(1.32)-PowerPoint Ch 12b商务统计课件

Chapter12,PartB

SimpleLinearRegressionUsingtheEstimatedRegressionEquation forEstimationandPredictionResidualAnalysis:ValidatingModelAssumptionsComputerSolutionUsingtheEstimatedRegressionEquation

forEstimationandPredictionwhere: confidencecoefficientis1-

and

t

/2isbasedonatdistribution withn-2degreesoffreedomConfidenceIntervalEstimateofE(yp)PredictionIntervalEstimateofyp If3TVadsarerunpriortoasale,weexpect themeannumberofcarssoldtobe:PointEstimation^y=10+5(3)=25carsEstimateoftheStandardDeviationofConfidenceIntervalforE(yp) The95%confidenceintervalestimateofthemeannumberofcarssoldwhen3TVadsarerunis:ConfidenceIntervalforE(yp)25+4.6125+3.1824(1.4491)20.39to29.61carsEstimateoftheStandardDeviationofanIndividualValueofypPredictionIntervalforyp The95%predictionintervalestimateofthenumberofcarssoldinoneparticularweekwhen3TVadsarerunis:PredictionIntervalforyp25+8.2825+3.1824(2.6013)16.72to33.28carsComputerSolution

RecallthattheindependentvariablewasnamedAdsandthedependentvariablewasnamedCarsintheexample.

OnthenextslideweshowMinitaboutputfortheReedAutoSalesexample.

Performingtheregressionanalysiscomputationswithoutthehelpofacomputercanbequitetimeconsuming.

Theregressionequationis

Cars=10+5.00Ads

PredictorCoefSECoefTp

Constant10.0002.3664.230.024

Ads5.00001.08014.630.019

S=2.2R-sq=87.7%R-sq(adj)=83.6%

AnalysisofVariance

SOURCEDFSSMSFp

Regression110010021.430.019

ResidualError3144.667

Total4114

PredictedValuesforNewObservations

New

ObsFitSEFit95%C.I.95%P.I.

125.002.60(20.39,29.61)(16.72,33.28)

ComputerSolutionMinitabOutput

Minitabprintsthestandarderroroftheestimate,s,aswellasinformationaboutthegoodnessoffit..

Foreachofthecoefficientsb0andb1,theoutputshowsitsvalue,standarddeviation,tvalue,andp-value.

MinitabprintstheestimatedregressionequationasCars=10.0+5.00Ads.

ThestandardANOVAtableisprinted.

Alsoprovidedarethe95%confidenceintervalestimateoftheexpectednumberofcarssoldandthe95%predictionintervalestimateofthenumberofcarssoldforanindividualweekendwith3ads.ResidualAnalysisMuchoftheresidualanalysisisbasedonanexaminationofgraphicalplots.ResidualforObservationi

Theresidualsprovidethebestinformationaboute

.Iftheassumptionsabouttheerrortermeappearquestionable,thehypothesistestsaboutthesignificanceoftheregressionrelationshipandtheintervalestimationresultsmaynotbevalid.ResidualPlotAgainstxIftheassumptionthatthevarianceofeisthesameforallvaluesofxisvalid,andtheassumedregressionmodelisanadequaterepresentationoftherelationshipbetweenthevariables,thenTheresidualplotshouldgiveanoverallimpressionofahorizontalbandofpointsx0GoodPatternResidualResidualPlotAgainstxResidualPlotAgainst