Ch.4 DescribingtheRelationbetweenTwoVariables
4.1 ScatterDiagramsandCorrelation
1 Drawandinterpretscatterdiagrams.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Constructascatterdiagramforthedata.
1) Thedatabelowarethefinalexamscoresof10randomlyselectedhistorystudentsandthenumberofhours
theystudiedfortheexam.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
x
y
x
y
2) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
x
y
x
y
Page83
3) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
x
y
x
y
4) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
literatureclass.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
x
y
x
y
Page84
5) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Milestraveled,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
x
y
x
y
6) Inorderforemployeesofacompanytoworkinaforeignoffice,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowtherelationshipbetweenthenumberofyearsthat
employeeshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
x
y
x
y
Page85
7) InanareaoftheGreatPlains,recordswerekeptontherelationshipbetweentherainfall(ininches)andthe
yieldofwheat(bushelsperacre).
Rainfall(ininches),x
Yield(bushelsperacre),y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
x
y
x
y
8) Fivebrandsofcigarettesweretestedfortheamountsoftarandnicotinetheycontained.Allmeasurementsare
inmilligramspercigarette.
Cigarette Tar Nicotine
BrandA 16 1.2
BrandB 13 1.1
BrandC 16 1.3
BrandD 18 1.4
BrandE 6 0.6
x
y
x
y
9) Thescoresofninemembersofalocalcommunitycollegewomenʹsgolfteamintworoundsoftournamentplay
arelistedbelow.
Player 123456789
Round1859087789285799386
Round2908785848678779182
x
y
x
y
Page86
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Makeascatterdiagramforthedata.Usethescatterdiagramtodescribehow,ifatall,thevariablesarerelated.
10) x164372
y 364452
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
A) Thevariablesappeartobe
positively,linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
B) Thevariablesdonotappeartobe
linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
C) Thevariablesappeartobe
negatively,linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
D) Thevariablesdonotappeartobe
linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
Page87
11) x1–1–6–2–33–4
y2022 18 21 24 20 27
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
A) Thevariablesdonotappeartobe
linearlyrelated.
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
B) Thevariablesappeartobe
negatively,linearlyrelated.
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
C) Thevariablesdonotappeartobe
linearlyrelated.
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
D) Thevariablesappeartobe
positively,linearlyrelated.
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
x
–12–8–4 4 8 121620
y
28
24
20
16
12
8
4
-4
Page88
12)
Subject A B C D E F G
xTimewatchingTV 8427756
yTimeonInternet 12 10 615 16 716
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
A) Thevariablesappeartobe
positively,linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
B) Thevariablesdonotappeartobe
linearlyrelated.
x
2 4 6 8 101214161820
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 101214161820
y
20
18
16
14
12
10
8
6
4
2
C) Thevariablesappeartobe
negatively,linearlyrelated.
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 10 12 14 16 18 20
y
20
18
16
14
12
10
8
6
4
2
D) Thevariablesdonotappeartobe
linearlyrelated.
x
2 4 6 8 101214161820
y
20
18
16
14
12
10
8
6
4
2
x
2 4 6 8 101214161820
y
20
18
16
14
12
10
8
6
4
2
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
13) Anagriculturalbusinesswantstodetermineiftherainfallininchescanbeusedtopredicttheyieldperacreon
awheatfarm.Identifythepredictorvariableandtheresponsevariable.
14) Acollegecounselorwantstodetermineifthenumberofhoursspentstudyingforatestcanbeusedtopredict
thegradesonatest.Identifythepredictorvariableandtheresponsevariable.
Page89
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
15) Thevariableisthevariablewhosevaluecanbeexplainedbythe variable.
A) response;predictor B) response;lurking
C) lurking;response D) predictorResponse
2 Describethepropertiesofthelinearcorrelationcoefficient.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Usethescatterdiagramsshown,labeledathroughftosolvetheproblem.
1) Inwhichscatterdiagramisr=0.01?
a
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
b
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
c
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
d
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
e
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
f
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
A) e B) c C) f D) d
Page90
2) Inwhichscatterdiagramisr=1?
a
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
b
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
c
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
d
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
e
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
f
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
A)
b
B) a C) f D) d
Page91
3) Inwhichscatterdiagramisr=–1?
a
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
b
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
c
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
d
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
e
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
f
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
A) a B)
b
C) f D) d
Page92
4) Whichscatterdiagramindicatesaperfectpositivecorrelation?
a
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
b
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
c
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
d
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
e
x
1234567
y
12
10
8
6
4
2
x
1234567
y
12
10
8
6
4
2
f
x
123456
y
12
10
8
6
4
2
x
123456
y
12
10
8
6
4
2
A)
b
B) a C) c D) f
Page93
Thescatterdiagramshowstherelationshipbetweenaveragenumberofyearsofeducationandbirthsperwomanof
childbearingageinselectedcountries.Usethescatterplottodeterminewhetherthestatementistrueorfalse.
5) Thereisastrongpositivecorrelationbetweenyearsofeducationandbirthsperwoman.
BirthsperWoman
2468101214
10
9
8
7
6
5
4
3
2
1
2468101214
10
9
8
7
6
5
4
3
2
1
Averagenumberofyearsofeducation
ofMarriedWomenofChild–BearingAge
A) False B) True
6) Thereisnocorrelationbetweenyearsofeducationandbirthsperwoman.
BirthsperWoman
2468101214
10
9
8
7
6
5
4
3
2
1
2468101214
10
9
8
7
6
5
4
3
2
1
Averagenumberofyearsofeducation
ofMarriedWomenofChild–BearingAge
A) False B) True
Page94
7) Thereisastrongnegativecorrelationbetweenyearsofeducationandbirthsperwoman.
BirthsperWoman
2468101214
10
9
8
7
6
5
4
3
2
1
2468101214
10
9
8
7
6
5
4
3
2
1
Averagenumberofyearsofeducation
ofMarriedWomenofChild–BearingAge
A) True B) False
8) Thereisacausalrelationshipbetweenyearsofeducationandbirthsperwoman.
BirthsperWoman
2468101214
10
9
8
7
6
5
4
3
2
1
2468101214
10
9
8
7
6
5
4
3
2
1
Averagenumberofyearsofeducation
ofMarriedWomenofChild–BearingAge
A) False B) True
Page95
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
9) Constructascatterdiagramforthegivendata.Determinewhetherthereisapositivelinearcorrelation,
negativelinearcorrelation,ornolinearcorrelation.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
10) Constructascatterdiagramforthegivendata.Determinewhetherthereisapositivelinearcorrelation,
negativelinearcorrelation,ornolinearcorrelation.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
Page96
11) Constructascatterdiagramforthegivendata.Determinewhetherthereisapositivelinearcorrelation,
negativelinearcorrelation,ornolinearcorrelation.
x
y
–5
11
–3
–6
4
8
1
–3
–1
–2
–2
1
0
5
2
–5
3
6
–4
7
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
x
–6–5–4–3–2–1 123456
y
12
10
8
6
4
2
-2
-4
-6
-8
-10
-12
12) ThenumbersofhomerunsthatMarkMcGwirehitinthefirst13yearsofhismajorleaguebaseballcareerare
listedbelow.(Source:MajorLeagueHandbook)Constructascatterdiagramforthedata.Istherearelationship
betweenthehomerunsandthebattingaverages?
