jl3.docx

1、jl3国内旅游收入的影响因素一 模型的设定我们把“国内旅游收入”设为被解释变量，“居民存款年末余额”， “旅游消费价格指数” “居民旅游人次”，“国内旅行社数量” 设为解释变量，设立了以下经济学模型： Y=国内旅游收入（百万元）=居民存款年末余额（亿元）=旅游消费价格指数=居民旅游人次（百万人次） =国内旅行社数量（个）数据如下：obsYX1X2X3X41991200.009241.60 103.40 430.001561.001992250.0011759.40 106.40 476.001785.001993864.00 15203.50 114.70 498.001966.0019941

2、023.51 21518.80 124.10 524.00 2360.0019951375.70 29662.30 117.10 629.00 2504.0019961638.38 38520.80 108.30 640.00 2821.00 19972112.70 46280.00 102.80 644.00 3399.00 19982391.18 53407.50 99.20 695.00 3275.00 19992831.92 59621.80 98.60 719.00 3995.00 20003175.54 64332.40 100.40 744.00 4910.00 20013522

3、.37 73762.40 100.70 784.00 6070.00 20023878.36 86910.60 99.20 878.00 7725.00 20033442.27 103617.70 101.20 870.00 9222.00 20044710.70 119555.40 103.90 1102.00 10203.00 20055285.90 141051.00 101.80 1212.00 11997.00 20066229.70 161587.30 101.50 1394.00 13467.00 20071110.60 172534.20 104.80 1610.00 1468

4、9.00 20088749.30 217885.40 105.86 1712.00 16303.00 200910183.70 260771.70 99.31 1902.00 17146.00 201012579.80 303302.50 103.30 2103.00 18140.00 资料来源：中国统计年鉴二 参数估计模型为Y=国内旅游收入（百万元）=居民存款年末余额（亿元）=旅游消费价格指数=居民旅游人次（百万人次） =国内旅行社数量（个）用Eviews估计结果为：Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time:

5、17:59Sample: 1991 2010Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C3099.1913745.2930.8274890.4209X10.1346340.0214276.2833060.0000X224.6620137.312750.6609540.5187X3-13.434093.965271-3.3879370.0041X4-0.2818490.192287-1.4657720.1634R-squared0.939567 Mean dependent var3777.781

6、Adjusted R-squared0.923451 S.D. dependent var3381.896S.E. of regression935.6858 Akaike info criterion16.73275Sum squared resid13132620 Schwarz criterion16.98169Log likelihood-162.3275 F-statistic58.30174Durbin-Watson stat3.021396 Prob(F-statistic)0.000000Y=3099.191+0.135X1+24.662X2-13.434X3-0.282X4T

7、:(0.827) (6.283) (0.661) (-3.388) (-1.466) R2=0.939567 调整后的：R2=0.923451 F=58.30174三 检验及修正1经济意义检验从上表中可以看出，符号为正，但由经验得知，“国内旅游收入”与“旅游消费价格指数”关系紧密，故不应剔除。、X4符号为负，故应剔除。2统计推断检验从回归结果可以看出，模型的拟和优度非常好(R2=0.939567),F统计量的值在给定显著性水平=0.05的情况下也较显著，说明各解释变量对的联合线性作用显著，但是X2, X4的值不显著（X2, X4的t统计量的值的绝对值均小于2），说明这两个变量对Y的影响不显著，

8、或者变量之间存在多重共线的影响使其t值不显著。3计量经济学意义检验（）多重共线性检验检验：=58.302F0.05(4,15)=3.06（显著水平为），表明国内旅游收入与解释变量间线性关系显著。这里采用简单相关系数矩阵法对其进行检验：X1X2X3X4X1 1.000000-0.360316 0.992001 0.976019X2-0.360316 1.000000-0.319220-0.362585X3 0.992001-0.319220 1.000000 0.979416X4 0.976019-0.362585 0.979416 1.000000从以上结果可以看出，之间存在高度线性相关。修正

