四川省居民消费水平的多因素分析

1、四川省居民消费水平的多因素分析（本文主要通过对居民消费水平的变动进行多因素分析，建立以居民消费水平为应变量，以其它可量化影响因素为自变量的多元线性回归模型，并利用模型对居民消费水平这一社会现象进行数量化分析，对如何提高居民消费水平提出一些可行性建议。一、研究目的本文主要对居民消费水平进行多因素分析，并搜集相关数据，建立模型，对此进行数量分析。在得到居民消费水平与各主要因素间的数量关系后，据模型方程中的各因素系数大小，分析主要因素和次要因素。 二、影响居民消费水平变动的主要影响因素如下：职工工资、物价指数、居民储蓄存款、社会总产值、人口数三、建立模型其中，y居民消费水平（元） x1职工工资（万元

2、） x2 物价指数（r=100）x3 居民储蓄存款（万元） x4 社会总产值（亿元） x5人口数（万人）四、数据收集使用数据使用同一地区时间序列数据进行拟合。我们使用的是1949年-1989年全国各省、直辖市、地区历史资料汇编中1952年-1983年四川省的数据作为分析对象。数据如下：obsyx1x2x3x4x51952 49.40000 203757.0 101.3000 5104.000 53.40000 6411.0001953 52.10000 251728.0 101.3000 11921.00 64.13000 6508.0001954 58.10000 282233.0 100.

3、8000 12458.00 76.11000 6649.0001955 61.50000 302724.0 102.1000 10483.00 84.61000 6791.0001956 73.60000 353468.0 102.7000 14934.00 101.7500 6945.0001957 81.10000 447513.0 103.9000 23468.00 118.6700 7081.0001958 85.30000 500084.0 101.4000 30995.00 144.8900 7078.0001959 78.70000 573084.0 100.6000 38148

4、.00 173.2400 6897.0001960 80.20000 634453.0 102.5000 38997.00 194.2600 6620.0001961 96.60000 553101.0 123.7000 36705.00 143.4100 6459.0001962 105.8000 451762.0 100.0000 24821.00 124.2600 6486.0001963 108.2000 455899.0 94.30000 24846.00 134.2800 6696.0001964 107.5000 516337.0 94.30000 30236.00 153.37

5、00 6898.0001965 112.0000 591352.0 97.00000 36539.00 183.2300 7137.0001966 119.4000 700196.0 101.8000 46734.00 220.2200 7368.0001967 121.9000 736530.0 101.4000 43975.00 193.9200 7603.0001968 107.2000 630657.0 100.0000 51461.00 146.2000 7830.0001969 109.8000 653166.0 99.70000 51454.00 189.0200 8063.00

6、01970 112.1000 736133.0 99.70000 52108.00 244.8400 8342.0001971 121.7000 794254.0 100.2000 57601.00 270.5600 8584.0001972 111.4000 874150.0 100.6000 67170.00 268.6200 8817.0001973 114.4000 906099.0 100.7000 72019.00 272.5700 9066.0001974 115.0000 927901.0 100.3000 77825.00 263.1500 9271.0001975 112.

7、5000 970667.0 100.3000 79635.00 303.2700 9467.0001976 109.3000 964650.0 100.4000 81250.00 279.0800 9579.0001977 113.4000 1055127. 99.90000 87266.00 352.1400 9659.0001978 137.6000 1204417. 99.60000 103252.0 428.9800 9708.0001979 168.9000 1462311. 105.4000 149975.0 502.5100 9774.0001980 191.9000 17703

8、20. 108.1000 214790.0 545.9300 9820.0001981 203.6000 1870685. 101.8000 308502.0 579.9600 9924.0001982 228.0000 2078137. 102.3000 399099.0 655.2700 10022.001983 247.0000 2308488. 100.7000 518710.0 728.3300 10075.00五、模型的参数估计、检验及修正1.模型的参数估计及其经济意义、统计推断的检验利用eviews软件，用ols方法估计表1dependent variable: ymethod:

9、 least squaresdate: 05/13/05 time: 09:25sample: 1952 1983included observations: 32variablecoefficientstd. errort-statisticprob. c204.372860.744123.3644870.0024x10.0001634.82e-053.3851660.0023x2-0.9274710.484455-1.9144610.0666x3-9.45e-057.46e-05-1.2658350.2168x4-0.0975640.117695-0.8289570.4147x5-0.01

10、21630.004379-2.7772400.0100r-squared0.948356 mean dependent var115.4750adjusted r-squared0.938425 s.d. dependent var47.10880s.e. of regression11.68973 akaike info criterion7.922660sum squared resid3552.897 schwarz criterion8.197485log likelihood-120.7626 f-statistic95.49002durbin-watson stat0.907768

