MATH 141 (4.1, 4.2, 4.3, AND 4.4)
HOMEWORK QUESTIONS WITH
CORRECT ANSWERS
The fftable ffto ffthe ffright ffshows ffthe ffnumber ffof ffpeople ffliving ffin ffa ffhouse ffand
ffthe ffweight ffof fftrash ff(in ffpounds) ffat ffthe ffcurb ffjust ffbefore fftrash ffpickup.
ffComplete ffparts ff(a) ffthrough ff(c) ffbelow.
People ffTrash ff(pounds)
3 ff30 ff
3 ff22
6 ff90
1 ff30
9 ff94 ff- ffAnswer ffa. ffFind ffthe ffcorrelation ffbetween ffthese ffnumbers ffby ffusing ffa
ffcomputer ffor ffa ffstatistical ffcalculator.
r= ff(0.901) ff
b. ffSuppose ffsome ffof ffthe ffweight ffwas fffrom ffthe ffcontainer ff(each ffcontainer
ffweighs ff5 ffpounds). ffSubtract ff5 ffpounds fffrom ffeach ffweight, ffand fffind ffthe ffnew
ffcorrelation ffwith ffthe ffnumber ffof ffpeople. ffWhat ffhappens ffto ffthe ffcorrelation
ffwhen ffa ffconstant ffis ffadded ff(we ffadded ffnegative ff5) ffto ffeach ffnumber?
(The ffcorrelation ffis ff
0.901. ffThe ffcorrelation ffcoefficient ffremains ffthe ffsame ffwhen ffa ffconstant ffis
ffadded ffto ffeach ffnumber.)
c. ffSuppose ffeach ffhouse ffcontained ffexactly fftwice ffthe ffnumber ffof ffpeople, ffbut
ffthe ffweight ffof ffthe fftrash ffwas ffthe ffsame. ffWhat ffhappens ffto ffthe ffcorrelation
ffwhen ffnumbers ffare ffmultiplied ffby ffa ffconstant?
(The ffcorrelation ffis ff0.901. ffThe ffcorrelation ffcoefficient ffremains ffthe ffsame ffwhen
ffthe ffnumbers ffare ffmultiplied ffby ffa ffpositive ffconstant.)
The fffigure ffshows ffa ffscatterplot ffof ffthe ffage ffof ffstudents ffand ffthe ffvalue ffof
fftheir ffcars. ffDoes ffit ffshow ffan ffincreasing fftrend, ffa ffdecreasing fftrend, ffa
ffchanging fftrend, ffor ffvery fflittle fftrend? ff- ffAnswer ffDecreasing fftrend
The fffigure ffshows ffa ffscatterplot ffof ffshoe ffsize ffand ffGPA fffor ffsome ffcollege
ffstudents. ffDoes ffit ffshow ffan ffincreasing fftrend, ffa ffdecreasing fftrend, ffor ffno
fftrend? ffIs ffthere ffa ffstrong ffrelationship? ff- ffAnswer ffThe ffgraph ffshows ff
(an ffincreasing)
, fflinear fftrend ffsince ffthe ffpoints ffshow ff
(an ffincreasing)
ffpattern ffby ffscanning ffthe ffgraph fffrom ffleft ffto ffright. ffThe ffrelationship ff
(is)
ffstrong ffbecause ffthe ffpoints ff
(Show)
ffconsistent ffand ffsmall ffvertical ffspread.
The ffscatterplot ffshows ffthe ffactual ffweight ffand ffdesired ffweight ffchange ffof ffsome
ffstudents. ffThus, ffif ffthey ffweighed ff220 ffand ffwanted ffto ffweigh ff190, ffthe ffdesired
ffweight ffchange ffwould ffbe ffnegative ff30. ffExplain ffwhat ffyou ffsee. ffIn ffparticular,
ffwhat ffdoes ffit ffmean ffthat ffthe fftrend ffis ffnegative? ff- ffAnswer ffThe ffmore ffpeople
ffweigh, ffthe ffmore ffweight ffthey fftend ffto ffwant ffto fflose.
