数据分析72.docx

数据分析72.docx

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数据分析72

Question1

Astatisticsinstructorwantstousethenumberofhoursstudiedtopredictexamscoresinherclass.Shewantstousealinearregressionmodel.Datafrompreviousyearsshowsthatthecorrelationbetweenthesetwovariablesis0.76.Whichofthefollowingisthebestresponseforwhetherornottheinstructorshoulduselinearregressiontopredictexamscoresforastudentwhostudied10hoursforthefinal?

YourAnswer

Score

Explanation

Linearregressioncouldbeappropriateifthescatterplotshowsaclearlinearrelationship.

Correct

1.00

Yes,becauselinearregressionisthestatisticalmethodusedtomakepredictionswhenyouhavebivariatequantitativedata.

Yes,thereisahighcorrelation,soitisappropriatetouselinearregression.

No,becausethereisnowaytoprovethatmorehoursofstudycauseshigherexamscores.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Whendescribingtheassociationbetweentwonumericalvariables,evaluate

 -direction:

positive（x↑,y↑）,negative（x↓,y↑）

 -form:

linearornot

 -strength:

determinedbythescatteraroundtheunderlyingrelationship

Question2

Whichofthefollowingisfalse?

YourAnswer

Score

Explanation

Twonumericalvariableswithacorrelationof0.01haveveryweaklinearassociation.

Correlationmeasuresthestrengthofthelinearassociationbetweentwonumericalvariables.

Correlationcoefficientandtheslopealwayshavethesamesign（positiveornegative）.

Ifthecorrelationcoefficientis1,thentheslopemustbe1aswell.

Correct

1.00

Theslopedoesnotnecessarilyhavetobe1.Imagineadependentvariablewhichincreasesbyprecisely2unitsforevery1unitincreaseintheexplanatoryvariable.ThesevariableshavecorrelationcoefficientR=1yettheslopeoftheregressionlinewouldbe2.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Notethatcorrelationco-efficient（R,alsocalledPearson’sR）hasthefollowingproperties:

 -themagnitude（absolutevalue）ofthecorrelationcoefficientmeasuresthestrengthofthelinearassociationbetweentwonumericalvariables

 -thesignofthecorrelationcoefficientindicatesthedirectionofassociation

 -thecorrelationcoefficientisalwaysbetween-1and1,-1indicatingperfectnegativelinearassociation,+1indicatingperfectpositivelinearassociation,and0indicatingnolinearrelationship

 -thecorrelationcoefficientisunitless

 -sincethecorrelationcoefficientisunitless,itisnotaffectedbychangesinthecenterorscaleofeithervariable（suchasunitconversions）

 -thecorrelationofXwithYisthesameasofYwithX

 -thecorrelationcoefficientissensitivetooutliers

Question3

Fillintheblank:

Residualsoflinearmodelsshouldbedistributednearlynormallyaround__________.

YourAnswer

Score

Explanation

themeanofy^（thepredictedvalues）

0

Correct

1.00

themeanofx

themeanofy

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

•Defineresidual（e）asthedifferencebetweentheobserved（y）andpredicted（y^）valuesoftheresponsevariable.

   ei=yi−y^i

•Definetheleastsquareslineasthelinethatminimizesthesumofthesquaredresiduals,andlistconditionsnecessaryforfittingsuchline:

（1）linearity

（2）nearlynormalresiduals

 （3）constantvariability

Question4

SixteenstudentvolunteersatOhioStateUniversitydrankarandomlyassignednumberbeers.Thirtyminuteslater,apoliceofficermeasuredtheirbloodalcoholcontent（BAC）ingramsofalcoholperdeciliterofblood.Thescatterplotdisplaystherela-tionshipbetweenBACandnumberofbeersconsumed.Supposeamistakewasfoundinthedata:

thestudentwhosupposedlydrankthehighestnumberofbeers（9beers）actuallyonlydrank6.HisBACwasrecordedcorrectly.Inanewscatterplot,howwouldthestrengthoftheassociationappear-comparedtothestrengthoftheassociationshownhere?

YourAnswer

Score

Explanation

Roughlythesameasthestrengthoftheassociationshownintheabovescatterplot.

Weakerthanthestrengthoftheassociationshownintheabovescatterplot.

Strongerthanthestrengthoftheassociationshownintheabovescatterplot.

It’simpossibletotell.

Inorrect

0.00

Movingtherightmostpointbacktox=6wouldresultinascatterplotwherethereismorescatteraroundthemaintrendofthedata.Thereforewewouldsaythenewstrengthofassociationwouldbeweakerthanthatshownabove.

Total

0.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

Whendescribingtheassociationbetweentwonumericalvariables,evaluate

 -direction:

positive（x↑,y↑）,negative（x↓,y↑）

 -form:

linearornot

 -strength:

determinedbythescatteraroundtheunderlyingrelationship.