HomeRuns
BattingAverage
33 39 22 42 9939 52 58 70
.231 .235 .201 .268 .33 .252 .274 .312 .274 .299
x
15 30 45 60 75
y
0.35
0.3
0.25
0.2
0.15
x
15 30 45 60 75
y
0.35
0.3
0.25
0.2
0.15
Page97
13) Thedatabelowrepresentthenumbersofabsencesandthefinalgradesof15randomlyselectedstudentsfrom
anastronomyclass.Constructascatterdiagramforthedata.Doyoudetectatrend?
Student Number
ofAbsences
FinalGrade
asaPercent
15 79
26 78
32 86
412 56
59 75
65 90
78 78
815 48
90 92
10 1 78
11 9 81
12 3 86
13 10 75
14 3 89
15 11 65
x
51015
y
100
90
80
70
60
50
40
x
51015
y
100
90
80
70
60
50
40
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
14) Aresearcherdeterminesthatthelinearcorrelationcoefficientis0.85forapaireddataset.Thisindicatesthat
thereis
A) astrongpositivelinearcorrelation.
B) astrongnegativelinearcorrelation.
C) nolinearcorrelationbutthattheremaybesomeotherrelationship.
D) insufficientevidencetomakeanydecisionaboutthecorrelationofthedata.
15) Aninstructorwishestodetermineifthereisarelationshipbetweenthenumberofabsencesfromhisclassand
astudentʹsfinalgradeinthecourse.Whatisthepredictorvariable?
A) Absences B) FinalGrade
C) Theinstructorʹspointscaleforattendance D) Studentʹsperformanceonthefinalexamination
16) Amedicalresearcherwishestodetermineifthereisarelationshipbetweenthenumberofprescriptionswritten
bymedicalprofessionals,per100,childrenandthechildʹsage.Shesurveysallthepediatricianʹsina
geographicalregiontocollectherdata.Whatistheresponsevariable?
A) Ageofthechild B) Numberofprescriptionswritten
C) Pediatricianssurveyed D) 100prescriptions
17) TrueorFalse:Adoctorwishestodeterminetherelationshipbetweenamaleʹsageandthatmaleʹstotal
cholesterollevel.Hetests200malesandrecordseachmaleʹsageandthatmaleʹstotalcholesterollevel.The
malescholesterollevelisthepredictorvariable?
A) False B) True
18) Ascatterdiagramlocatesapointinatwodimensionalplane.Thediagramlocatesthe
variableonthehorizontalaxisandthe variableontheverticalaxis.
A) predictor;response B) response;predictor
C) response;study D) study;predictor
Page98
19) Ahistoryinstructorhasgiventhesamepretestandthesamefinalexaminationeachsemester.Heisinterested
indeterminingifthereisarelationshipbetweenthescoresofthetwotests.Hecomputesthelinearcorrelation
coefficientandnotesthatitis1.15.Whatdoesthiscorrelationcoefficientvaluetelltheinstructor?
A) Thehistoryinstructorhasmadeacomputationalerror.
B) Thereisastrongpositivecorrelationbetweenthetests.
C) Thereisastrongnegativecorrelationbetweenthetests.
D) Thecorrelationissomethingotherthanlinear.
20) Atrafficofficeriscompilinginformationabouttherelationshipbetweenthehourorthedayandthespeedover
thelimitatwhichthemotorististicketed.Hecomputesacorrelationcoefficientof0.12.Whatdoesthistell
theofficer?
A) Thereisaweakpositivelinearcorrelation.
B) Thereisamoderatepositivelinearcorrelation.
C) Thereisamoderatenegativelinearcorrelation.
D) Thereisinsufficientevidencetomakeanyconclusionsabouttherelationshipbetweenthevariables.
3 Computeandinterpretthelinearcorrelationcoefficient.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Calculatethelinearcorrelationcoefficientforthedatabelow.
x
y
–13
–12
–11
–10
–4
7
–7
–1
–9
–4
–10
–8
–8
–3
–6
1
–5
4
–12
–10
A) 0.990 B) 0.881 C) 0.819 D) 0.792
2) Calculatethelinearcorrelationcoefficientforthedatabelow.
x
y
–2
15
0
10
7
–2
4
3
2
7
1
8
3
5
5
0
6
–1
–1
12
A) –0.995 B) –0.671 C) –0.778 D) –0.885
3) Calculatethelinearcorrelationcoefficientforthedatabelow.
x
y
–9
16
–7
–1
0
13
–3
2
–5
3
–6
6
–4
10
–2
0
–1
11
–8
12
A) –0.104 B) –0.132 C) –0.549 D) –0.581
4) Thedatabelowarethefinalexamscoresof10randomlyselectedcalculusstudentsandthenumberofhours
theysleptthenightbeforetheexam.Calculatethelinearcorrelationcoefficient.
Hours,x
Scores,y
4
74
6
89
3
69
9
97
3
75
5
87
5
94
6
99
7
99
4
80
A) 0.847 B) 0.991 C) 0.761 D) 0.654
5) Thedatabelowaretheaverageone–waycommutetimes(inminutes)ofselectedstudentsduringasummer
literatureclassandthenumberofabsencesforthosestudentsfortheterm.Calculatethelinearcorrelation
coefficient.
Commutetime(min),x
Numberofabsences,y
71
–1
84
3
90
6
89
6
87
4
97
11
74
0
99
11
79
1
A) 0.980 B) 0.890 C) 0.881 D) 0.819
6) Thedatabelowaretheagesandannualpharmacybills(indollars)of9randomlyselectedemployees.
Calculatethelinearcorrelationcoefficient.
Age,x
Pharmacybill($),y
31
111
34
115
38
118
41
126
44
137
46
140
50
143
54
145
58
147
A) 0.960 B) 0.998 C) 0.890 D) 0.908
Page99
7) Thedatabelowarethenumberofhoursworked(perweek)andthefinalgradesof9randomlyselected
studentsfromadramaclass.Calculatethelinearcorrelationcoefficient.
Hoursworked,x
FinalGrade,y
3
91
6
79
9
73
7
75
12
64
5
85
18
48
11
69
8
75
A) –0.991 B) –0.888 C) –0.918 D) –0.899
8) Amanagerwishestodeterminetherelationshipbetweenthenumberofyearsthemanagerʹssales
representativeshavebeenwiththecompanyandtheiraveragemonthlysales(inthousandsofdollars).
Calculatethelinearcorrelationcoefficient.
Yearswithcompany,x
Sales,y
2
36
3
38
10
83
7
67
8
70
15
66
3
53
1
60
11
125
A) 0.632 B) 0.561 C) 0.717 D) 0.791
9) Inorderforacompanyʹsemployeestoworkinaforeignoffice,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
employeeshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Calculate
thelinearcorrelationcoefficient.