The ffscatterplot ffshows ffthe ffsalary ffand ffyear ffof fffirst ffemployment fffor ffsome
ffprofessors ffat ffa ffcollege. ffExplain, ffin ffcontext, ffwhat ffthe ffnegative fftrend ffshows.
ffWho ffmakes ffthe ffmost ffand ffwho ffmakes ffthe ffleast? ff- ffAnswer ffThe ffpeople
ffhired ffthe ffmost ffrecently fftend ffto ffhave fflower ffsalaries, ffand ffthe ffpeople ffhired
ffmany ffyears ffago fftend ffto ffhave ffhigher ffsalaries.
The ffscatterplot ffshows ffdata fffrom ffthe ff50 ffstates fftaken fffrom ffthe ffU.S.
ffCensuslong ffdashthe ffpercentage ffof ffthe ffpopulation ff(25 ffyears ffor ffolder) ffwith ffa
ffcollege ffdegree ffor ffhigher ffand ffthe ffmedian fffamily ffincome. ffDescribe ffand
ffinterpret ffthe fftrend. ff- ffAnswer ffWhat ffis ffthe fftrend? ffWhat ffdoes ffthe ffdirection
ffof ffthe fftrend ffmean? ffChoose ffthe ffcorrect ffanswer ffbelow?
(The fftrend ffis ffpositive. ffStates ffwith ffa fflarger ffproportion ffof ffcollege-educated
ffpeople fftend ffto ffhave ffhigher ffmedian fffamily ffincome.)
The ffscatterplot ffshows ffthe ffnumber ffof ffwork ffhours ffand ffthe ffnumber ffof ffTV
ffhours ffper ffweek fffor ffsome ffcollege ffstudents ffwho ffwork. ffThere ffis ffa ffvery
ffslight fftrend. ffIs ffthe fftrend ffpositive ffor ffnegative? ffWhat ffdoes ffthe ffdirection ffof
ffthe fftrend ffmean ffin ffthis ffcontext? ffIdentify ffany ffunusual ffpoints. ff- ffAnswer ffA.
ffWhat ffis ffthe fftrend? ffWhat ffdoes ffthe ffdirection ffof ffthe fftrend ffmean? ffChoose
ffthe ffcorrect ffanswer ffbelow.
(The fftrend ffis ffnegative. ffThe ffmore ffhours ffof ffwork ffa ffstudent ffhas, ffthe fffewer
ffhours ffof ffTV ffthe ffstudent fftends ffto ffwatch.)
B. ffIdentify ffany ffunusual ffpoints. ffSelect ffthe ffcorrect ffchoice ffbelow ffand, ffif
ffnecessary, fffill ffin ffthe ffanswer ffbox ffto ffcomplete ffyour ffchoice.
(The ffperson ffwho ffworks ff
70
70 ffhours ffappears ffto ffbe ffan ffoutlier, ffbecause ffthat ffpoint ffis ffseparated fffrom
ffthe ffother ffpoints ffby ffa fflarge ffamount.)
, The fffigure ffshows ffa ffscatterplot ffof ffthe ffheights ffand ffweights ffof ffsome ffwomen
fftaking ffstatistics. ffDescribe ffwhat ffyou ffsee. ffIs ffthe fftrend ffpositive, ffnegative, ffor
ffnear ffzero? ffExplain. ff- ffAnswer ffDoes ffthe ffgraph ffshow ffan ffincreasing fftrend, ffa
ffdecreasing fftrend, ffor ffno fftrend? ffChoose ffthe ffcorrect ffanswer ffbelow.
(Increasing fftrend)
ffExplain ffwhat ffthis fftrend ffmeans ffin ffthe ffcontext ffof ffthis ffproblem.
(Taller ffwomen fftend ffto ffweigh ffmore)
Since, ffin ffgeneral, ffthe fflonger ffa ffcar ffis ffowned ffthe ffmore ffmiles ffit fftravels ffone
ffcan ffsay ffthere ffis ffa ff_______ ffbetween ffage ffof ffa ffcar ffand ffmileage. ff- ffAnswer
ffA ffPositive ffAssociation
A fflarge ffamount ffof ffscatter ffin ffa ffscatterplot ffis ffan ffindication ffthat ffthe
ffassociation ffbetween ffthe fftwo ffvariables ffis ff_______. ff- ffAnswer ffWeak ff(not
ffnon-linear)
When ffdescribing fftwo-variable ffassociations, ffa ffwritten ffdescription ffshould ffalways
ffinclude fftrend, ffshape, ffstrength, ffand ffwhich ffof ffthe fffollowing? ff- ffAnswer ffThe
ffcontext ffof ffthe ffdata
Complete ffparts ff(a) ffand ff(b) ffbelow.