Question5

TheR2forthelinearregressionoftwovariablesxandyis0.60.Thevariablesarenegativelyassociated.Whichofthefollowingthecorrectcorrelationcoefficient?

Choosetheclosestanswer.

YourAnswer

Score

Explanation

0.40

-0.77

Correct

1.00

0.60−−−−√≈0.77,butthecorrelationcoefficientisnegativesincethevariablesarenegativelyassociated.

-0.36

0.36

0.77

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

DefineR2asthepercentageofthevariabilityintheresponsevariableexplainedbythetheexplanatoryvariable.

 -Foragoodmodel,wewouldlikethisnumbertobeascloseto100%aspossible.

 -Thisvalueiscalculatedasthesquareofthecorrelationcoefficient.

Question6

Thescatterplotontherightshowstherelationshipbetweenpercentageofwhiteresidentsandpercentageofhouseholdswithafemalehead（wherenohusbandispresent）inall50USStatesandtheDistrictofColumbia（DC）.WhichofthebelowbestdescribesthetwopointsmarkedasDCandHawaii?

YourAnswer

Score

Explanation

HawaiihashigherleverageandismoreinfluentialthanDC.

Correct

1.00

HawaiihashigherleveragethanDCbecauseitisfartherawayfromthebulkofthedatainthexdirection.

DCismoreinfluentialthanHawaii,butithaslowerleveragethanHawaii.

Hawaiiisnotanoutlier,andDCisnotaleveragepoint.

DCisnotanoutlier,andHawaiiisaleveragepoint.

DCandHawaiishouldbothbeexcludedfromasimplelinearregressionanalysis.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

 -Definealeveragepointasapointthatliesawayfromthecenterofthedatainthehorizontaldirection.

 -Defineaninfluentialpointasapointthatinfluences（changes）theslopeoftheregressionline.Thisisusuallyaleveragepointthatisawayfromthetrajectoryoftherestofthedata.

Question7

Acolleagueneedssomehelpwithastatisticsproblem:

Hebringsyoutheplotshownbelow,alongwithacorrelationcoefficientof0.03whichhecalculatedhimself.Theplotshowstwonumericalvariableswhichareobviouslystronglyrelated,andasaresultyourcolleagueisafraidhemadeamistakecalculatingthecorrelationcoefficient:

thatis,hewassurprisedtogetananswersocloseto0.Givenonlythisinformation,whichofthefollowingresponsesisthebesttogiveyourcolleague?

YourAnswer

Score

Explanation

Thecorrelationcoefficientmeasuresthestrengthofthelinearrelationship,thereforetwovariablesthathaveastrongnon-linearassociationmightstillhavealowcorrelationcoefficient.

Correct

1.00

Yourcolleaguemusthavemadeamistakeinhiscalculations.Amuchhighercorrelationcoefficientisexpectedforvariablesthatshowaclearassociation.

Total

1.00/1.00

QuestionExplanationThisquestionreferstothefollowinglearningobjective（s）:

 -Definecorrelationasthelinearassociationbetweentwonumericalvariables.

 -Notethatarelationshipthatisnonlinearissimplycalledanassociation.

 -Notethatcorrelationcoefficient（R,alsocalledPearson’sR）hasthefollowingproperties:

  -themagnitude（absolutevalue）ofthecorrelationcoefficientmeasuresthestrengthofthelinearassociationbetweentwonumericalvariables

  -thesignofthecorrelationcoefficientindicatesthedirectionofassociation

  -thecorrelationcoefficientisalwaysbetween-1and1,-1indicatingperfectnegativelinearassociation,+1indicatingperfectpositivelinearassociation,and0indicatingnolinearrelationship

  -thecorrelationcoefficientisunitless

  -sincethecorrelationcoefficientisunitless,itisnotaffectedbychangesinthecenterorscaleofeithervariable（suchasunitconversions）

  -thecorrelationofXwithYisthesameasofYwithX

  -thecorrelationcoefficientissensitivetooutliers

Question8

Basedonarandomsampleof170marriedcouplesinBritain,aresearcherfindsthattherelationshipbetweenthehusbands’andwives’agesisdescribedbythefollowingequation:

Whichofthefollowingisthebestinterpretationoftheslopeestimate?

YourAnswer

Score

Explanation

MostwivesinBritainare0.91yearsyoungerthantheirhusbands.

Onaverage,whenahusbandinBritaingets1yearolder,hiswifeonlygets0.91yearsolder.

Foreachadditionalyearincreaseofhusband’sage,wewouldexpectthewife’sagetobe0.91yearshigher,onaverage.

Correct

1.00

Foreachadditionalyearincreaseofwife’s