11、 prob(f-statistic)0.000000y =204.3728 + 0.000163*x1 0.927471*x2 0.0000945*x3-0.097564*x4-0.012163x5(3.364487) (3.385166) (-1.914461) (-1.265835) (-0.828957) (-2.777240)r2=0.948356 f=95.49002(1)经济意义检验从上表中可以看出，各指标符号与先验信息相符，所估计结果只有x4与经济原理相悖，说明x1、x2、x3、x5具有经济意义。(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=0.948356）

12、，f统计量的值在给定显著性水平=0.05的情况下也较显著，但是x2、x3、x4的t统计值均不显著（x2、x3、x4的t统计量的值的绝对值均小于2），说明x2、x3、x4这三个变量对y的影响不显著，或者变量之间存在多重共线的影响使其t值不显著。2.计量经济学检验（1） 多重共线性检验分析：由f=95.49002(5,26)=2.59(显著性水平=0.05), 表明模型从整体上看居民消费水平与解释变量间线形关系显著。检验：这里采用简单相关系数矩阵法对其进行检验：表2x1x2x3x4x5x1 1.000000 0.092218 0.939907 0.994078 0.863481x2 0.09221

13、8 1.000000 0.066885 0.070689-0.040907x3 0.939907 0.066885 1.000000 0.923380 0.700203x4 0.994078 0.070689 0.923380 1.000000 0.871609x5 0.863481-0.040907 0.700203 0.871609 1.000000由表2可以看出，解释变量之间存在高度线性相关。同时由表1也可以看出，尽管整体上线性回归拟合较好，但x2、x3、x4变量的参数t值并不显著，x4系数的符号与经济意义相悖。表明模型中解释变量确实存在严重的多重共线性。修正：采用逐步回归法对其进行补救

14、。根据以上分析，由于x1的t值最大，线形关系强，拟合程度最好，因此把x1作为基本变量。y=-44.52284+0.0000848x1(10.43408) (19.64810)r2=0.927893 s.e.=12.85912 f=386.0477然后将其余解释变量逐一代入x1的回归方程，重新回归。y=84.10367+0.0000852x1-0.392533x2(1.705961) (19.52407) (-0.805919)adjusted r-squared=0.924609 s.e.=12.93490 f=191.0935x2对y 的影响并不显著，故将x2删去。加入x3进行回归的情况和x

15、2相同，拟合优度仅略有变动，但对x1的t值影响很大，统计检验t=1.027048，不显著。因此变量x3引起了多重共线性，应舍去。加入x5进行回归的情况如下:y=92.37976+0.000101x1-0.007665x5(4570160) (12.76272) (-2.414339)adjusted r-squared =30.935820 s.e.=11.93442 f=227.0090经过上述逐步回归分析，表明y对x1、x5的回归模型为最优。表3dependent variable: ymethod: least squaresdate: 05/13/05 time: 11:45sampl

16、e: 1952 1983included observations: 32variablecoefficientstd. errort-statisticprob. x10.0001017.95e-0612.762720.0000x5-0.0076650.003175-2.4143390.0223c92.3797620.213684.5701600.0001r-squared0.939961 mean dependent var115.4750adjusted r-squared0.935820 s.d. dependent var47.10880s.e. of regression11.93

17、442 akaike info criterion7.885790sum squared resid4130.479 schwarz criterion8.023202log likelihood-123.1726 f-statistic227.0090durbin-watson stat1.550611 prob(f-statistic)0.000000模型修改为如下形式:y=c+c1x1+c5x5+u（2）异方差检验检验：利用goldfeld-quandt检验法检验模型是否存在异方差。先对x1检验,结果如下：dependent variable: ymethod: least square

18、sdate: 05/13/05 time: 11:30sample: 1952 1963included observations: 12variablecoefficientstd. errort-statisticprob. c22.7499213.661791.6652220.1268x10.0001403.22e-054.3524610.0014r-squared0.654504 mean dependent var79.82500adjusted r-squared0.619955 s.d. dependent var21.53412s.e. of regression13.2753

19、2 akaike info criterion8.160701sum squared resid1762.340 schwarz criterion8.241519log likelihood-46.96421 f-statistic18.94392durbin-watson stat1.469509 prob(f-statistic)0.001438时间定义为19521963，y=22.74992+0.000140x1(1.665222) (4.352461) r-squared=0.654504 sum squared resid=1762.340dependent variable: y

20、method: least squaresdate: 05/13/05 time: 11:32sample: 1972 1983included observations: 12variablecoefficientstd. errort-statisticprob. c19.136434.3590114.3900850.0014x19.90e-053.00e-0632.988370.0000r-squared0.990894 mean dependent var154.4167adjusted r-squared0.989984 s.d. dependent var51.15314s.e.

