(1.16)-FC5e-Ch12商務(wù)統(tǒng)計(jì)課件

BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc.Chap12-1Chapter12SimpleLinearRegressionBusinessStatistics:AFirstCourse

FifthEditionBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-2LearningObjectivesInthischapter,youlearn:

HowtouseregressionanalysistopredictthevalueofadependentvariablebasedonanindependentvariableThemeaningoftheregressioncoefficientsb0andb1HowtoevaluatetheassumptionsofregressionanalysisandknowwhattodoiftheassumptionsareviolatedTomakeinferencesabouttheslopeandcorrelationcoefficientToestimatemeanvaluesandpredictindividualvaluesBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-3Correlationvs.RegressionAscatterplotcanbeusedtoshowtherelationshipbetweentwovariablesCorrelationanalysisisusedtomeasurethestrengthoftheassociation(linearrelationship)betweentwovariablesCorrelationisonlyconcernedwithstrengthoftherelationshipNocausaleffectisimpliedwithcorrelationScatterplotswerefirstpresentedinCh.2CorrelationwasfirstpresentedinCh.3相關(guān)不蘊(yùn)涵因果BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-4Introductionto

RegressionAnalysisRegressionanalysisisusedto:PredictthevalueofadependentvariablebasedonthevalueofatleastoneindependentvariableExplaintheimpactofchangesinanindependentvariableonthedependentvariableDependentvariable:thevariablewewishto predictorexplainIndependentvariable:thevariableusedtopredict orexplainthedependent variable因變量自變量回歸分析BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-5SimpleLinearRegressionModelOnlyoneindependentvariable,XRelationshipbetweenXandYisdescribedbyalinearfunctionChangesinYareassumedtoberelatedtochangesinXBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-6TypesofRelationshipsYXYXYYXXLinearrelationshipsCurvilinearrelationshipsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-7TypesofRelationshipsYXYXYYXXStrongrelationshipsWeakrelationships(continued)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-8TypesofRelationshipsYXYXNorelationship(continued)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-9LinearcomponentSimpleLinearRegressionModelPopulation

YinterceptPopulationSlope

CoefficientRandomErrortermDependentVariableIndependentVariableRandomErrorcomponentBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-10(continued)RandomErrorforthisXivalueYXObservedValueofYforXiPredictedValueofYforXi

XiSlope=β1Intercept=β0

εiSimpleLinearRegressionModelBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-11ThesimplelinearregressionequationprovidesanestimateofthepopulationregressionlineSimpleLinearRegressionEquation(PredictionLine)Estimateoftheregression

interceptEstimateoftheregressionslope

Estimated(orpredicted)YvalueforobservationiValueofXforobservationiBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-12TheLeastSquaresMethodb0andb1areobtainedbyfindingthevaluesofthatminimizethesumofthesquareddifferencesbetweenYand:最小二乘法BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-13FindingtheLeastSquaresEquationThecoefficientsb0andb1,andotherregressionresultsinthischapter,willbefoundusingExcelorMinitabBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-14b0istheestimatedmeanvalueofYwhenthevalueofXiszerob1istheestimatedchangeinthemeanvalueofYasaresultofaone-unitchangeinXInterpretationofthe

SlopeandtheInterceptBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-15SimpleLinearRegressionExampleArealestateagentwishestoexaminetherelationshipbetweenthesellingpriceofahomeanditssize(measuredinsquarefeet)Arandomsampleof10housesisselectedDependentvariable(Y)=housepricein$1000sIndependentvariable(X)=squarefeetBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-16SimpleLinearRegressionExample:DataHousePricein$1000s(Y)SquareFeet(X)2451400312160027917003081875199110021915504052350324245031914252551700BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-17SimpleLinearRegressionExample:ScatterPlotHousepricemodel:ScatterPlotBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-18SimpleLinearRegressionExample:UsingExcelBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-19SimpleLinearRegressionExample:ExcelOutputRegressionStatisticsMultipleR0.76211RSquare0.58082AdjustedRSquare0.52842StandardError41.33032Observations10ANOVA

dfSSMSFSignificanceFRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000

CoefficientsStandardErrortStatP-valueLower95%Upper95%Intercept98.2483358.033481.692960.12892-35.57720232.07386SquareFeet0.109770.032973.329380.010390.033740.18580Theregressionequationis:BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-20SimpleLinearRegressionExample:MinitabOutputTheregressionequationisPrice=98.2+0.110SquareFeet