Numberofyears,x
Gradesontest,y
7
62
8
69
8
76
9
83
7
74
10
91
6
59
11
94
7
73
A) 0.934 B) 0.911 C) 0.891 D) 0.902
10) InanareaoftheGreatPlains,recordswerekeptontherelationshipbetweentherainfall(ininches)andthe
yieldofwheat(bushelsperacre).Calculatethelinearcorrelationcoefficient.
Rainfall(ininches),x
Yield(bushelsperacre),y
9.8
48.5
8.1
44.2
12.7
56.8
11.8
57
18.1
80.4
9.6
47.2
6.3
29.9
14.9
74
15.3
76.8
A) 0.981 B) 0.998 C) 0.900 D) 0.899
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
11) Calculatethecoefficientofcorrelation,r,lettingRow1representthex–valuesandRow2representthe
y–values.Nowcalculatethecoefficientofcorrelation,r,lettingRow2representthex–valuesandRow1
representthey–values.Whateffectdoesswitchingtheexplanatoryandresponsevariableshaveonthelinear
correlationcoefficient?
Row1
Row2
–10
0
–8
18
–1
19
–4
11
–6
8
–7
4
–5
9
–3
13
–2
16
–9
18
4 Determinewhetheralinearrelationexistsbetweentwovariables.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Computethelinearcorrelationcoefficientbetweenthetwovariablesanddeterminewhetheralinearrelationexists.
1) x23556
y1.3 1.6 2.1 2.2 2.7
A) r=0.983;linearrelationexists B) r=0.983;nolinearrelationexists
C) r=0.883;linearrelationexists D) r=0.883;nolinearrelationexists
2) x2411 8657910 3
y0219 11 84913 16 2
A) r=0.990;linearrelationexists B) r=0.881;nolinearrelationexists
C) r=0.819;linearrelationexists D) r=0.792;nolinearrelationexists
3) x–11 –9–2–5–7–8–6–4–3–10
y19 14 2711 12 94316
A) r=–0.995;linearrelationexists B) r= –0.995;nolinearrelationexists
C) r=–0.885;nolinearrelationexists D) r= –0.885;linearrelationexists
Page100
4) x923425910
y85 52 55 68 67 86 83 73
A) r=0.708;linearrelationexists B) r=0.235;nolinearrelationexists
C) r=–0.708;linearrelationexists D) r=0.708;nolinearrelationexists
5) x10 11 16 9715 16 10
y96 51 62 58 89 81 46 51
A) r=–0.335;nolinearrelationexists B) r=0.462;linearrelationexists
C) r=–0.335;linearrelationexists D) r= –0.284;nolinearrelationexists
6) Thetablebelowshowsthescoresonanend–of–yearprojectof10randomlyselectedarchitecturestudentsand
thenumberofdayseachstudentspentworkingontheproject.
Days,x
Score,y
5
73
7
88
4
68
10
96
4
74
6
86
6
93
7
98
8
98
5
79
A) r=0.847;linearrelationexists B) r=0.847;nolinearrelationexists
C) r=0.761;linearrelationexists D) r=0.761;nolinearrelationexists
7) Thetablebelowshowstheagesandweights(inpounds)of9randomlyselectedtenniscoaches.
Age,x
Weight(pounds),y
36
112
39
116
43
119
46
127
49
138
51
141
55
144
59
146
63
148
A) r=0.960;linearrelationexists B) r=0.960;nolinearrelationexists
C) r=0.908;nolinearrelationexists D) r=0.908;linearrelationexists
8) Thetableshowsthenumberofdaysofflastyearandtheearningsfortheyear(inthousandsofdollars)fornine
randomlyselectedinsurancesalesmen.
Numberofdaysoff,x
Earningsfortheyear(thousandsofdollars),y
0
97
3
85
6
79
4
81
9
70
2
91
15
54
8
75
5
81
A) r=–0.991;linearrelationexists B) r= –0.991;nolinearrelationexists
C) r=–0.899;linearrelationexists D) r= –0.899;nolinearrelationexists
9) Amanagerwishestodeterminewhetherthereisarelationshipbetweenthenumberofyearshersales
representativeshavebeenwiththecompanyandtheiraveragemonthlysales.Thetableshowstheyearsof
serviceforeachofhersalesrepresentativesandtheiraveragemonthlysales(inthousandsofdollars).
Yearswithcompany,x6 714 11 12 19 7515
Sales,y36 38 83 67 70 66 53 60 125
A) r=0.632;nolinearrelationexists B) r=0.632;linearrelationexists
C) r=0.717;linearrelationexists D) r=0.717;nolinearrelationexists
10) Toinvestigatetherelationshipbetweenyieldofsoybeansandtheamountoffertilizerused,aresearcher
dividesafieldintoeightplotsofequalsizeandappliesadifferentamountoffertilizertoeachplot.Thetable
showstheyieldofsoybeansandtheamountoffertilizerusedforeachplot.
Amountoffertilizer(pounds),x 11.5 22.5 33.5 44.5
Yieldofsoybeans(pounds),y25 21 27 28 36 35 32 34
A) r=0.819;linearrelationexists B) r=0.729;nolinearrelationexists
C) r=0.683;linearrelationexists D) r=0.683;nolinearrelationexists
5 Explainthedifferencebetweencorrelationandcausation.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Avariablethatisrelatedtoeithertheresponsevariableorthepredictorvariableorboth,butwhichisexcluded
fromtheanalysisisa
A) lurkingvariable. B) randomvariable.
C) discretevariable. D) qualitativevariable.
Page101
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
2) Forarandomsampleof100Americancities,thelinearcorrelationcoefficientbetweenthenumberofrobberies
lastyearandthenumberofschoolsinthecitywasfoundtober=0.725.Whatdoesthisimply?Doesthis
suggestthatbuildingmoreschoolsinacitycouldleadtomorerobberies?Whyorwhynot?Whatisalikely
lurkingvariable?
3) Forarandomsampleof30countries,thelinearcorrelationcoefficientbetweentheinfantmortalityrateandthe
averagenumberofcarspercapitawasfoundtober=–0.717.Whatdoesthisimply?Doesthissuggestthatif
peoplebuymorecars,thiscouldlowertheinfantmortalityrate?Whyorwhynot?Whatisalikelylurking
variable?
4) Arandomsampleof200menagedbetween20and60wasselectedfromacertaincity.Thelinearcorrelation
coefficientbetweenincomeandbloodpressurewasfoundtober=0.807.Whatdoesthisimply?Doesthis
suggestthatifamangetsasalaryraisehisbloodpressureislikelytorise?Whyorwhynot?Whatarelikely
lurkingvariables?
