相關(guān)與回歸資料統(tǒng)計(jì)

分析中的錯(cuò)誤實(shí)例杜麗娜文章題目及出處西水地區(qū)旱獺鼠疫流行時(shí)某些指標(biāo)的相互關(guān)系地方病通報(bào)2001年8月第16卷第3期原先的設(shè)計(jì)資料統(tǒng)計(jì)方法結(jié)果與結(jié)論在喜馬拉雅旱獺鼠疫自然疫源地，蚤在鼠疫的傳播中起到重要作用。作者針對(duì)該地區(qū)1982-1999年所獲監(jiān)測(cè)資料，以旱獺密度，體蚤指數(shù)，洞干蚤指數(shù)同鼠疫菌檢出量進(jìn)行相關(guān)回歸統(tǒng)計(jì)處理，結(jié)果見表1，2，3。表1旱獺密度與動(dòng)物媒介

檢菌量相關(guān)比較時(shí)間密度(X)檢菌量(Y)X2Y2XY19820.37260.13696769.6219830.590.25814.519840.6120.372141.1219850.6490.4096815.7619860.660.36363.619870.48150.23042257.219880.3170.0961492.1219890.3400.11560019900.42004770.2209493.819920.2700.07290019930.470.16492.819940.39003520.122540.719960.3730.136991.1119970.3100.09610019980.0610.0003610.0619990.0520.0002540.1R=0.2763P>0.01表2旱獺體蚤指數(shù)與動(dòng)物媒介

檢菌量的相關(guān)統(tǒng)計(jì)時(shí)間密度（X)檢菌量（Y）198210.12619838.2919847.4219854.3919865.76198731519886.3719896.9019902.1019915.3719927.4019937.9719942.8019958.2219966319974.3019980.06119990.052r=0.396,p>0.01表3旱獺洞干蚤指數(shù)與動(dòng)物昆蟲

檢菌量的相關(guān)分析時(shí)間密度（x)檢菌量(y)19820.352619830.33919840.08219850.19619860.07919870.241519880.28719890.04019900.1019910.05719920.04019930.35719940.05019950.04219960.04319970.04019980.02119990.012R=0.7601P<0.01原作者分別對(duì)三張表進(jìn)行相關(guān)分析，得到結(jié)果是：旱獺密度，體蚤指數(shù)與檢出量在年度上呈正相關(guān)，但并不存在顯著差異。但是洞干蚤指數(shù)與檢出量呈正相關(guān)且具統(tǒng)計(jì)學(xué)意義。對(duì)過失的分析原作者目的在于研究動(dòng)物媒介檢菌量與旱獺密度，體蚤指數(shù)，洞干蚤指數(shù)之間的相關(guān)性，應(yīng)該用多元線性回歸進(jìn)行研究。正確統(tǒng)計(jì)分析過程將動(dòng)物檢菌量〔y〕對(duì)旱獺密度〔x1),體蚤指數(shù)〔x2〕，洞干蚤指數(shù)(x3)進(jìn)行多元線性回歸?？梢酝ㄟ^共線性診斷來發(fā)現(xiàn)自變量之間是否有較強(qiáng)的線性關(guān)系，用SAS運(yùn)行結(jié)果如下。TheSASSystemParameterEstimatesParameterStandardTforH0:VariableDFEstimateErrorParameter=0Prob>|T|INTERCEP1-0.8312513.57481227-0.2330.8195X112.1797298.998512520.2420.8121X210.1674710.548319450.3050.7645X3135.13495212.520215372.8060.0140

CollinearityDiagnosticsConditionVarPropVarPropVarPropVarPropNumberEigenvalueIndexINTERCEPX1X2X313.510061.000000.00910.00850.01090.021520.309133.369650.06660.03620.00200.817330.108775.680690.14140.10010.98600.148440.072036.980680.78290.85520.00110.0127TheSASSystem

CollinearityDiagnostics(interceptadjusted)ConditionVarPropVarPropVarPropNumberEigenvalueIndexX1X2X311.816171.000000.12950.14400.135820.689751.622680.71310.01370.409930.494081.917260.15740.84230.4543

StepwiseProcedureforDependentVariableYStep1VariableX3EnteredR-square=0.67726611C(p)=-0.72776750DFSumofSquaresMeanSquareFProb>FRegression1858.77342419858.7734241935.670.0001Error17409.2265758124.07215152Total181268.00000000ParameterStandardTypeIIVariableEstimateErrorSumofSquaresFProb>FX340.318001146.75020790858.7734241935.670.0001Boundsonconditionnumber:1,1-----------------------------------------------------------------------------