9、：采用逐步回归法对其进行补救。根据以上分析，由于前的符号为正，但由经验得知，“国内旅游收入”与“旅游消费价格指数”关系紧密，故不应剔除。分别作Y与之间的回归：Y=157.48+0.036X1 (0.333) (9.987)R2=0.847126 F=99.74432 D.W.=2.079172Y=22951.39-182.90X2 (1.962854) (-1.642927)R2=0.130402 F=2.699208 D.W.=0.570306Y=-1939.253+5.843846X3 (-2.348336) (7.758457)R2=0.769802 F=60.19366 D.W.= 1

10、.856527Y=-70.41734+0.501270X4 (-0.102244) (6.918602)R2=0.726722 F=47.86706 D.W.= 1.466658由于的t值最大，线性关系强，拟合程度最好，因此把作为基本变量，将剩下的三个因素重新进行参数估计：在原模型的基础上剔除，再进行参数估计，所得结果如下：Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time: 19:22Sample: 1991 2010Included observations: 20VariableCoefficientStd. Err

11、ort-StatisticProb. C157.4804472.94930.3329750.7430X10.0363750.0036429.9872080.0000R-squared0.847126 Mean dependent var3777.781Adjusted R-squared0.838633 S.D. dependent var3381.896S.E. of regression1358.523 Akaike info criterion17.36082Sum squared resid33220537 Schwarz criterion17.46040Log likelihood

12、-171.6082 F-statistic99.74432Durbin-Watson stat2.079172 Prob(F-statistic)0.000000Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time: 19:28Sample: 1991 2010Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C2004.2065544.8180.3614560.7222X10.0358930.0040058.9631340.0000

13、X2-17.1586251.32149-0.3343360.7422R-squared0.848125 Mean dependent var3777.781Adjusted R-squared0.830257 S.D. dependent var3381.896S.E. of regression1393.336 Akaike info criterion17.45427Sum squared resid33003528 Schwarz criterion17.60363Log likelihood-171.5427 F-statistic47.46708Durbin-Watson stat2

14、.098577 Prob(F-statistic)0.000000剔除x2Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time: 19:29Sample: 1991 2010Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C6005.6831399.2084.2922010.0005X10.1240860.0205336.0431650.0000X3-14.901123.460478-4.3060860.0005R-squared0

15、.926880 Mean dependent var3777.781Adjusted R-squared0.918278 S.D. dependent var3381.896S.E. of regression966.7855 Akaike info criterion16.72331Sum squared resid15889460 Schwarz criterion16.87267Log likelihood-164.2331 F-statistic107.7476Durbin-Watson stat2.654245 Prob(F-statistic)0.000000保留x3Depende

16、nt Variable: YMethod: Least SquaresDate: 06/19/11 Time: 19:31Sample: 1991 2010Included observations: 20VariableCoefficientStd. Errort-StatisticProb. C5394.0851379.2683.9108330.0012X10.1298750.0198236.5517430.0000X3-12.438283.602769-3.4524230.0033X4-0.3092260.184439-1.6765800.1131R-squared0.937807 Me

17、an dependent var3777.781Adjusted R-squared0.926145 S.D. dependent var3381.896S.E. of regression919.0720 Akaike info criterion16.66146Sum squared resid13515094 Schwarz criterion16.86061Log likelihood-162.6146 F-statistic80.42054Durbin-Watson stat2.977833 Prob(F-statistic)0.000000保留x4X1X2X3X4Y=f(x1)0.

18、036375（9.987208）0.847126Y=f(x1,x2)0.035893（8.963134）-17.15862（-0.334336）0.848125Y=f(x1,x3)0.124086（6.043165）-14.90112（-4.306086）0.926880Y=f(x1, x3,x4)0.129875（6.551743）-12.43828(-3.452423)-0.309226（-1.676580）0.937807从表中我们可以看出x3,x4相邻两个之间的变化明显，选择保留，因此最后应保留x1，x3,x4。最后结果为：Y= 5394.085+ 0.129875X1+-12.438