4.2 Least–SquaresRegression
1 Findtheleast–squaresregressionlineandusethelinetomakepredictions.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Findtheequationoftheregressionlineforthegivendata.Roundvaluestothenearestthousandth.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) y
^
=2.097x–0.552 B) y
^
=0.522x–2.097
C) y
^
=2.097x+0.552 D) y
^
=–0.552x+2.097
2) Findtheequationoftheregressionlineforthegivendata.Roundvaluestothenearestthousandth.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
A) y
^
=–1.885x+0.758 B) y
^
=0.758x+1.885 C) y
^
=–0.758x–1.885 D) y
^
=1.885x–0.758
3) Findtheequationoftheregressionlineforthegivendata.Roundvaluestothenearestthousandth.
x
y
–5
11
–3
–6
4
8
1
–3
–1
–2
–2
1
0
5
2
–5
3
6
–4
7
A) y
^
=–0.206x+2.097 B) y
^
=2.097x–0.206 C) y
^
=0.206x–2.097 D) y
^
=–2.097x+0.206
4) Thedatabelowarethefinalexamscoresof10randomlyselectedhistorystudentsandthenumberofhours
theysleptthenightbeforetheexam.Findtheequationoftheregressionlineforthegivendata.Whatwouldbe
thepredictedscoreforahistorystudentwhoslept7hoursthepreviousnight?Isthisareasonablequestion?
Roundtheregressionlinevaluestothenearesthundredth,androundthepredictedscoretothenearestwhole
number.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
A) y
^
=5.04x+56.11;91;Yes,itisreasonable.
B) y
^
=5.04x+56.11;91;No,itisnotreasonable.7hoursiswelloutsidethescopeofthemodel.
C) y
^
=–5.04x+56.11;21;No,itisnotreasonable.7hoursiswelloutsidethescopeofthemodel.
D) y
^
=–5.04x+56.11;21;Yes,itisreasonable.
Page102
5) Thedatabelowarethefinalexamscoresof10randomlyselectedhistorystudentsandthenumberofhours
theysleptthenightbeforetheexam.Findtheequationoftheregressionlineforthegivendata.Whatwouldbe
thepredictedscoreforahistorystudentwhoslept15hoursthepreviousnight?Isthisareasonablequestion?
Roundyourpredictedscoretothenearestwholenumber.Roundtheregressionlinevaluestothenearest
hundredth.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
A) y
^
=5.04x+56.11;132;No,itisnotreasonable.15hoursiswelloutsidethescopeofthemodel.
B) y
^
=5.04x+56.11;132;Yes,itisreasonable.
C) y
^
=–5.04x+56.11;–20;No,itisnotreasonable.
D) y
^
=–5.04x+56.11;–20;Yes,itisreasonable.
6) Thedatabelowaretheaverageone–waycommutetimes(inminutes)forselectedstudentsandthenumberof
absencesforthosestudentsduringtheterm.Findtheequationoftheregressionlineforthegivendata.What
wouldbethepredictednumberofabsencesifthecommutetimewas95minutes?Isthisareasonablequestion?
Roundthepredictednumberofabsencestothenearestwholenumber.Roundtheregressionlinevaluestothe
nearesthundredth.
Commutetime(min),x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) y
^
=0.45x–30.27;12absences;Yes,itisreasonable.
B) y
^
=0.45x–30.27;12absences;No,itisnotreasonable.95minutesiswelloutsidethescopeofthemodel.
C) y
^
=0.45x+30.27;73absences;Yes,itisreasonable.
D) y
^
=0.45x+30.27;73absences;No,itisnotreasonable.95minutesiswelloutsidethescopeofthemodel.
7) Thedatabelowaretheaverageone–waycommutetimes(inminutes)forselectedstudentsandthenumberof
absencesforthosestudentsduringtheterm.Findtheequationoftheregressionlineforthegivendata.What
wouldbethepredictednumberofabsencesifthecommutetimewas40minutes?Isthisareasonablequestion?
Roundthepredictednumberofabsencestothenearestwholenumber.Roundtheregressionlinevaluestothe
nearesthundredth.
Commutetime(min),x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) y
^
=0.45x–30.27;–12absences;No,itisnotreasonable.40minutesiswelloutsidethescopeofthemodel.
B) y
^
=0.45x–30.27;–12absences;Yes,itisreasonable.
C) y
^
=0.45x+30.27;48absences;Yes,itisreasonable.
D) y
^
=0.45x+30.27;48absences;No,itisnotreasonable.40minutesiswelloutsidethescopeofthemodel.
8) Thedatabelowareagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Findtheequationoftheregressionlineforthegivendata.Whatwouldbethepredicted
pressureiftheagewas60?Roundthepredictedpressuretothenearestwholenumber.Roundtheregression
linevaluestothenearesthundredth.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) y
^
=1.49x+60.46;150mm B) y
^
=60.46x–1.49;3626mm
C) y
^
=1.49x–60.46;29mm D) y
^
=60.46x+1.49;3629mm
Page103
9) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
literatureclass.Findtheequationoftheregressionlineforthegivendata.Whatwouldbethepredictedfinal
gradeifastudentwasabsent14times?Roundtheregressionlinevaluestothenearesthundredth.Roundthe
predictedgradetothenearestwholenumber.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) y
^
=–2.75x+96.14;58 B) y
^
=96.14x–2.75;1343
C) y
^
=–2.75x–96.14;134.64 D) y
^
=–96.14x+2.75;1343
10) Amanagerwishestodeterminetherelationshipbetweenthenumberofmilestraveled(inhundredsofmiles)
byhersalesrepresentativesandtheiramountofsales(inthousandsofdollars)permonth.Findtheequationof
theregressionlineforthegivendata.Whatwouldbethepredictedsalesifthesalesrepresentativetraveled0
miles?Isthisreasonable?Whyorwhynot?Roundtheregressionlinevaluestothenearesthundredth.
Milestraveled,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
A) y
^
=3.53x+37.92;$37,920;No;itisnotreasonableforarepresentativetotravel0milesandhaveapositive
amountofsales.
B) y
^
=3.53x+37.92;$3792;No;itisnotreasonableforarepresentativetotravel0milesandhaveapositive
amountofsales.
C) y
^
=3.53x+37.92;$37,920;Yes,itisreasonable.
D) y
^
=37.92x+3.53;$3792;Yes,itisreasonable.
11) Amanagerwishestodeterminetherelationshipbetweenthenumberofyearshersalesrepresentativeshave
beenemployedbythefirmandtheiramountofsales(inthousandsofdollars)permonth.Findtheequationof
theregressionlineforthegivendata.Whatwouldbethepredictedsalesifthesalesrepresentativewas
employedbythefirmfor30yearsIsthisreasonable?Whyorwhynot?Roundtheregressionlinevaluestothe
nearesthundredth.
Yearsemployed,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
A) y
^
=3.53x+37.92;$143,820;No;itisnotreasonable.30yearsofemploymentiswelloutsidethescopeof
themodel.
B) y
^
=3.53x+37.92;$143,820;;Yes,itisreasonable.
C) y
^
=3.53x–37.92;$67,980;No;itisnotreasonable.30yearsofemploymentiswelloutsidethescopeofthe
model.
D) y
^
=3.53x–37.92;$67,980;Yes;itisreasonable.
12) Inorderforacompanyʹsemployeestoworkinaforeignoffice,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
employeeshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Findthe
equationoftheregressionlineforthegivendata.Roundtheregressionlinevaluestothenearesthundredth.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) y
^
=6.91x+46.26 B) y
^
=6.91x–46.26 C) y
^
=46.26x–6.91 D) y
^
=46.26x+6.91
Page104
13) InanareaoftheGreatPlains,recordswerekeptontherelationshipbetweentherainfall(ininches)andthe
yieldofwheat(bushelsperacre).Findtheequationoftheregressionlineforthegivendata.Roundthe
regressionlinevaluestothenearestthousandth.
