statistics for economics accounting and business accounting(下）

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1、STFE_C07.qxd26/02/200910:52Page254Chapter7•Correlationandregressionanda=T−bS(7.13)whereSandTarethemeanvaluesofXandYrespectively.Thevaluesneces-sarytoevaluateequations(7.12)and(7.13)canbeobtainedfromTable7.2whichwasusedtocalculatethecorrelationcoefficient.Thesev

2、aluesarerepeatedforconvenience2∑Y=380∑Y=125642∑X=40.2∑X=184.04∑XY=1139.70n=12Usingthesevaluesweobtain12×1139.70−40.2×380b==−2.700212×184.04−40.2and38040.2a=−(−2.700)×=40.7111212Thustheregressionequationcanbewritten,totwodecimalplacesforclar-ity,asYi=40.71−2.70

3、Xi+eiInterpretationoftheslopeandinterceptThemostimportantpartoftheresultistheslopecoefficientb=−2.7sinceitmeasurestheeffectofXuponY.Thisresultimpliesthataunitincreaseinthegrowthrate(e.g.from2%to3%p.a.)wouldlowerthebirthrateby2.7,forexamplefrom30birthsper1000pop

4、ulationto27.3.Giventhatthegrowthdatarefertoa20-yearperiod(1961to1981),thisincreaseinthegrowthratewouldhavetobesustainedoversuchatime,notaneasytask.Howbigistheeffectuponthebirthrate?Theaveragebirthrateinthesampleis31.67,soareductionof2.7foranaveragecountrywould

5、beafallof8.5%(2.7/31.67×100).Thisisreasonablysubstantial(althoughnotenoughtobringthebirthratedowntodevelopedcountrylevels)butwouldneedaconsiderable,sustainedincreaseinthegrowthratetobringitabout.Thevalueofa,theintercept,maybeinterpretedasthepredictedbirthrateo

6、facountrywithzerogrowth(sinceZi=aatX=0).Thisvalueof40.71isfairlyclosetothatofSenegal,whichactuallyhadnegativegrowthovertheperiodandwhosebirthratewas48,alittlehigherthantheinterceptvalue.Althoughahasasensibleinterpretationinthiscase,thisisnotalwaysso.Forexample

7、,inaregressionofthedemandforagoodonitsprice,awouldrepresentdemandatzeroprice,whichisunlikelyevertobeobserved.Exercise7.4(a)Calculatetheregressionlinerelatingthebirthratetotheincomeratio.(b)Interpretthecoefficientsofthisequation.?254STFE_C07.qxd26/02/200910:52Pa

8、ge255RegressionanalysisMeasuringthegoodnessoffitoftheregressionlineHavingcalculatedtheregressionlinewenowaskwhetheritprovidesagoodfitforthedata,i.e.dotheobservationstendtoliecloseto,