19、28 X 3+-0.309226 X 4 (3.910833) (6.551743) (-3.452423) (-1.676580)= 0.937807 F= 80.42054 D.W.= 2.977833(2) 异方差检验检验：利用Goid_Quandt检验法检验模型是否存在异方差。由于“居民存款年末余额”最有可能引起异方差性，故将20组样本观测值按从小到大的顺序排列，将序列中的m=4除去，并将剩下的观测值划分为较小与较大的容量相同的两个子样本，每个子样本的容量均为8。将时间定义在1991年1998年，然后对Y C X1 X3 X4进行普通最小二乘法估计，所得结果如下：Dependent V

20、ariable: YMethod: Least SquaresDate: 06/19/11 Time: 19:45Sample: 1991 1998Included observations: 8VariableCoefficientStd. Errort-StatisticProb. C-1339.6361146.694-1.1682600.3076X10.0208380.0227270.9168520.4111X31.4780512.3415140.6312370.5622X40.4660300.4445101.0484120.3536R-squared0.976285 Mean depe

21、ndent var1231.934Adjusted R-squared0.958498 S.D. dependent var802.9735S.E. of regression163.5819 Akaike info criterion13.33936Sum squared resid107036.2 Schwarz criterion13.37908Log likelihood-49.35743 F-statistic54.88896Durbin-Watson stat2.542863 Prob(F-statistic)0.001046Y= -1339.636+ 0.020838X1+1.4

22、78051 X 3+0.466030X 4 (-1.168260) (0.916852) (0.631237) (1.048412)= 0.976285 F= 54.88896 D.W.= 2.542863 =107036.2将时间定义在2003年2010年,然后对Y C X1 X3 X4进行普通最小二乘法估计，所得结果如下：Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time: 19:49Sample: 2003 2010Included observations: 8VariableCoefficientStd. Err

23、ort-StatisticProb. C2930.1904425.9700.6620450.5441X10.1371480.0373823.6688640.0214X3-20.8892312.79120-1.6330940.1778X40.6703051.3791500.4860270.6524R-squared0.893271 Mean dependent var6536.496Adjusted R-squared0.813225 S.D. dependent var3755.498S.E. of regression1623.031 Akaike info criterion17.9288

24、3Sum squared resid10536924 Schwarz criterion17.96855Log likelihood-67.71533 F-statistic11.15941Durbin-Watson stat2.750548 Prob(F-statistic)0.020582Y= 2930.190+ 0.137148X1+-20.88923 X 3+0.670305X 4 (0.662045) (3.668864) (-1.633094) (0.486027)=0.893271 F= 11.15941 D.W.= 2.750548 e22=10536924 =10536924

25、/107036.2=98.44262 大于F0.05(3,3)=9.28，拒绝假设，故存在异方差性。修正：下面采用加权最小二乘法对原模型进行回归分析：用原模型的普通最小二乘法的估计量作为随机干扰项方差协方差距阵的主对角线元素，这相当于用1/为权重进行加权最小二乘估计。加权最小二乘估计的回归结果如下：Dependent Variable: YMethod: Least SquaresDate: 06/19/11 Time: 20:02Sample(adjusted): 2003 2010Included observations: 8 after adjusting endpointsWeigh

26、ting series: EEVariableCoefficientStd. Errort-StatisticProb. C4728.550758.41716.2347610.0034X10.0987190.0246534.0043070.0161X3-6.9485066.974809-0.9962290.3755X4-0.4122260.369055-1.1169750.3266Weighted StatisticsR-squared1.000000 Mean dependent var8088.466Adjusted R-squared0.999999 S.D. dependent var

27、14377.89S.E. of regression10.69237 Akaike info criterion7.883791Sum squared resid457.3073 Schwarz criterion7.923512Log likelihood-27.53516 F-statistic4219091.Durbin-Watson stat3.079447 Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.834977 Mean dependent var6536.496Adjusted R-squared0.711210 S.D. dependent var3755.498S.E. of regression2018.173 Sum squared resid16292094Durbin-Watson stat2.639530Y= 4728.550+ 0.098719X1+-6.948506X 3+-0.412226X 4 (6.234761) (4.004307) (-0.996229) (-1.116975)=1.000000 F= 4219091 D.W.= 3.079447 可以看出，无论是拟合优度，还是各参数的t统计量值都有了显