Rainfall(ininches),x
Yield(bushelsperacre),y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
A) y
^
=4.379x+4.267 B) y
^
=–4.379x+4.267 C) y
^
=4.267x+4.379 D) y
^
=4.267x–4.379
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
14) FindtheequationoftheregressionlinebylettingRow1representthex–valuesandRow2representthe
y–values.NowfindtheequationoftheregressionlinelettingRow2representthex–valuesandRow1
representthey–values.Whateffectdoesswitchingtheexplanatoryandresponsevariableshaveonthe
regressionline?
Row1
Row2
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
15) Isthenumberofgameswonbyamajorleaguebaseballteaminaseasonrelatedtotheteamʹsbattingaverage?
Datafrom14teamswerecollectedandthesummarystatisticsyield:
y=
∑1,134,x
∑=3.642,y2
∑=93,110,x2
∑=0.948622,andxy
∑=295.54
Findtheleastsquarespredictionequationforpredictingthenumberofgameswon,y,usingastraight–line
relationshipwiththeteamʹsbattingaverage,x.
16) Thetableshows,fortheyears1997–2012,themeanhourlywageforresidentsofthetownofPityMeandthe
meanweeklyrentpaidbytheresidents.
Year Meanweeklyrent
(dollars)
Meanhourlywage
(dollars)
Year Meanweeklyrent
(dollars)
Meanhourlywage
(dollars)
1997 57 10.38 2005 116 28.99
1998 59 10.89 2006 113 28.63
1999 62 11.96 2007 112 36.75
2000 63 12.46 2008 86 14.55
2001 86 17.72 2009 90 17.90
2002 119 28.07 2010 90 14.67
2003 131 35.24 2011 100 17.97
2004 122 31.87 2012 115 22.23
Summarystatisticsyield:SSxx=1222.2771,SSxy=3031.7125,SSyy=9144.9375,x=21.2675,and
y=95.0625.Findtheleastsquareslinethatusesmeanhourlywagetopredictmeanweeklyrent.Roundvalues
tothenearestten–thousandth.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
17) Aresidualisthedifferencebetween
A) theobservedvalueofyandthepredictedvalueofy.
B) theobservedvalueofxandthepredictedvalueofx.
C) theobservedvalueofyandthepredictedvalueofx.
D) theobservedvalueofxandthepredictedvalueofy.
18) Theleastsquaresregressionline
A) minimizesthesumoftheresidualssquared.
B) maximizesthesumoftheresidualssquared.
C) minimizesthemeandifferencebetweentheresidualssquared.
D) maximizesthemeandifferencebetweentheresidualssquared.
Page105
19) Foragivendataset,theequationoftheleastsquaresregressionlinewillalwayspassthrough
A) (x,y). B) everypointinthegivendataset.
C) atleasttwopointinthegivendataset. D) they–interceptandtheslope.
2 Interprettheslopeandthey–interceptoftheleast–squaresregressionline.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Acountyrealestateappraiserwantstodevelopastatisticalmodeltopredicttheappraisedvalueofhousesina
sectionofthecountycalledEastMeadow.Oneofthemanyvariablesthoughttobeanimportantpredictorof
appraisedvalueisthenumberofroomsinthehouse.Consequently,theappraiserdecidedtofitthesimple
linearregressionmodel,y
^=β0+β1x,wherey=appraisedvalueofthehouse(in$thousands)andx=number
ofrooms.Usingdatacollectedforasampleofn=74housesinEastMeadow,thefollowingresultswere
obtained:
y
^=74.80+20.86x
sβ=71.24,t=1.05(fortestingβ0)
sβ=2.63,t=7.49(fortestingβ1)
SSE=60,775,MSE=841,s=29,r2=.44
Rangeofthex–values:5–11
Rangeofthey–values:160–300
Giveapracticalinterpretationoftheestimateoftheslopeoftheleastsquaresline.
A) Foreachadditionalroominthehouse,weestimatetheappraisedvaluetoincrease$20
,
860.
B) Foreachadditionalroominthehouse,weestimatetheappraisedvaluetoincrease$74,800.
C) Foreachadditionaldollarofappraisedvalue,weestimatethenumberofroomsinthehousetoincrease
by20.86rooms.
D) Forahousewith0rooms,weestimatetheappraisedvaluetobe$74,800.
2) Acountyrealestateappraiserwantstodevelopastatisticalmodeltopredicttheappraisedvalueofhousesina
sectionofthecountycalledEastMeadow.Oneofthemanyvariablesthoughttobeanimportantpredictorof
appraisedvalueisthenumberofroomsinthehouse.Consequently,theappraiserdecidedtofitthesimple
linearregressionmodel,y
^=β0+β1x,wherey=appraisedvalueofthehouse(in$thousands)andx=number
ofrooms.Usingdatacollectedforasampleofn=74housesinEastMeadow,thefollowingresultswere
obtained:
y
^=74.80+19.72x
sβ=71.24,t=1.05(fortestingβ0)
sβ=2.63,t=7.49(fortestingβ1)
SSE=60,775,MSE=841,s=29,r2=0.44
Rangeofthex–values:5–11
Rangeofthey–values:160–300
Giveapracticalinterpretationoftheestimateofthey–interceptoftheleastsquaresline.
A) Thereisnopracticalinterpretation,sinceahousewith0roomsisnonsensical.
B) Foreachadditionalroominthehouse,weestimatetheappraisedvaluetoincrease$74,800.
C) Foreachadditionalroominthehouse,weestimatetheappraisedvaluetoincrease$19,720.
D) Weestimatethebaseappraisedvalueforanyhousetobe$74,800.
Page106
3) IstherearelationshipbetweentheraisesadministratorsatStateUniversityreceiveandtheirperformanceon
thejob?Afacultygroupwantstodeterminewhetherjobrating(x)isausefullinearpredictorofraise(y).
Consequently,thegroupconsideredthestraight–lineregressionmodel,y
^=β0+β1x.Usingthemethodofleast
squares,thefacultygroupobtainedthefollowingpredictionequation,y
^=14,000+2,000x.Interpretthe
estimatedslopeoftheline.
A) Fora1–pointincreaseinanadministratorʹsrating,weestimatetheadministratorʹsraisetoincrease
$2,000.
B) Fora1–pointincreaseinanadministratorʹsrating,weestimatetheadministratorʹsraisetodecrease
$2,000.
C) Foranadministratorwitharatingof1.0,weestimatehis/herraisetobe$2,000.
D) Fora$1increaseinanadministratorʹsraise,weestimatetheadministratorʹsratingtodecrease2,000
points.
4) IstherearelationshipbetweentheraisesadministratorsatStateUniversityreceiveandtheirperformanceon
thejob?Afacultygroupwantstodeterminewhetherjobrating(x)isausefullinearpredictorofraise(y).
Consequently,thegroupconsideredthestraight–lineregressionmodel,y
^=β0+β1x.Usingthemethodofleast
squares,thefacultygroupobtainedthefollowingpredictionequation,y
^=14,000+2,000x.
