在校學(xué)生總數(shù)變動的多因素分析

1、在校學(xué)生總數(shù)變動的多因素分析摘要：本文主要通過對中國各級各類學(xué)校在校學(xué)生總數(shù)的變動進(jìn)行多因素分析，建立以在校學(xué)生總數(shù)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，并利用模型對在校學(xué)生總數(shù)進(jìn)行數(shù)量化分析，觀察各因素是如何分別影響在校學(xué)生總數(shù)的。關(guān)鍵詞：在校學(xué)生總數(shù) 多因素分析 模型 計量經(jīng)濟(jì)學(xué) 檢驗一、引言部分改革開放以來，中國的教育事業(yè)取得了長足的發(fā)展，各項教育指標(biāo)都較以往有了很大提高，受教育的人數(shù)也是逐年上升，文盲比例直線下降。隨著有知識、有文化的人數(shù)的不斷增加，中國的經(jīng)濟(jì)也隨之高速發(fā)展，眾多畢業(yè)生們在各行各業(yè)上表現(xiàn)都十分出色，取得了一系列令人矚目的成就。二、研究目的本文主要對中

2、國在校學(xué)生總數(shù)（應(yīng)變量）進(jìn)行多因素分析（具體分析見下圖），并搜集相關(guān)數(shù)據(jù)，建立模型，對此進(jìn)行數(shù)量分析。在得到在校學(xué)生總數(shù)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，分析各因素的重要性，并找出影響在校學(xué)生總數(shù)最大的因素。影響在校學(xué)生總數(shù)變動的主要影響因素如下圖：人口總數(shù) 這是影響在校學(xué)生總數(shù)的一個重要因素學(xué)?？倲?shù) 這也是影響在校學(xué)生總數(shù)的重要因素人均gdp 我認(rèn)為這個因素同樣重要（注：1.由于其他因素或是不好量化，或是數(shù)據(jù)資料難于查找，故為了分析的簡便，這里僅用此三個因素來進(jìn)行回歸分析。2.學(xué)?？倲?shù)包括普通高等學(xué)校、普通中等學(xué)校、小學(xué)、特殊教育學(xué)校和幼兒園等，故學(xué)生總數(shù)也是以上學(xué)校

3、的人數(shù)之和。）三、建立模型 y=+1x1+2x2+3x3+u其中，y在校學(xué)生總數(shù)（應(yīng)變量） x1人口總數(shù)（解釋變量） x2 各級各類學(xué)校總數(shù)（解釋變量） x3 人均gdp（解釋變量）（注：有關(guān)模型的一些假定：（1）假定不考慮學(xué)生轉(zhuǎn)學(xué)的影響。（2）假定各統(tǒng)計量計算準(zhǔn)確。四、數(shù)據(jù)搜集數(shù)據(jù)說明在這里，使用同一地區(qū)（即中國）的時間序列數(shù)據(jù)進(jìn)行擬合。 數(shù)據(jù)的搜集情況采用1985年到2003年的時間序列數(shù)據(jù)，具體情況見表一。表一：obsx1（人口總數(shù)/萬）x2（學(xué)校總數(shù)/萬）x3（人均gdp/元）y（學(xué)生總數(shù)/萬）198510585111.108185320117198610750711.00635956

4、20325.8198710930010.90899110420248198811102610.71226135519848.8198911270410.54347151219489.4199011433310.40992163419532.519911158239.94932187919813.219921171719.85393228720215.319931185179.6081293920627.919941198509.5612839232146119951211219.46772485422418.119961223899.29882557623251.219971236269.06

5、617605423861.119981247618.85622630824074.219991257868.61273655124327.620001267438.25667708624369.920011276277.01097765124224.420021284536.62013821424389.320031292276.34737910124452.5 五、模型的參數(shù)估計、檢驗及修正1.模型的參數(shù)估計及其經(jīng)濟(jì)意義、統(tǒng)計推斷的檢驗利用eviews軟件，用ols方法估計，得：（見表二）表二：dependent variable: ymethod: least squaresdate: 0

6、6/07/05 time: 09:35sample: 1985 2003included observations: 19variablecoefficientstd. errort-statisticprob. c18008.664856.6553.7080380.0021x1-0.0803410.038584-2.0822410.0549x2851.4523174.17774.8884100.0002x31.3242340.12480010.610840.0000r-squared0.978300 mean dependent var21949.85adjusted r-squared0.

