影響我國人口預期壽命的可能因素分析 摘要：現實中存在著這種現象：各個地區間的人均壽命存在差異， 是什么因素造成了地區間的這種差異呢？在這篇文章中，我以2000年全國的各地區的人均壽命（每10年才統計一次）以及一些相關數據來進行分析。尋找造成各地人均壽命存在差異的原因。關鍵詞：人均壽命人均GDP衛生機構數單位面積污染比教育支出（由于造成壽命的長短的因素很多，只是找到幾個關鍵因素進行分析）地區地區人均壽命y人均GDP（萬元）x1衛生機構數x2單位面積污染比x3教育支出（萬元）x4北京76.11.8266476176184402503068天津74.911.637722298314822.0339685499.8河北72.540.762505206634978.787881559084.1山西71.650.506099137364070.55215794624.1內蒙古69.870.5906457852387.642276580861.6遼寧73.341.115932125646205.263161463314.7吉林73.10.67904255441580.51282902941.6黑龍江72.370.8544798038884.6625771175133上海78.142.7734513689086.68732008864.6江蘇73.911.171384128138484.112152905677.2浙江74.71.31339170346140.566042200449.9安徽71.850.48333467052720.689661129954福建72.551.14958198072262.41225753.9江西68.950.48278480481275.86207752776.6山東73.920.949371171187659.748432462775.5河南71.540.54149107644273.563221709181.4湖北71.080.717503110652909.743591706416.4湖南70.660.562615246781629.680371523036.8廣東73.271.253695134994291.752583609720.5廣西71.290.431608137071872.76423934717.9海南72.920.65713626891225.9887223093.3重慶71.730.51401793752234.19204698720.6四川71.20.466233351940.7480311619987.5貴州65.960.26451889922193.22034528486.6云南65.490.46099713356668.856448976174.5西藏64.370.45527112371.1811023681549.8陜西70.070.455796107371111.682241014584.4甘肅67.470.3845767191597.014925535287.2青海66.030.509845184780.9333333128177.5寧夏70.170.479368136120884新疆67.410.7378916705116.407186702243.4表一（來源于國家統計局網站）一、建立模型并回歸建立回歸方程：Y=a0+a1*X1+a2*X2+a3*X3+a4*X4+u(式1)Y地區人均壽命，X1人均GDP（萬元），X2衛生機構數，X3單位面積污染比，X4教育支出（萬元）運用OLS估計方法對式1中的參數進行估計，得回歸分析結果：（表2）DependentVariable:YMethod:LeastSquaresDate:12/25/10Time:20:49Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

C65.976461.13033158.369160.0000X14.9821041.6594543.0022540.0059X27.02E-057.05E-050.9958130.3285X3-2.99E-054.42E-05-0.6769880.5044X45.41E-077.19E-070.7534090.4580R-squared0.652727

Meandependentvar71.24387AdjustedR-squared0.599300

S.D.dependentvar3.191195S.E.ofregression2.020053

Akaikeinfocriterion4.390815Sumsquaredresid106.0960

Schwarzcriterion4.622103Loglikelihood-63.05763

F-statistic12.21726Durbin-Watsonstat1.285255

Prob(F-statistic)0.000010

從以上的報告單可得到回歸方程為:Y=65.97646203+4.982103524*X1+7.01887465e-005*X2-2.990581087e-005*X3+5.414193515e-007*X4二、模型的經濟意義檢驗Y=65.97646203+4.982103524*X1+7.01887465e-005*X2-2.990581087e-005*X3+5.414193515e-007*X4回歸方程表明：⑴X1人均GDP（萬元），X2衛生機構數，X3單位面積污染比，X4教育支出都=0時，地區人均壽命是65.97646203表明沒有任何衛生機構沒有污染和教育支出等因素的影響下人均壽命約是66歲。⑵當其他條件不變，每增加一單位的人均GDP，人均壽命增長五歲。⑶當其他條件不變時，每增加一單位的衛生機構，人均壽命增加7.01887465e-005個單位。⑷當其他條件不變時，每增加一單位的面積污染比，人均壽命減少-2.990581087e-005。⑸當其他條件不變時，每增加一單位教育支出，人均壽命增加5.414193515e-007個單位。經濟意義檢驗表明衛生機構、面積污染比、教育支出與人均壽命的關系微乎其微。我們可以得出人均壽命只與人均GDP存在很明顯的關系。現在單獨對人均壽命和人均GDP進行回歸。結果的報告單為DependentVariable:YMethod:LeastSquaresDate:12/25/10Time:21:18Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

C67.510130.70612395.606750.0000X14.5951260.7326516.2719170.0000R-squared0.575632

Meandependentvar71.24387AdjustedR-squared0.560999

S.D.dependentvar3.191195S.E.ofregression2.114395

Akaikeinfocriterion4.397756Sumsquaredresid129.6494

Schwarzcriterion4.490271Loglikelihood-66.16521

F-statistic39.33694Durbin-Watsonstat1.169499

Prob(F-statistic)0.000001

報告單數據表明最后的回歸方程為Y=67.51013261+4.595125638*X1經濟意義是：⑴當人均GDP=0時人均壽命約是67.5⑵當人均GDP沒增加一個單位，人均壽命4.6個單位。三、統計意義的檢驗報告單數據表明：１、F-statistic39.33694Prob(F-statistic)0.000001F檢驗的P值是0.000001<0.05T檢驗的P值是0<0.05F檢驗和T檢驗說明人居ＧＤＰ在方程中顯著２、R-squared0.575632AdjustedR-squared0.560999Ｒ＝0.575632＞0.3表明樣本方程唄解釋變量解釋的程度是57.5632%四、經濟計量學檢驗⑴異方差檢驗散點圖檢驗做出ｘ１與殘差的散點圖散點圖表明可能不存在異方差。②、進一步進行異方差檢驗，采用懷特檢驗。懷特檢驗的報告單為WhiteHeteroskedasticityTest:F-statistic2.303808

Probability0.118507Obs*R-squared4.380453

Probability0.111891TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/25/10Time:21:49Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

C11.565183.7171093.1113360.0043X1-13.661637.092647-1.9261680.0643X1^24.0023112.5403491.5754960.1264R-squared0.141305

Meandependentvar4.182237AdjustedR-squared0.079970

S.D.dependentvar6.093022S.E.ofregression5.844318

Akaikeinfocriterion6.460583Sumsquaredresid956.3694

Schwarzcriterion6.599355Loglikelihood-97.13903

F-statistic2.303808Durbin-Watsonstat1.862642

Prob(F-statistic)0.118507

懷特檢驗結果：Obs*R-squared4.380453

Probability0.111891懷特檢驗的統計量＝4.380453，Ｐ值為0.11189＞0.05懷特檢驗表明不存在異方差。（二）自相關性檢驗①、殘差的圖示檢驗殘差的圖示表明殘差之間可能不存在自行相關性。②、ＬＭ檢驗ＬＭ的檢驗報告表如下ARCHTest:F-statistic0.758037

Probability0.478663Obs*R-squared1.597835

Probability0.449816TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/25/10Time:22:11Sample(adjusted):331Includedobservations:29afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

C3.4098191.5219552.2404200.0338RESID^2(-1)0.2281300.2030581.1234720.2715RESID^2(-2)0.0334500.2029260.1648400.8703R-squared0.055098

Meandependentvar4.468796AdjustedR-squared-0.017587

S.D.dependentvar6.201487S.E.ofregression6.255782

Akaikeinfocriterion6.602587Sumsquaredresid1017.505

Schwarzcriterion6.744031Loglikelihood-92.73750

F-statistic0.75803