Interprettheestimatedy–interceptoftheline.
A) Foranadministratorwhoreceivesaratingofzero,weestimatehisorherraisetobe$14,000.
B) ThebaseadministratorraiseatStateUniversityis$14,000.
C) Fora1–pointincreaseinanadministratorʹsrating,weestimatetheadministratorʹsraisetoincrease
$14,000.
D) Thereisnopracticalinterpretation,sinceratingof0isnonsensicalandoutsidetherangeofthesample
data.
5) Alargenationalbankchargeslocalcompaniesforusingitsservices.Abankofficialreportedtheresultsofa
regressionanalysisdesignedtopredictthebankʹscharges(y),measuredindollarspermonth,forservices
renderedtolocalcompanies.Oneindependentvariableusedtopredictservicechargetoacompanyisthe
companyʹssalesrevenue(x),measuredinmillionsofdollars.Datafor21companieswhousethebankʹs
serviceswereusedtofitthemodel,y
^=β0+β1x.Theresultsofthesimplelinearregressionareprovidedbelow.
y
^=2,700+20x,s=65,2–tailedp–value=0.064(fortestingβ1)
Interprettheestimateofβ0,they–interceptoftheline.
A) Thereisnopracticalinterpretationsinceasalesrevenueof$0isanonsensicalvalue.
B) Allcompanieswillbechargedatleast$2,700bythebank.
C) About95%oftheobservedservicechargesfallwithin$2,700oftheleastsquaresline.
D) Forevery$1millionincreaseinsalesrevenue,weexpectaservicechargetoincrease$2,700.
Page107
6) Civilengineersoftenusethestraight–lineequation,y
^
=β0+β1x,tomodeltherelationshipbetweenthemean
shearstrengthofmasonryjointsandprecompressionstress,x.Totestthistheory,aseriesofstresstestswere
performedonsolidbricksarrangedintripletsandjoinedwithmortar.Theprecompressionstresswasvaried
foreachtripletandtheultimateshearloadjustbeforefailure(calledtheshearstrength)wasrecorded.The
stressresultsforn=7triplettestsisshownintheaccompanyingtablefollowedbyaSASprintoutofthe
regressionanalysis.
TripletTest 1234567
ShearStrength(tons),y1.00 2.18 2.24 2.41 2.59 2.82 3.06
Precomp.Stress(tons),x00.60 1.20 1.33 1.43 1.75 1.75
AnalysisofVariance
 Sumof Mean
Source DF Squares Square FValue Prob>F
Model 1 2.39555 2.39555 47.732 0.0010
Error 5 0.25094 0.05019
CTotal 6 2.64649
RootMSE 0.22403 R–square 0.9052
DepMean 2.32857 AdjR–sq 0.8862
C.V. 9.62073
ParameterEstimates
Parameter Standard TforHO:
Variable DF Estimate Error Parameter=0 Prob>|T|
INTERCEP 1 1.191930 0.18503093 6.442 0.0013
X 1 0.987157 0.14288331 6.909 0.0010
Giveapracticalinterpretationoftheestimateoftheslopeoftheleastsquaresline.
A) Forevery1tonincreaseinprecompressionstress,weestimatetheshearstrengthofthejointtoincrease
by0.987ton.
B) Foratriplettestwithaprecompressionstressof1ton,weestimatetheshearstrengthofthejointtobe
0.987ton.
C) Forevery0.987tonincreaseinprecompressionstress,weestimatetheshearstrengthofthejointto
increaseby1ton.
D) Foratriplettestwithaprecompressionstressof0tons,weestimatetheshearstrengthofthejointtobe
1.19tons.
Page108
7) Civilengineersoftenusethestraight–lineequation,y
^
=β0+β1x,tomodeltherelationshipbetweenthemean
shearstrengthofmasonryjointsandprecompressionstress,x.Totestthistheory,aseriesofstresstestswere
performedonsolidbricksarrangedintripletsandjoinedwithmortar.Theprecompressionstresswasvaried
foreachtripletandtheultimateshearloadjustbeforefailure(calledtheshearstrength)wasrecorded.The
stressresultsforn=7triplettestsisshownintheaccompanyingtablefollowedbyaSASprintoutofthe
regressionanalysis.
TripletTest 1234567
ShearStrength,y
(tons)
1.00 2.18 2.24 2.41 2.59 2.82 3.06
Precomp.Stress,x
(tons)
00.60 1.20 1.33 1.43 1.75 1.75
AnalysisofVariance
 Sumof Mean
Source DF Squares Square FValue Prob>F
Model 1 2.39555 2.39555 47.732 0.0010
Error 5 0.25094 0.05019
CTotal 6 2.64649
RootMSE 0.22403 R–square 0.9052
DepMean 2.32857 AdjR–sq 0.8862
C.V. 9.62073
ParameterEstimates
Parameter Standard TforHO:
Variable DF Estimate Error Parameter=0 Prob>|T|
INTERCEP 1 1.191930 0.18503093 6.442 0.0013
X 1 0.987157 0.14288331 6.909 0.0010
Giveapracticalinterpretationoftheestimateofthey–interceptoftheleastsquaresline.
A) Foratriplettestwithaprecompressionstressof0tons,weestimatetheshearstrengthofthejointtobe
1.19tons.
B) Forevery1tonincreaseinprecompressionstress,weestimatetheshearstrengthofthejointtoincrease
by0.987ton.
C) Thereisnopracticalinterpretationsinceatriplettestwithaprecompressionstressof0tonsisoutsidethe
rangeofthesampledata.
D) Foratriplettestwithaprecompressionstressof0tons,weestimatetheshearstrengthofthejointto
increase1.19tons.
Page109
8) EachyearanationallyrecognizedpublicationconductsitsʺSurveyofAmericaʹsBestGraduateand
ProfessionalSchools.ʺAnacademicadvisorwantstopredictthetypicalstartingsalaryofagraduateatatop
businessschoolusingGMATscoreoftheschoolasapredictorvariable.TotalGMATscoresrangefrom200to
800.AsimplelinearregressionofSALARYversusGMATusing25datapointsshownbelow.
β0
^=–92040β
^1=228s=3213R2=0.66r=0.81df=23t=6.67
Giveapracticalinterpretationofβ0
^=–92040.
A) ThevaluehasnopracticalinterpretationsinceaGMATof0isnonsensicalandoutsidetherangeofthe
sampledata.
B) WeexpecttopredictSALARYtowithin2(92040)=$184,080ofitstruevalueusingGMATina
straight–linemodel.
C) WeestimateSALARYtodecrease$92,040forevery1–pointincreaseinGMAT.
D) WeestimatethebaseSALARYofgraduatesofatopbusinessschooltobe$–92,040.
9) EachyearanationallyrecognizedpublicationconductsitsʺSurveyofAmericaʹsBestGraduateand
ProfessionalSchools.ʺAnacademicadvisorwantstopredictthetypicalstartingsalaryofagraduateatatop
businessschoolusingGMATscoreoftheschoolasapredictorvariable.TotalGMATscoresrangefrom200to
800.AsimplelinearregressionofSALARYversusGMATusing25datapointsshownbelow.
