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1、Chapter10LinearRegressionandCorrelationMostreal-lifestatisticalproblemshaveoneormorenonstandardfeatures.Therearenoroutinestatisticalquestions;onlyquestionablestatisticalroutines.D.Cox,Britishstatistician10.1OrientationScientistsarefrequentlyinterestedinstudyingthefunctio
2、nalrelationshipbetweentwovariablesyandx.Forexample,inanagriculturalexperiment,thecropyieldymaydependontheamountoffertilizerx;inametallurgicalexperimentoneisinterestedintheshearstrengthyofaspotweldasafunctionofthewelddiameterx.Thevariablexisvariouslycalledtheexplanatoryva
3、riable,theregressorvariable,orthepredictorvariable;yiscalledthedependentvariableandalsotheresponsevariable.Weassumethattherelationshipbetweentheexplanatoryandresponsevariablesisgivenbyafunctiony=f(x),wherefisunknown.Inmostcasesthefunctionisspecifiedbyatheoreticalmodel.For
4、example,Hooke’slawassertsthattheforcerequiredtostretchaspringbyadistancexfromitsrelaxedlengthisgivenbyy=βx,whereβisaconstantthatischaracteristicofthespring.Inthisexampletherelationshipbetweenthevariablesisderivedfromthebasicprinciplesofmechanics.Inmostcases,however,thesc
5、ientistisuncertainastotheexactformofthefunctionalrelationshipy=f(x)andheproceedstostudyitbyperformingaseriesofexperimentsanddrawingthescatterplotoftheobservedvalues(xi,yi),i=1,...n,whereyiisthevalueoftheresponsecorrespondingtothechosenvaluexi.Theshapeofthescatterplotwill
6、thenprovidesomeinsightintothefunctionalrelationshipbetweenyandx.Regressionanalysisisamethodfordeterminingthefunctionthatbestfitstheobserveddata.OrganizationofChapter1.Section10.2:MethodofLeastSquares2.Section10.2.1:FittingaStraightLineviaOrdinaryLeastSquares3.Section10.3:
7、TheSimpleLinearRegressionModel4.Section10.3.1:TheSamplingDistributionofβˆ1,βˆ0,SSE,andSSR5.Section10.3.2:TestsofHypothesesConcerningtheRegressionParameters6.Section10.3.3:ConfidenceIntervalsandPredictionIntervals7.Section10.3.4:DisplayingtheOutputofaRegressionAnalysisinan
8、ANOVATable8.Section10.3.5:CurvilinearRegression389390IntroductiontoProbabilityandStatisticsforScience,E