A. ffThe ffscatterplot ffto ffthe ffright ffshows ffthe ffcollege fftuition ffand ffpercentage
ffacceptance ffat ffsome ffcolleges. ffWould ffit ffmake ffsense ffto fffind ffthe ffcorrelation
ffusing ffthis ffdata ffset? ffWhy ffor ffwhy ffnot?
B. ffThe ffscatterplot ffto ffthe ffright ffshows ffthe ffcomposite ffgrade ffon ffthe ffACT
ff(American ffCollege ffTesting) ffexam ffand ffthe ffEnglish ffgrade ffon ffthe ffsame
ffexam. ffWould ffit ffmake ffsense ffto fffind ffthe ffcorrelation ffusing ffthis ffdata ffset?
ffWhy ffor ffwhy ffnot? ff- ffAnswer ffA. ff(No. ffLinear ffregression ffis ffnot ffappropriate
ffbecause ffthe fftrend ffis ffnot fflinear.) ffthis ffis ffbecause ffthere ffis ffa ffcurvature ffin
ffthe ffpoints ff
B. ff(Yes. ffThere ffis ffno ffreason ffwhy fflinear ffregression ffwould ffnot ffbe ffappropriate
ffbecause ffthe fftrend ffis fflinear.)
The fffigure ffshows ffa ffscatterplot ffof ffbirthrate ff(live ffbirths ffper ff1000 ffwomen) ffand
ffage ffof ffthe ffmother ffin ffthe ffUnited ffStates. ffWould ffit ffmake ffsense ffto fffind ffthe
ffcorrelation fffor ffthis ffdata ffset? ffExplain. ffAccording ffto ffthis ffgraph, ffat
ffapproximately ffwhat ffage ffdoes ffthe ffhighest fffertility ffrate ffoccur?
Would ffit ffmake ffsense ffto fffind ffthe ffcorrelation fffor ffthis ffdata ffset? ff- ffAnswer ff
No, ffit ffwould ffnot ffmake ffsense ffto fffind ffthe ffcorrelation ffbecause ffthe fftrend ffis
ffnot fflinear.
HOMEWORK QUESTIONS WITH
CORRECT ANSWERS
The fftable ffto ffthe ffright ffshows ffthe ffnumber ffof ffpeople ffliving ffin ffa ffhouse ffand
ffthe ffweight ffof fftrash ff(in ffpounds) ffat ffthe ffcurb ffjust ffbefore fftrash ffpickup.
ffComplete ffparts ff(a) ffthrough ff(c) ffbelow.
People ffTrash ff(pounds)
3 ff30 ff
3 ff22
6 ff90
1 ff30
9 ff94 ff- ffAnswer ffa. ffFind ffthe ffcorrelation ffbetween ffthese ffnumbers ffby ffusing ffa
ffcomputer ffor ffa ffstatistical ffcalculator.
r= ff(0.901) ff
b. ffSuppose ffsome ffof ffthe ffweight ffwas fffrom ffthe ffcontainer ff(each ffcontainer
ffweighs ff5 ffpounds). ffSubtract ff5 ffpounds fffrom ffeach ffweight, ffand fffind ffthe ffnew
ffcorrelation ffwith ffthe ffnumber ffof ffpeople. ffWhat ffhappens ffto ffthe ffcorrelation
ffwhen ffa ffconstant ffis ffadded ff(we ffadded ffnegative ff5) ffto ffeach ffnumber?
(The ffcorrelation ffis ff
0.901. ffThe ffcorrelation ffcoefficient ffremains ffthe ffsame ffwhen ffa ffconstant ffis
ffadded ffto ffeach ffnumber.)
c. ffSuppose ffeach ffhouse ffcontained ffexactly fftwice ffthe ffnumber ffof ffpeople, ffbut
ffthe ffweight ffof ffthe fftrash ffwas ffthe ffsame. ffWhat ffhappens ffto ffthe ffcorrelation
ffwhen ffnumbers ffare ffmultiplied ffby ffa ffconstant?
(The ffcorrelation ffis ff0.901. ffThe ffcorrelation ffcoefficient ffremains ffthe ffsame ffwhen
ffthe ffnumbers ffare ffmultiplied ffby ffa ffpositive ffconstant.)