β0
^=–92040β
^1=228s=3213R2=0.66r=0.81df=23t=6.67
Giveapracticalinterpretationofβ1
^=228.
A) WeestimateSALARYtoincrease$228forevery1–pointincreaseinGMAT.
B) WeexpecttopredictSALARYtowithin2(228)=$456ofitstruevalueusingGMATinastraight–line
model.
C) WeestimateGMATtoincrease228pointsforevery$1increaseinSALARY.
D) ThevaluehasnopracticalinterpretationsinceaGMATof0isnonsensicalandoutsidetherangeofthe
sampledata.
10) Arealestatemagazinereportedtheresultsofaregressionanalysisdesignedtopredicttheprice(y),measured
indollars,ofresidentialpropertiesrecentlysoldinanorthernVirginiasubdivision.Oneindependentvariable
usedtopredictsalepriceisGLA,grosslivingarea(x),measuredinsquarefeet.Datafor157propertieswere
usedtofitthemodel,y
^=β0+β1x.Theresultsofthesimplelinearregressionareprovidedbelow.
y
^=96,600+22.5xs=6500r2=–0.77t=6.1(fortestingβ1)
Interprettheestimateofβ0,they–interceptoftheline.
A) Thereisnopracticalinterpretation,sinceagrosslivingareaof0isanonsensicalvalue.
B) AllresidentialpropertiesinVirginiawillsellforatleast$96,600.
C) About95%oftheobservedsalepricesfallwithin$96,600oftheleastsquaresline.
D) Forevery1–sqft.increaseinGLA,weexpectapropertyʹssalepricetoincrease$96,600.
Page110
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
11) Inacomprehensiveroadtestonallnewcarmodels,onevariablemeasuredisthetimeittakesacarto
acceleratefrom0to60milesperhour.Tomodelaccelerationtime,aregressionanalysisisconductedona
randomsampleof129newcars.
TIME60:y=Elapsedtime(inseconds)from0mphto60mph
MAX:x1=Maximumspeedattained(milesperhour)
Initially,thesimplelinearmodelE(y)=β0+β1x1wasfittothedata.Computerprintoutsfortheanalysisare
givenbelow:
UNWEIGHTEDLEASTSQUARESLINEARREGRESSIONOFTIME60
PREDICTOR
VARIABLES COEFFICIENT STDERROR STUDENTʹSTP
CONSTANT 18.7171 0.63708 29.38 0.0000
MAX –0.08365 0.00491 –17.05 0.0000
R–SQUARED 0.6960 RESID.MEANSQUARE(MSE) 1.28695
ADJUSTEDR–SQUARED 0.6937 STANDARDDEVIATION 1.13444
SOURCE DF SS MS F P
REGRESSION 1374.285 374.285 290.83 0.0000
RESIDUAL 127 163.443 1.28695
TOTAL 128 537.728
CASESINCLUDED129MISSINGCASES0
Findandinterprettheestimateb1intheprintoutabove.
12) Inastudyoffeedingbehavior,zoologistsrecordedthenumberofgruntsofawarthogfeedingbyalakeinthe
15minuteperiodfollowingtheadditionoffood.Thedatashowingtheweeklynumberofgruntsandtheage
ofthewarthog(indays)arelistedbelow:
Week NumberofGrunts Age(days)
187 122
265 138
336 152
441 157
560 164
637 171
759 180
814 186
917 192
a.Writetheequationofastraight–linemodelrelatingnumberofgrunts(y)toage(x).
b.Givetheleastsquarespredictionequation.
c.Giveapracticalinterpretationofthevalueofβ0
^ifpossible.
d.Giveapracticalinterpretationofthevalueofβ1
^ifpossible.
Page111
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
13) Giventhefollowingleastsquarespredictionequation,y
^
=–173+74x,weestimateyto by
witheach1–unitincreaseinx.
A) increase;74 B) decrease;74 C) decrease;173 D) increase;173
14) Giventheequationofaregressionlineisy
^
=3x–8,whatisthebestpredictedvalueforygivenx=2?
A) –2B)14C)13D)
–3
15) Giventheequationofaregressionlineisy
^
=–3.5x–2.6,whatisthebestpredictedvalueforygivenx=9.6?
A) –36.20 B) –31.00 C) 31.00 D) 36.20
16) Usetheregressionequationtopredictthevalueofyforx= –0.6.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) –1.810 B) –0.706 C) 2.428 D) 1.766
17) Usetheregressionequationtopredictthevalueofyforx=0.2.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
A) 0.381 B) 1.135 C) –1.733 D) 2.037
18) Thedatabelowarethefinalexamscoresof10randomlyselectedchemistrystudentsandthenumberofhours
theysleptthenightbeforetheexam.Whatisthebestpredictedvalueforygivenx=6?
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
A) 86 B) 85 C) 84 D) 87
19) Thedatabelowarethetemperaturesonrandomlychosendaysduringthesummerinonecityandthenumber
ofemployeeabsencesonthosedaysforacompanylocatedinthesamecity.Whatisthebestpredictedvalue
forygivenx=102?
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) 16 B) 17 C) 18 D) 19
20) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Whatisthebestpredictedvalueforygivenx=37?
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) 116 B) 118 C) 114 D) 112
21) Thedatabelowarethenumberofabsencesandthesalaries(inthousandsofdollars)of9randomlyselected
employeesfromanengineeringfirm.Whatisthebestpredictedvalueforygivenx=1?
.Numberofabsences,x
Salary,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) 93 B) 94 C) 95 D) 92
Page112
22) Inorderforacompanyʹsemployeestoworkfortheforeignoffice,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowtherelationshipbetweenthenumberofyearsthat
employeeshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Whatis
thebestpredictedvalueforygivenx=5.5?
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) 84 B) 82 C) 80 D) 86
23) InanareaoftheGreatPlains,recordswerekeptontherelationshipbetweentherainfall(ininches)andthe
yieldofwheat(bushelsperacre).Whichisthebestpredictedvalueforygivenx=15.6?
Rainfall(ininches),x
Yield(bushelsperacre),y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
A) 72.6 B) 72.9 C) 72.4 D) 73.1
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
24) Acalculusinstructorisinterestedinfindingthestrengthofarelationshipbetweenthefinalexamgradesof
studentsenrolledinCalculusIandCalculusIIathiscollege.Thedata(inpercentages)arelistedbelow.
CalculusI
CalculusII
88
81
78
80
62
55
75
78
95
90
91
90
83
81
86
80
98
100
a)Graphascatterdiagramofthedata.
b)Findanequationoftheregressionline.
c)PredictaCalculusIIexamscoreforastudentwhoreceivesan80inCalculusI.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
25) InoneareaofRussia,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyieldof
wheat(bushelsperacre).Thedatafora9yearperiodisasfollows:
RainFall,x13.1 11.4 16.0 15.1 21.4 12.9 9.6 18.2 18.6
Yield,y48.5 44.2 56.8 80.4 47.2 29.9 74.0 74.0 76.8
Theequationofthelineofleastsquaresisgivenasy
^=–9.12+4.38x.Howmanybushelsofwheatperacrecan
bepredictedifitisexpectedthattherewillbe17inchesofrain?
