 X3 0.087950

t-Statistic 1.562660 7.016265 2.043471

0.0392 0.0004 114619.2 112728.1 25.75923 25.85175 25.78939 1.829839 Prob. 0.7384 0.0000 0.0122 114619.2 112728.1 24.18480 24.32357 24.23004 1.893654 Prob. 0.1294 0.0000 0.0505

Std. Error 10798.59 0.036788 0.043040

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