The fffigure ffshows ffa ffscatterplot ffof ffthe ffage ffof ffstudents ffand ffthe ffvalue ffof
fftheir ffcars. ffDoes ffit ffshow ffan ffincreasing fftrend, ffa ffdecreasing fftrend, ffa
ffchanging fftrend, ffor ffvery fflittle fftrend? ff- ffAnswer ffDecreasing fftrend
The fffigure ffshows ffa ffscatterplot ffof ffshoe ffsize ffand ffGPA fffor ffsome ffcollege
ffstudents. ffDoes ffit ffshow ffan ffincreasing fftrend, ffa ffdecreasing fftrend, ffor ffno
fftrend? ffIs ffthere ffa ffstrong ffrelationship? ff- ffAnswer ffThe ffgraph ffshows ff
(an ffincreasing)
, fflinear fftrend ffsince ffthe ffpoints ffshow ff
(an ffincreasing)
ffpattern ffby ffscanning ffthe ffgraph fffrom ffleft ffto ffright. ffThe ffrelationship ff
(is)
ffstrong ffbecause ffthe ffpoints ff
(Show)
ffconsistent ffand ffsmall ffvertical ffspread.
The ffscatterplot ffshows ffthe ffactual ffweight ffand ffdesired ffweight ffchange ffof ffsome
ffstudents. ffThus, ffif ffthey ffweighed ff220 ffand ffwanted ffto ffweigh ff190, ffthe ffdesired
ffweight ffchange ffwould ffbe ffnegative ff30. ffExplain ffwhat ffyou ffsee. ffIn ffparticular,
ffwhat ffdoes ffit ffmean ffthat ffthe fftrend ffis ffnegative? ff- ffAnswer ffThe ffmore ffpeople
ffweigh, ffthe ffmore ffweight ffthey fftend ffto ffwant ffto fflose.
The ffscatterplot ffshows ffthe ffsalary ffand ffyear ffof fffirst ffemployment fffor ffsome
ffprofessors ffat ffa ffcollege. ffExplain, ffin ffcontext, ffwhat ffthe ffnegative fftrend ffshows.
ffWho ffmakes ffthe ffmost ffand ffwho ffmakes ffthe ffleast? ff- ffAnswer ffThe ffpeople
ffhired ffthe ffmost ffrecently fftend ffto ffhave fflower ffsalaries, ffand ffthe ffpeople ffhired
ffmany ffyears ffago fftend ffto ffhave ffhigher ffsalaries.
The ffscatterplot ffshows ffdata fffrom ffthe ff50 ffstates fftaken fffrom ffthe ffU.S.
ffCensuslong ffdashthe ffpercentage ffof ffthe ffpopulation ff(25 ffyears ffor ffolder) ffwith ffa
ffcollege ffdegree ffor ffhigher ffand ffthe ffmedian fffamily ffincome. ffDescribe ffand
ffinterpret ffthe fftrend. ff- ffAnswer ffWhat ffis ffthe fftrend? ffWhat ffdoes ffthe ffdirection
ffof ffthe fftrend ffmean? ffChoose ffthe ffcorrect ffanswer ffbelow?
(The fftrend ffis ffpositive. ffStates ffwith ffa fflarger ffproportion ffof ffcollege-educated
ffpeople fftend ffto ffhave ffhigher ffmedian fffamily ffincome.)
The ffscatterplot ffshows ffthe ffnumber ffof ffwork ffhours ffand ffthe ffnumber ffof ffTV
ffhours ffper ffweek fffor ffsome ffcollege ffstudents ffwho ffwork. ffThere ffis ffa ffvery
ffslight fftrend. ffIs ffthe fftrend ffpositive ffor ffnegative? ffWhat ffdoes ffthe ffdirection ffof
ffthe fftrend ffmean ffin ffthis ffcontext? ffIdentify ffany ffunusual ffpoints. ff- ffAnswer ffA.
ffWhat ffis ffthe fftrend? ffWhat ffdoes ffthe ffdirection ffof ffthe fftrend ffmean? ffChoose
ffthe ffcorrect ffanswer ffbelow.
(The fftrend ffis ffnegative. ffThe ffmore ffhours ffof ffwork ffa ffstudent ffhas, ffthe fffewer
ffhours ffof ffTV ffthe ffstudent fftends ffto ffwatch.)