21、of regression5.119427 akaike info criterion6.254974sum squared resid262.0854 schwarz criterion6.335792log likelihood-35.52984 f-statistic1088.233durbin-watson stat1.384266 prob(f-statistic)0.000000时间定义为19721983，y=19.13643+0.0000990x1 (4.390085) (32.98837)r-squared=0.990894 sum squared resid=262.0854

22、f=262.0854/1762.340=0.1487144再对x5检验，结果如下：dependent variable: ymethod: least squaresdate: 05/13/05 time: 11:33sample: 1952 1963included observations: 12variablecoefficientstd. errort-statisticprob. c-43.65686205.8680-0.2120620.8363x50.0184100.0306970.5997370.5620r-squared0.034720 mean dependent var79

23、.75000adjusted r-squared-0.061808 s.d. dependent var21.53084s.e. of regression22.18626 akaike info criterion9.187835sum squared resid4922.302 schwarz criterion9.268653log likelihood-53.12701 f-statistic0.359684durbin-watson stat2.735517 prob(f-statistic)0.562024时间定义为19521963，y=-43.65686+0.018410x5 (

24、-0.212062) (0.599737)r-squared=0.034720 sum squared resid=4922.302dependent variable: ymethod: least squaresdate: 05/13/05 time: 11:35sample: 1972 1983included observations: 12variablecoefficientstd. errort-statisticprob. c-860.4537245.0936-3.5107140.0056x50.1057320.0255164.1437920.0020r-squared0.63

25、1961 mean dependent var154.4167adjusted r-squared0.595157 s.d. dependent var51.15314s.e. of regression32.54736 akaike info criterion9.954281sum squared resid10593.30 schwarz criterion10.03510log likelihood-57.72569 f-statistic17.17101durbin-watson stat0.323991 prob(f-statistic)0.002000时间定义为19721983，

26、y=-860.4537+0.105732x5 (-3.510714) (4.143792)r-squared=0.631961 sum squared resid=10593.30f=10593.30/4922.302=2.1521028综上，临界值(10,10 )=2.98,比较f=0.1487144(10,10 )，f=2.1521028(10,10 )，则表明随机误差不存在异方差。（3）自相关检验检验：从模型设定来看，没有违背d-w检验的假设条件，因此可以用d-w检验来检验模型是否存在一阶自相关。先对x1检验如下：dependent variable: ymethod: least sq

27、uaresdate: 05/13/05 time: 10:11sample: 1952 1983included observations: 32variablecoefficientstd. errort-statisticprob. c44.522844.26705810.434080.0000x18.48e-054.32e-0619.648100.0000r-squared0.927893 mean dependent var115.4750adjusted r-squared0.925489 s.d. dependent var47.10880s.e. of regression12.

28、85912 akaike info criterion8.006445sum squared resid4960.710 schwarz criterion8.098054log likelihood-126.1031 f-statistic386.0477durbin-watson stat0.378253 prob(f-statistic)0.000000根据上表中估计的结果，由dw=0.378253 ，给定显著性水平=0.05，查durbin-watson表，n=32，k=1，得=1.373,=1.502 。因为dw统计量为0.378253 dl=1.373，根据判定域知，存在一阶自相关

29、，需要进行修正。再对x5检验如下：dependent variable: ymethod: least squaresdate: 05/13/05 time: 11:50sample: 1952 1983included observations: 32variablecoefficientstd. errort-statisticprob. x50.0273220.0040506.7465580.0000c-104.491133.03791-3.1627650.0036r-squared0.602733 mean dependent var115.4750adjusted r-squared

30、0.589491 s.d. dependent var47.10880s.e. of regression30.18306 akaike info criterion9.712900sum squared resid27330.51 schwarz criterion9.804509log likelihood-153.4064 f-statistic45.51604durbin-watson stat0.657032 prob(f-statistic)0.000000根据上表中估计的结果，由dw=0.657032 ，给定显著性水平=0.05，查durbin-watson表，n=32，k=1，

31、得=1.373,=1.502 。因为dw统计量为0.657032dl=1.373，根据判定域知，存在一阶自相关，需要进行修正。修正：用cochrane-orcutt迭代法进行修正。对x1、x5的修正：dependent variable: ymethod: least squaresdate: 05/21/05 time: 21:26sample(adjusted): 1953 1983included observations: 31 after adjusting endpointsconvergence achieved after 12 iterationsvariablecoeffi

32、cientstd. errort-statisticprob. c92.8023246.909951.9783080.0582x19.04e-051.11e-058.1476230.0000x5-0.0060970.006214-0.9812040.3352ar(1)0.7712490.1259986.1211240.0000r-squared0.975129 mean dependent var117.6065adjusted r-squared0.972365 s.d. dependent var46.29243s.e. of regression7.695493 akaike info

33、criterion7.039061sum squared resid1598.957 schwarz criterion7.224091log likelihood-105.1054 f-statistic352.8653durbin-watson stat1.544642 prob(f-statistic)0.000000inverted ar roots .77根据上表中估计的结果，由dw=1.544642 ，给定显著性水平=0.05，查durbin-watson表，n=31，k=2，得=1.297，=1.570。因为dw统计量为1.544642，根据判定域知，不能确定存在自相关。而且x5的t检验值不显著，舍去。于是对x1修正如下：dependent variable: ymethod: l