Predictor

Coef

SECoef

T

PConstant

98.25

58.03

1.69

0.129SquareFeet

0.10977

0.03297

3.33

0.010

S=41.3303

R-Sq=58.1%

R-Sq(adj)=52.8%

AnalysisofVariance

Source

DF

SS

MS

F

PRegression

1

18935

18935

11.08

0.010ResidualError

8

13666

1708Total

9

32600Theregressionequationis:houseprice=98.24833+ 0.10977(squarefeet)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-21SimpleLinearRegressionExample:GraphicalRepresentationHousepricemodel:ScatterPlotandPredictionLineSlope=0.10977Intercept=98.248BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-22SimpleLinearRegressionExample:Interpretationofbob0istheestimatedmeanvalueofYwhenthevalueofXiszero(ifX=0isintherangeofobservedXvalues)Becauseahousecannothaveasquarefootageof0,b0hasnopracticalapplicationBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-23SimpleLinearRegressionExample:Interpretingb1b1estimatesthechangeinthemeanvalueofYasaresultofaone-unitincreaseinXHere,b1=0.10977tellsusthatthemeanvalueofahouseincreasesby0.10977($1000)=$109.77,onaverage,foreachadditionalonesquarefootofsizeBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-24Predictthepriceforahousewith2000squarefeet:Thepredictedpriceforahousewith2000squarefeetis317.85($1,000s)=$317,850SimpleLinearRegressionExample:MakingPredictionsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-25SimpleLinearRegressionExample:MakingPredictionsWhenusingaregressionmodelforprediction,onlypredictwithintherelevantrangeofdataRelevantrangeforinterpolationDonottrytoextrapolatebeyondtherangeofobservedX’sBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-26MeasuresofVariationTotalvariationismadeupoftwoparts:TotalSumofSquaresRegressionSumofSquaresErrorSumofSquareswhere:

=Meanvalueofthedependentvariable

Yi=Observedvalueofthedependentvariable =PredictedvalueofYforthegivenXivalue回歸平方和殘差平方和BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-27SST=totalsumofsquares(TotalVariation)MeasuresthevariationoftheYivaluesaroundtheirmeanYSSR=regressionsumofsquares(ExplainedVariation)VariationattributabletotherelationshipbetweenXandYSSE=errorsumofsquares(UnexplainedVariation)VariationinYattributabletofactorsotherthanX(continued)MeasuresofVariationBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-28(continued)XiYXYiSST

=

(Yi

-

Y)2SSE

=

(Yi

-

Yi)2

SSR=

(Yi

-

Y)2

___Y

YY_Y

MeasuresofVariationBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-29ThecoefficientofdeterminationistheportionofthetotalvariationinthedependentvariablethatisexplainedbyvariationintheindependentvariableThecoefficientofdeterminationisalsocalledr-squaredandisdenotedasr2CoefficientofDetermination,r2note:判定系數(shù)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-30r2=1Examplesofr2ValuesYXYXr2=1r2=1PerfectlinearrelationshipbetweenXandY:100%ofthevariationinYisexplainedbyvariationinXBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-31Examplesofr2ValuesYXYX0<r2<1WeakerlinearrelationshipsbetweenXandY:SomebutnotallofthevariationinYisexplainedbyvariationinXBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-32Examplesofr2Valuesr2=0NolinearrelationshipbetweenXandY:ThevalueofYdoesnotdependonX.(NoneofthevariationinYisexplainedbyvariationinX)YXr2=0BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-33SimpleLinearRegressionExample:CoefficientofDetermination,r2inExcelRegressionStatisticsMultipleR0.76211RSquare0.58082AdjustedRSquare0.52842StandardError41.33032Observations10ANOVA

dfSSMSFSignificanceFRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000

CoefficientsStandardErrortStatP-valueLower95%Upper95%Intercept98.2483358.033481.692960.12892-35.57720232.07386SquareFeet0.109770.032973.329380.010390.033740.1858058.08%ofthevariationinhousepricesisexplainedbyvariationinsquarefeetBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-34SimpleLinearRegressionExample:CoefficientofDetermination,r2inMinitabTheregressionequationisPrice=98.2+0.110SquareFeet

