四川省居民消費(fèi)水平的多因素分析

1、四川省居民消費(fèi)水平的多因素分析（本文主要通過對(duì)居民消費(fèi)水平的變動(dòng)進(jìn)行多因素分析，建立以居民消費(fèi)水平為應(yīng)變量，以其它可量化影響因素為自變量的多元線性回歸模型，并利用模型對(duì)居民消費(fèi)水平這一社會(huì)現(xiàn)象進(jìn)行數(shù)量化分析，對(duì)如何提高居民消費(fèi)水平提出一些可行性建議。一、研究目的本文主要對(duì)居民消費(fèi)水平進(jìn)行多因素分析，并搜集相關(guān)數(shù)據(jù)，建立模型，對(duì)此進(jìn)行數(shù)量分析。在得到居民消費(fèi)水平與各主要因素間的數(shù)量關(guān)系后，據(jù)模型方程中的各因素系數(shù)大小，分析主要因素和次要因素。 二、影響居民消費(fèi)水平變動(dòng)的主要影響因素如下：職工工資、物價(jià)指數(shù)、居民儲(chǔ)蓄存款、社會(huì)總產(chǎn)值、人口數(shù)三、建立模型其中，y居民消費(fèi)水平（元） x1職工工資（萬元

2、） x2 物價(jià)指數(shù)（r=100）x3 居民儲(chǔ)蓄存款（萬元） x4 社會(huì)總產(chǎn)值（億元） x5人口數(shù)（萬人）四、數(shù)據(jù)收集使用數(shù)據(jù)使用同一地區(qū)時(shí)間序列數(shù)據(jù)進(jìn)行擬合。我們使用的是1949年-1989年全國各省、直轄市、地區(qū)歷史資料匯編中1952年-1983年四川省的數(shù)據(jù)作為分析對(duì)象。數(shù)據(jù)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、模型的參數(shù)估計(jì)、檢驗(yàn)及修正1.模型的參數(shù)估計(jì)及其經(jīng)濟(jì)意義、統(tǒng)計(jì)推斷的檢驗(yàn)利用eviews軟件，用ols方法估計(jì)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)經(jīng)濟(jì)意義檢驗(yàn)從上表中可以看出，各指標(biāo)符號(hào)與先驗(yàn)信息相符，所估計(jì)結(jié)果只有x4與經(jīng)濟(jì)原理相悖，說明x1、x2、x3、x5具有經(jīng)濟(jì)意義。(2)統(tǒng)計(jì)推斷檢驗(yàn)從回歸結(jié)果可以看出，模型的擬和優(yōu)度非常好（r2=0.948356）

12、，f統(tǒng)計(jì)量的值在給定顯著性水平=0.05的情況下也較顯著，但是x2、x3、x4的t統(tǒng)計(jì)值均不顯著（x2、x3、x4的t統(tǒng)計(jì)量的值的絕對(duì)值均小于2），說明x2、x3、x4這三個(gè)變量對(duì)y的影響不顯著，或者變量之間存在多重共線的影響使其t值不顯著。2.計(jì)量經(jīng)濟(jì)學(xué)檢驗(yàn)（1） 多重共線性檢驗(yàn)分析：由f=95.49002(5,26)=2.59(顯著性水平=0.05), 表明模型從整體上看居民消費(fèi)水平與解釋變量間線形關(guān)系顯著。檢驗(yàn)：這里采用簡單相關(guān)系數(shù)矩陣法對(duì)其進(jìn)行檢驗(yàn)：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，解釋變量之間存在高度線性相關(guān)。同時(shí)由表1也可以看出，盡管整體上線性回歸擬合較好，但x2、x3、x4變量的參數(shù)t值并不顯著，x4系數(shù)的符號(hào)與經(jīng)濟(jì)意義相悖。表明模型中解釋變量確實(shí)存在嚴(yán)重的多重共線性。修正：采用逐步回歸法對(duì)其進(jìn)行補(bǔ)救

14、。根據(jù)以上分析，由于x1的t值最大，線形關(guān)系強(qiáng)，擬合程度最好，因此把x1作為基本變量。y=-44.52284+0.0000848x1(10.43408) (19.64810)r2=0.927893 s.e.=12.85912 f=386.0477然后將其余解釋變量逐一代入x1的回歸方程，重新回歸。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對(duì)y 的影響并不顯著，故將x2刪去。加入x3進(jìn)行回歸的情況和x

15、2相同，擬合優(yōu)度僅略有變動(dòng)，但對(duì)x1的t值影響很大，統(tǒng)計(jì)檢驗(yàn)t=1.027048，不顯著。因此變量x3引起了多重共線性，應(yīng)舍去。加入x5進(jìn)行回歸的情況如下:y=92.37976+0.000101x1-0.007665x5(4570160) (12.76272) (-2.414339)adjusted r-squared =30.935820 s.e.=11.93442 f=227.0090經(jīng)過上述逐步回歸分析，表明y對(duì)x1、x5的回歸模型為最優(yōu)。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模型修改為如下形式:y=c+c1x1+c5x5+u（2）異方差檢驗(yàn)檢驗(yàn)：利用goldfeld-quandt檢驗(yàn)法檢驗(yàn)?zāi)Ｐ褪欠翊嬖诋惙讲睢Ｏ葘?duì)x1檢驗(yàn),結(jié)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時(shí)間定義為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時(shí)間定義為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再對(duì)x5檢驗(yàn)，結(jié)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時(shí)間定義為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時(shí)間定義為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綜上，臨界值(10,10 )=2.98,比較f=0.1487144(10,10 )，f=2.1521028(10,10 )，則表明隨機(jī)誤差不存在異方差。（3）自相關(guān)檢驗(yàn)檢驗(yàn)：從模型設(shè)定來看，沒有違背d-w檢驗(yàn)的假設(shè)條件，因此可以用d-w檢驗(yàn)來檢驗(yàn)?zāi)Ｐ褪欠翊嬖谝浑A自相關(guān)。先對(duì)x1檢驗(yàn)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根據(jù)上表中估計(jì)的結(jié)果，由dw=0.378253 ，給定顯著性水平=0.05，查durbin-watson表，n=32，k=1，得=1.373,=1.502 。因?yàn)閐w統(tǒng)計(jì)量為0.378253 dl=1.373，根據(jù)判定域知，存在一階自相關(guān)

29、，需要進(jìn)行修正。再對(duì)x5檢驗(yàn)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根據(jù)上表中估計(jì)的結(jié)果，由dw=0.657032 ，給定顯著性水平=0.05，查durbin-watson表，n=32，k=1，

31、得=1.373,=1.502 。因?yàn)閐w統(tǒng)計(jì)量為0.657032dl=1.373，根據(jù)判定域知，存在一階自相關(guān)，需要進(jìn)行修正。修正：用cochrane-orcutt迭代法進(jìn)行修正。對(duì)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根據(jù)上表中估計(jì)的結(jié)果，由dw=1.544642 ，給定顯著性水平=0.05，查durbin-watson表，n=31，k=2，得=1.297，=1.570。因?yàn)閐w統(tǒng)計(jì)量為1.544642，根據(jù)判定域知，不能確定存在自相關(guān)。而且x5的t檢驗(yàn)值不顯著，舍去。于是對(duì)x1修正如下：dependent variable: ymethod: l