7、973960 s.d. dependent var2024.050s.e. of regression326.6198 akaike info criterion14.60013sum squared resid1600207. schwarz criterion14.79896log likelihood-134.7013 f-statistic225.4140durbin-watson stat1.074996 prob(f-statistic)0.000000y=18008.66-0.080341x1+851.4523x2+1.324234x3 （1.1） (3.708038)(-2.0

8、82241)(4.888410)(10.61084)r2=0.978300 r2 =0.973960 f=225.4140可見。x1, x2, x3的t值均是顯著的，表明人口總數(shù)、學(xué)?？倲?shù)、人均gdp都是影響在校學(xué)生總數(shù)的主要因素。x2, x3的系數(shù)符合經(jīng)濟(jì)意義，但x1的系數(shù)不符合經(jīng)濟(jì)意義，因為從經(jīng)濟(jì)意義上講，在校學(xué)生的總?cè)藬?shù)應(yīng)該都是隨著人口總數(shù)（x1）、學(xué)?？倲?shù)（x2）、人均gdp（x3）的增加而增加的。另外，可決系數(shù)為0.978300，修正可決系數(shù)為0.973960，都比較大，說明模型的擬合程度較高，而f值為225.4140，說明模型總體是顯著的。2.計量經(jīng)濟(jì)學(xué)檢驗 （1）多重共線性檢驗用

9、eviews軟件，得相關(guān)系數(shù)矩陣表：x1x2x3x1 1.000000-0.926023 0.962222x2-0.926023 1.000000-0.950977x3 0.962222-0.950977 1.000000由上表可以看出，解釋變量x1與x3之間高度正相關(guān)，x1與x2，x2與x3之間高度負(fù)相關(guān)，可見存在嚴(yán)重的多重共線性。下面用逐步回歸法進(jìn)行修正：，用ols法逐一求y對各個解釋變量的回歸。dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:14sample: 1985 2003included obse

10、rvations: 19variablecoefficientstd. errort-statisticprob. c-7419.8323436.949-2.1588430.0454x10.2467150.0288198.5608690.0000r-squared0.811715 mean dependent var21949.85adjusted r-squared0.800639 s.d. dependent var2024.050s.e. of regression903.7356 akaike info criterion16.55025sum squared resid1388454

11、8 schwarz criterion16.64967log likelihood-155.2274 f-statistic73.28848durbin-watson stat0.213248 prob(f-statistic)0.000000y=-7419.832+0.246715x1 (-2.158843) (8.560869) r2=0.811715 s.e.=903.7356 f=73.28848dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:17sample: 1985 2003included ob

12、servations: 19variablecoefficientstd. errort-statisticprob. c33176.351653.65020.062490.0000x2-1203.754175.3386-6.8653080.0000r-squared0.734924 mean dependent var21949.85adjusted r-squared0.719331 s.d. dependent var2024.050s.e. of regression1072.306 akaike info criterion16.89231sum squared resid19547

13、273 schwarz criterion16.99173log likelihood-158.4770 f-statistic47.13246durbin-watson stat0.296483 prob(f-statistic)0.000003y=33176.35-1203.754x2 (20.06249) (-6.865308) r2=0.734924 s.e.=1072.306 f=47.13246dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:19sample: 1985 2003included o

14、bservations: 19variablecoefficientstd. errort-statisticprob. c19004.71228.167383.292860.0000x30.7008990.04561015.367390.0000r-squared0.932848 mean dependent var21949.85adjusted r-squared0.928898 s.d. dependent var2024.050s.e. of regression539.7130 akaike info criterion15.51925sum squared resid495193

15、3. schwarz criterion15.61867log likelihood-145.4329 f-statistic236.1566durbin-watson stat0.344201 prob(f-statistic)0.000000y=19004.71+0.700899x3 (83.29286) (15.36739) r2=0.932848 s.e.=539.7130 f=236.1566經(jīng)分析可見，在三個一元回歸模型中，在校學(xué)生總數(shù)y對人均gdp x3的線性關(guān)系強(qiáng)，擬合程度好，即：y=19004.71+0.700899x3 （1.2） (83.29286) (15.36739)

16、 r2=0.932848 s.e.=539.7130 f=236.1566 逐步回歸。將其余解釋變量逐一帶入式1.2中，得如下幾個模型：dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:28sample: 1985 2003included observations: 19variablecoefficientstd. errort-statisticprob. c30370.246464.9514.6976750.0002x1-0.1049180.059646-1.7589980.0977x30.9684340

17、.1580666.1267600.0000r-squared0.943729 mean dependent var21949.85adjusted r-squared0.936696 s.d. dependent var2024.050s.e. of regression509.2583 akaike info criterion15.44773sum squared resid4149504. schwarz criterion15.59685log likelihood-143.7534 f-statistic134.1703durbin-watson stat0.430949 prob(