Predictor

Coef

SECoef

T

PConstant

98.25

58.03

1.69

0.129SquareFeet

0.10977

0.03297

3.33

0.010

S=41.3303

R-Sq=58.1%

R-Sq(adj)=52.8%

AnalysisofVariance

Source

DF

SS

MS

F

PRegression

1

18935

18935

11.08

0.010ResidualError

8

13666

1708Total

9

3260058.08%ofthevariationinhousepricesisexplainedbyvariationinsquarefeetBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-35StandardErrorofEstimateThestandarddeviationofthevariationofobservationsaroundtheregressionlineisestimatedbyWhere SSE=errorsumofsquares n=samplesizeBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-36SimpleLinearRegressionExample:

StandardErrorofEstimateinExcelRegressionStatisticsMultipleR0.76211RSquare0.58082AdjustedRSquare0.52842StandardError41.33032Observations10ANOVA

dfSSMSFSignificanceFRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000

CoefficientsStandardErrortStatP-valueLower95%Upper95%Intercept98.2483358.033481.692960.12892-35.57720232.07386SquareFeet0.109770.032973.329380.010390.033740.18580BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-37SimpleLinearRegressionExample:

StandardErrorofEstimateinMinitabTheregressionequationisPrice=98.2+0.110SquareFeet

Predictor

Coef

SECoef

T

PConstant

98.25

58.03

1.69

0.129SquareFeet

0.10977

0.03297

3.33

0.010

S=41.3303

R-Sq=58.1%

R-Sq(adj)=52.8%

AnalysisofVariance

Source

DF

SS

MS

F

PRegression

1

18935

18935

11.08

0.010ResidualError

8

13666

1708Total

9

32600BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-38ComparingStandardErrorsYYXXSYXisameasureofthevariationofobservedYvaluesfromtheregressionlineThemagnitudeofSYXshouldalwaysbejudgedrelativetothesizeoftheYvaluesinthesampledatai.e.,SYX=$41.33Kis

moderatelysmallrelativetohousepricesinthe$200K-$400KrangeBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-39AssumptionsofRegression

L.I.N.ELinearityTherelationshipbetweenXandYislinearIndependenceofErrorsErrorvaluesarestatisticallyindependentNormalityofErrorErrorvaluesarenormallydistributedforanygivenvalueofXEqualVariance(alsocalledhomoscedasticity)TheprobabilitydistributionoftheerrorshasconstantvarianceBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-40ResidualAnalysisTheresidualforobservationi,ei,isthedifferencebetweenitsobservedandpredictedvalueChecktheassumptionsofregressionbyexaminingtheresidualsExamineforlinearityassumptionEvaluateindependenceassumptionEvaluatenormaldistributionassumptionExamineforconstantvarianceforalllevelsofX(homoscedasticity)GraphicalAnalysisofResidualsCanplotresidualsvs.X殘差分析BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-41ResidualAnalysisforLinearityNotLinearLinear

xresidualsxYxYxresidualsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-42ResidualAnalysisforIndependenceNotIndependentIndependentXXresidualsresidualsXresiduals

BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-43CheckingforNormalityExaminetheStem-and-LeafDisplayoftheResidualsExaminetheBoxplotoftheResidualsExaminetheHistogramoftheResidualsConstructaNormalProbabilityPlotoftheResidualsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-44ResidualAnalysisforNormalityPercentResidualWhenusinganormalprobabilityplot,normalerrorswillapproximatelydisplayinastraightline-3-2-101230100BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-45ResidualAnalysisfor

EqualVarianceNon-constantvariance

ConstantvariancexxYxxYresidualsresidualsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-46SimpleLinearRegressionExample:ExcelResidualOutputRESIDUALOUTPUTPredictedHousePriceResiduals1251.92316-6.9231622273.8767138.123293284.85348-5.8534844304.062843.9371625218.99284-19.992846268.38832-49.388327356.2025148.797498367.17929-43.179299254.667464.3326410284.85348-29.85348DoesnotappeartoviolateanyregressionassumptionsBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-47InferencesAbouttheSlopeThestandarderroroftheregressionslopecoefficient(b1)isestimatedbywhere:

=Estimateofthestandarderroroftheslope =StandarderroroftheestimateBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-48InferencesAbouttheSlope:

tTestttestforapopulationslopeIstherealinearrelationshipbetweenXandY?NullandalternativehypothesesH0:β1=0 (nolinearrelationship)H1:β1≠0 (linearrelationshipdoesexist)Teststatistic

where:b1=regressionslopecoefficient

β1=hypothesizedslopeSb1=standarderroroftheslopeBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-49InferencesAbouttheSlope:

tTestExampleHousePricein$1000s(y)SquareFeet(x)2451400312160027917003081875199110021915504052350324245031914252551700EstimatedRegressionEquation:Theslopeofthismodelis0.1098Istherearelationshipbetweenthesquarefootageofthehouseanditssalesprice?BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-50InferencesAbouttheSlope:

tTestExampleH0:β1=0H1:β1≠0FromExceloutput:

CoefficientsStandardErrortStatP-valueIntercept98.2483358.033481.692960.12892SquareFeet0.109770.032973.329380.01039b1Predictor

Coef

SECoef

T

PConstant

98.25

58.03

1.69

0.129SquareFeet

0.10977

0.03297

3.33

0.010FromMinitaboutput:b1BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-51InferencesAbouttheSlope:

tTestExampleTestStatistic:tSTAT=3.329ThereissufficientevidencethatsquarefootageaffectshousepriceDecision:RejectH0RejectH0RejectH0a/2=.025-tα/2DonotrejectH00tα/2a/2=.025-2.30602.30603.329d.f.=10-2=8H0:β1=0H1:β1≠0BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-52InferencesAbouttheSlope:

tTestExampleH0:β1=0H1:β1≠0FromExceloutput:

CoefficientsStandardErrortStatP-valueIntercept98.2483358.033481.692960.12892SquareFeet0.109770.032973.329380.01039p-valueThereissufficientevidencethatsquarefootageaffectshouseprice.Decision:RejectH0,sincep-value<αPredictor

Coef

SECoef

T

PConstant

98.25

58.03

1.69

0.129SquareFeet

0.10977

0.03297

3.33

0.010FromMinitaboutput:BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-53FTestforSignificanceFTeststatistic:

where

whereFSTATfollowsanFdistributionwith1numerator

and(n–2)denominatordegreesoffreedom

BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-54F-TestforSignificance

ExcelOutputRegressionStatisticsMultipleR0.76211RSquare0.58082AdjustedRSquare0.52842StandardError41.33032Observations10ANOVA

dfSSMSFSignificanceFRegression118934.934818934.934811.08480.01039Residual813665.56521708.1957Total932600.5000

With1and8degreesoffreedomp-valuefortheF-TestBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-55F-TestforSignificance

MinitabOutputAnalysisofVariance

Source

DF

SS

MS

F

PRegression

1

18935

18935

11.08

0.010ResidualError

8

13666

1708Total

9

32600With1and8degreesoffreedomp-valuefortheF-TestBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-56H0:β1=0H1:β1≠0

=.05df1=1df2=8TestStatistic:Decision:Conclusion:RejectH0at

=0.05Thereissufficientevidencethathousesizeaffectssellingprice0

=.05F.05=5.32RejectH0DonotrejectH0CriticalValue:F

=5.32FTestforSignificance(continued)FBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-57ConfidenceIntervalEstimate

fortheSlopeConfidenceIntervalEstimateoftheSlope:ExcelPrintoutforHousePrices:At95%levelofconfidence,theconfidenceintervalfortheslopeis(0.0337,0.1858)

CoefficientsStandardErrortStatP-valueLower95%Upper95%Intercept98.2483358.033481.692960.12892-35.57720232.07386SquareFeet0.109770.032973.329380.010390.033740.18580d.f.=n-2BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-58Sincetheunitsofthehousepricevariableis$1000s,weare95%confidentthattheaverageimpactonsalespriceisbetween$33.74and$185.80persquarefootofhousesize

CoefficientsStandardErrortStatP-valueLower95%Upper95%Intercept98.2483358.033481.692960.12892-35.57720232.07386SquareFeet0.109770.032973.329380.010390.033740.18580This95%confidenceintervaldoesnotinclude0.Conclusion:Thereisasignificantrelationshipbetweenhousepriceandsquarefeetatthe.05levelofsignificanceConfidenceIntervalEstimate

fortheSlope(continued)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-59tTestforaCorrelationCoefficientHypotheses H0:ρ=0 (nocorrelationbetweenXandY)