B. ffIdentify ffany ffunusual ffpoints. ffSelect ffthe ffcorrect ffchoice ffbelow ffand, ffif
ffnecessary, fffill ffin ffthe ffanswer ffbox ffto ffcomplete ffyour ffchoice.
(The ffperson ffwho ffworks ff
70
70 ffhours ffappears ffto ffbe ffan ffoutlier, ffbecause ffthat ffpoint ffis ffseparated fffrom
ffthe ffother ffpoints ffby ffa fflarge ffamount.)
, The fffigure ffshows ffa ffscatterplot ffof ffthe ffheights ffand ffweights ffof ffsome ffwomen
fftaking ffstatistics. ffDescribe ffwhat ffyou ffsee. ffIs ffthe fftrend ffpositive, ffnegative, ffor
ffnear ffzero? ffExplain. ff- ffAnswer ffDoes ffthe ffgraph ffshow ffan ffincreasing fftrend, ffa
ffdecreasing fftrend, ffor ffno fftrend? ffChoose ffthe ffcorrect ffanswer ffbelow.
(Increasing fftrend)
ffExplain ffwhat ffthis fftrend ffmeans ffin ffthe ffcontext ffof ffthis ffproblem.
(Taller ffwomen fftend ffto ffweigh ffmore)
Since, ffin ffgeneral, ffthe fflonger ffa ffcar ffis ffowned ffthe ffmore ffmiles ffit fftravels ffone
ffcan ffsay ffthere ffis ffa ff_______ ffbetween ffage ffof ffa ffcar ffand ffmileage. ff- ffAnswer
ffA ffPositive ffAssociation
A fflarge ffamount ffof ffscatter ffin ffa ffscatterplot ffis ffan ffindication ffthat ffthe
ffassociation ffbetween ffthe fftwo ffvariables ffis ff_______. ff- ffAnswer ffWeak ff(not
ffnon-linear)
When ffdescribing fftwo-variable ffassociations, ffa ffwritten ffdescription ffshould ffalways
ffinclude fftrend, ffshape, ffstrength, ffand ffwhich ffof ffthe fffollowing? ff- ffAnswer ffThe
ffcontext ffof ffthe ffdata
Complete ffparts ff(a) ffand ff(b) ffbelow.
A. ffThe ffscatterplot ffto ffthe ffright ffshows ffthe ffcollege fftuition ffand ffpercentage
ffacceptance ffat ffsome ffcolleges. ffWould ffit ffmake ffsense ffto fffind ffthe ffcorrelation
ffusing ffthis ffdata ffset? ffWhy ffor ffwhy ffnot?
B. ffThe ffscatterplot ffto ffthe ffright ffshows ffthe ffcomposite ffgrade ffon ffthe ffACT
ff(American ffCollege ffTesting) ffexam ffand ffthe ffEnglish ffgrade ffon ffthe ffsame
ffexam. ffWould ffit ffmake ffsense ffto fffind ffthe ffcorrelation ffusing ffthis ffdata ffset?
ffWhy ffor ffwhy ffnot? ff- ffAnswer ffA. ff(No. ffLinear ffregression ffis ffnot ffappropriate
ffbecause ffthe fftrend ffis ffnot fflinear.) ffthis ffis ffbecause ffthere ffis ffa ffcurvature ffin
ffthe ffpoints ff
B. ff(Yes. ffThere ffis ffno ffreason ffwhy fflinear ffregression ffwould ffnot ffbe ffappropriate
ffbecause ffthe fftrend ffis fflinear.)
The fffigure ffshows ffa ffscatterplot ffof ffbirthrate ff(live ffbirths ffper ff1000 ffwomen) ffand
ffage ffof ffthe ffmother ffin ffthe ffUnited ffStates. ffWould ffit ffmake ffsense ffto fffind ffthe
ffcorrelation fffor ffthis ffdata ffset? ffExplain. ffAccording ffto ffthis ffgraph, ffat
ffapproximately ffwhat ffage ffdoes ffthe ffhighest fffertility ffrate ffoccur?
Would ffit ffmake ffsense ffto fffind ffthe ffcorrelation fffor ffthis ffdata ffset? ff- ffAnswer ff
No, ffit ffwould ffnot ffmake ffsense ffto fffind ffthe ffcorrelation ffbecause ffthe fftrend ffis
ffnot fflinear.