18、f-statistic)0.000000y=30370.24-0.104918x1+0.968434x3 (1.3) (4.697675) (-1.758998) (6.126760) r2=0.936696 s.e.=509.2583 f=134.1703dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:33sample: 1985 2003included observations: 19variablecoefficientstd. errort-statisticprob. c8767.1462167.8

19、974.0440780.0009x2898.7100189.84294.7339660.0002x31.1425950.09811311.645660.0000r-squared0.972028 mean dependent var21949.85adjusted r-squared0.968531 s.d. dependent var2024.050s.e. of regression359.0565 akaike info criterion14.74878sum squared resid2062745. schwarz criterion14.89790log likelihood-1

20、37.1134 f-statistic277.9958durbin-watson stat0.751167 prob(f-statistic)0.000000y=8767.146+898.7100x2+1.142595x3 （1.4） (4.044078) (4.733966) (11.64566)r2=0.968531 s.e.=359.0565 f=277.9958 在式1.3中x1對y的影響并不顯著，故將x1刪去，得如下模型：dependent variable: ymethod: least squaresdate: 06/07/05 time: 11:33sample: 1985 2

21、003included observations: 19variablecoefficientstd. errort-statisticprob. c8767.1462167.8974.0440780.0009x2898.7100189.84294.7339660.0002x31.1425950.09811311.645660.0000r-squared0.972028 mean dependent var21949.85adjusted r-squared0.968531 s.d. dependent var2024.050s.e. of regression359.0565 akaike

22、info criterion14.74878sum squared resid2062745. schwarz criterion14.89790log likelihood-137.1134 f-statistic277.9958durbin-watson stat0.751167 prob(f-statistic)0.000000從上表可以看出，在刪去x1后，模型的統(tǒng)計檢驗效果均有較大改善。y=8767.146+898.7100x2+1.142595x3 (4.044078) (4.733966) (11.64566)r2=0.968531 s.e.=359.0565 f=277.9958

23、 （2）異方差檢驗（arch檢驗）利用y對x回歸所得殘差平方e2（=resid）在ols對話框的estimate equation 欄里鍵入e2 c e2(-1) e2(-2) e2(-3) 可輸出結(jié)果：dependent variable: e2method: least squaresdate: 06/07/05 time: 11:56sample(adjusted): 1988 2003included observations: 16 after adjusting endpointsvariablecoefficientstd. errort-statisticprob. c1036

24、67.647344.292.1896530.0490e2(-1)0.0452740.2971700.1523490.8814e2(-2)-0.2479630.234276-1.0584230.3107e2(-3)0.0570590.2446420.2332350.8195r-squared0.085889 mean dependent var87868.45adjusted r-squared-0.142638 s.d. dependent var83723.94s.e. of regression89496.09 akaike info criterion25.85410sum square

25、d resid9.61e+10 schwarz criterion26.04724log likelihood-202.8328 f-statistic0.375838durbin-watson stat1.836162 prob(f-statistic)0.772076計算有(n-p)r2=130.085889=1.116557,查 分布表，給定=0.05，自由度為p=3，得臨界值 0.05(3)=7.81，因為(n-p)r2=1.116557 0.05(3)=7.81，所以接受h0，表明模型中隨機(jī)誤差項不存在異方差。（3）自相關(guān)檢驗（dw檢驗）如下表：dependent variable:

26、 ymethod: least squaresdate: 06/07/05 time: 11:33sample: 1985 2003included observations: 19variablecoefficientstd. errort-statisticprob. c8767.1462167.8974.0440780.0009x2898.7100189.84294.7339660.0002x31.1425950.09811311.645660.0000r-squared0.972028 mean dependent var21949.85adjusted r-squared0.9685

27、31 s.d. dependent var2024.050s.e. of regression359.0565 akaike info criterion14.74878sum squared resid2062745. schwarz criterion14.89790log likelihood-137.1134 f-statistic277.9958durbin-watson stat0.751167 prob(f-statistic)0.000000dw=0.751167，給定顯著性水平=0.05，查durbin-watson表，n=19，k(解釋變量個數(shù))=2，得下限臨界值dl=1.

28、074, 得上限臨界值du=1.536，因為dw=0.751167 dl=1.074，表明該模型中的隨機(jī)誤差項存在一階自相關(guān)。修正：由dw=0.751167，根據(jù) =1dw/2，計算得 =0.6244165。用genr分別對x2，x3，y作廣義差分。即：genr dy=y-0.6244165*y（-1）genr dx2=x2-0.6244165*x2（-1）genr dx3=x3-0.6244165*x3（-1）然后用ols法估計其參數(shù)，得：dependent variable: dymethod: least squaresdate: 06/07/05 time: 14:27sample(adjusted): 1986 2003included observations: 18 after adjusting endpointsvariable