H1:ρ

≠0 (correlationexists)Teststatistic

(withn–2degreesoffreedom)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-60t-testForACorrelationCoefficientIsthereevidenceofalinearrelationshipbetweensquarefeetandhousepriceatthe.05levelofsignificance?H0:ρ

=0(Nocorrelation)H1:ρ≠0(correlationexists)

=.05,df

=

10-2=8(continued)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-61t-testForACorrelationCoefficientConclusion:

Thereisevidenceofalinearassociationatthe5%levelofsignificanceDecision:

RejectH0RejectH0RejectH0a/2=.025-tα/2DonotrejectH00tα/2a/2=.025-2.30602.30603.329d.f.=10-2=8(continued)BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-62EstimatingMeanValuesandPredictingIndividualValuesYX

XiY=b0+b1Xi

ConfidenceIntervalforthemeanofY,givenXiPredictionIntervalforanindividualY,givenXiGoal:FormintervalsaroundYtoexpressuncertaintyaboutthevalueofYforagivenXiY

BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-63ConfidenceIntervalfor

theAverageY,GivenXConfidenceintervalestimateforthemeanvalueofYgivenaparticularXiSizeofintervalvariesaccordingtodistanceawayfrommean,

XBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-64PredictionIntervalfor

anIndividualY,GivenXPredictionintervalestimateforanIndividualvalueofYgivenaparticularXiThisextratermaddstotheintervalwidthtoreflecttheaddeduncertaintyforanindividualcaseBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-65EstimationofMeanValues:ExampleFindthe95%confidenceintervalforthemeanpriceof2,000square-foothousesPredictedPriceYi=317.85($1,000s)

ConfidenceIntervalEstimateforμY|X=XTheconfidenceintervalendpointsare280.66and354.90,orfrom$280,660to$354,900iBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-66EstimationofIndividualValues:ExampleFindthe95%predictionintervalforanindividualhousewith2,000squarefeetPredictedPriceYi=317.85($1,000s)

PredictionIntervalEstimateforYX=XThepredictionintervalendpointsare215.50and420.07,orfrom$215,500to$420,070iBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-67FindingConfidenceand

PredictionIntervalsinExcelFromExcel,use PHStat|regression|simplelinearregression…Checkthe

“confidenceandpredictionintervalforX=”

boxandentertheX-valueandconfidenceleveldesiredBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-68InputvaluesFindingConfidenceand

PredictionIntervalsinExcel(continued)ConfidenceIntervalEstimateforμY|X=XiPredictionIntervalEstimateforYX=XiY

BusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-69FindingConfidenceand

PredictionIntervalsinMinitabPredictedValuesforNewObservations

NewObs

Fit

SEFit

95%CI

95%PI

1

317.8

16.1

(280.7,354.9)

(215.5,420.1)

ValuesofPredictorsforNewObservations

New

SquareObs

Feet

1

2000Y

InputvaluesConfidenceIntervalEstimateforμY|X=XiPredictionIntervalEstimateforYX=XiBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-70PitfallsofRegressionAnalysisLackinganawarenessoftheassumptionsunderlyingleast-squaresregressionNotknowinghowtoevaluatetheassumptionsNotknowingthealternativestoleast-squaresregressionifaparticularassumptionisviolatedUsingaregressionmodelwithoutknowledgeofthesubjectmatterExtrapolatingoutsidetherelevantrangeBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-71StrategiesforAvoiding

thePitfallsofRegressionStartwithascatterplotofXvs.YtoobservepossiblerelationshipPerformresidualanalysistochecktheassumptionsPlottheresidualsvs.XtocheckforviolationsofassumptionssuchashomoscedasticityUseahistogram,stem-and-leafdisplay,boxplot,ornormalprobabilityplotoftheresidualstouncoverpossiblenon-normalityBusinessStatistics:AFirstCourse,5e?2009Prentice-Hall,Inc..Chap12-72StrategiesforAvoiding

thePitfallsofRegressionIfthereisviolationofanyassumption,usealternativemethodsormodelsIfthereisnoevidenceofassumptionviolation,thentestforthesignificanceoftheregressioncoefficientsandconstructconfidenceintervalsandpredictionintervalsAvoidmakingpredictionsorforecastsoutsidetherelevantrange(continued)BusinessSta