A) 65.34 B) 5.96 C) 61.18 D) 52.06
26) InanareaofRussia,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyieldof
wheat(bushelsperacre).Thedatafora9yearperiodisasfollows:
RainFall,x13.1 11.4 16.0 15.1 21.4 12.9 9.6 18.2 18.6
Yield,y48.5 44.2 56.8 80.4 47.2 29.9 74.0 74.0 76.8
Theequationofthelineofleastsquaresisgivenasy
^=–9.12+4.38x.Whatwouldbetheexpectednumberof
inchesofrainiftheyieldis60bushelsofwheatperacre?
A) 15.78 B) 253.68 C) 11.62 D) 64.74
27) InanareaofRussia,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyieldof
wheat(bushelsperacre).Thedatafora9yearperiodisasfollows:
RainFall,x13.1 11.4 16.0 15.1 21.4 12.9 9.6 18.2 18.6
Yield,y48.5 44.2 56.8 80.4 47.2 29.9 74.0 74.0 76.8
Theequationofthelineofleastsquaresisgivenasy
^=–9.12+4.38x.Howmanybushelsofwheatperacrecan
bepredictedifitisexpectedthattherewillbe30inchesofrain?
A) Cannotbecertainoftheresultbecause30inchesofrainexceedstheobserveddata.
B) 122.28
C) 140.52
D) 8.93
Page113
3 Computethesumofsquaredresiduals.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Theregressionlineforthegivendataisy
^
=2.097x–0.552.Determinetheresidualofadatapointforwhichx=
–1andy=–2.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) 0.649 B) –4.649 C) –2.649 D) 3.746
2) Theregressionlineforthegivendataisy
^
=–1.885x+0.758.Determinetheresidualofadatapointforwhichx
=1andy=–1.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
A) 0.127 B) –2.127 C) –1.127 D) –1.643
3) Theregressionlineforthegivendataisy
^
=–0.206x+2.097.Determinetheresidualofadatapointforwhichx
=2andy=–5.
x
y
–5
11
–3
–6
4
8
1
–3
–1
–2
–2
1
0
5
2
–5
3
6
–4
7
A) –6.685 B) –3.315 C) 1.685 D) –1.127
4) Theregressionlineforthegivendataisy
^
=5.044x+56.11.Determinetheresidualofadatapointforwhichx=
2andy=66.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
A) –0.198 B) 132.198 C) 66.198 D) –387.014
5) Theregressionlineforthegivendataisy
^
=0.449x–30.27.Determinetheresidualofadatapointforwhichx=
85andy=7.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) –0.895 B) 14.895 C) 7.895 D) 112.127
6) Theregressionlineforthegivendataisy
^
=1.488x+60.46.Determinetheresidualofadatapointforwhichx=
53andy=145.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) 5.676 B) 284.324 C) 139.324 D) –223.22
7) Theregressionlineforthegivendataisy
^
=–2.75x+96.14.Determinetheresidualofadatapointforwhichx=
8andy=76.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) 1.86 B) 150.14 C) 74.14 D) 120.86
8) Theregressionlineforthegivendataisy
^
=3.53x+37.92.Determinetheresidualofadatapointforwhichx=
3andy=33.
Yearsemployed,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
A) –15.51 B) 81.51 C) 48.51 D) –151.41
Page114
9) Theregressionlineforthegivendataisy
^
=6.91x+46.26.Determinetheresidualofadatapointforwhichx=4
andy=75.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) 1.1 B) 148.9 C) 73.9 D) –560.51
10) Theregressionlineforthegivendataisy
^
=4.379x+4.267.Determinetheresidualofadatapointforwhichx=
13.4andy=58.8.
Rainfall(ininches),x
Yield(bushelsperacre),y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
A) –4.1456 B) 121.7456 C) 62.9456 D) –248.3522
11) Computethesumofthesquaredresidualsoftheleast–squareslineforthegivendata.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) 7.624 B) 1.036 C) 2.097 D) 0
12) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theysleptthenightbeforetheexam.Computethesumofthesquaredresidualsoftheleast –squareslineforthe
givendata.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
A) 318.038 B) 804.062 C) 1122.1 D) 39.755
13) InanareaoftheGreatPlains,recordswerekeptontherelationshipbetweentherainfall(ininches)andthe
yieldofwheat(bushelsperacre).Computethesumofthesquaredresidualsoftheleast–squareslineforthe
givendata.
Rainfall(ininches),x
Yield(bushelsperacre),y
10.5
50.5
8.8
46.2
13.4
58.8
12.5
59.0
18.8
82.4
10.3
49.2
7.0
31.9
15.6
76.0
16.0
78.8
A) 87.192 B) 2207.628 C) 4.379 D) 0
14) Inastudyoffeedingbehavior,zoologistsrecordedthenumberofgruntsofawarthogfeedingbyalakeina15
minutetimeperiodfollowingtheadditionoffood.Thedatashowingtheweeklynumberofgruntsandtheage
ofthewarthog(indays)arelistedbelow.Computethesumofthesquaredresidualsoftheleastsquaredline
forthegivendata.
Week Numberof
Grunts
Age(days)
1 90 125
2 68 141
3 39 155
4 44 160
5 63 167
6 40 174
7 62 183
8 17 189
9 20 195
A) 5533.53 B) 188.84 C) 74.39 D) 13.74
Page115
15) Thedatabelowaretheagesandsystolicbloodpressure(measuredinMillimetersofmercury)of9randomly
selectedadults.
Age,x Pressure,y
38 116
41 12.
45 123
48 131
51 142
53 145
57 148
61 150
65 152
A) 123.63 B) 1.41 C) 1.99 D) 11.11
16) AcalculusinstructorisinterestedtheperformanceofhisstudentsfromCalculusIthatgoontoCalculusII.
Theirfinalgradesineachcourse(inpercent)aregivenbelow.Computethesumofthesquaredresidualsofthe
leastsquaredlineforthegivendata.
CalculusI88 78 62 75 95 91 83 86 98
CalculusII 81 80 55 78 90 90 81 80 100
A) 130.14 B) 30.85 C) 11.41 D) 1075.9
4.3 DiagnosticsontheLeast–SquaresRegressionLine
1 Computeandinterpretthecoefficientofdetermination.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Choosethecoefficientofdeterminationthatmatchesthescatterplot.Assumethatthescalesonthehorizontaland
verticalaxesarethesame.
1) Response
Explanatory
A) R2=0.77 B) R2=0.38 C) R2=0.96 D) R2=0.51
Page116
2) Response
Explanatory
A) R2=0.43 B) R2=–0.43 C) R2=0.82 D) R2=0.12
3) Response
Explanatory
A) R2=0.097 B) R2=–0.31 C) R2=0.76 D) R2=0.41
Usethelinearcorrelationcoefficientgiventodeterminethecoefficientofdetermination,R2.
4) r=0.66
A) R2=43.56% B) R2=81.24% C) R2=8.12% D) R2=4.356%
5) r=–0.11
A) R2=1.21% B) R2=33.17% C) R2=–1.21% D) R2=–33.17%
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
6) Calculatethecoefficientofdeterminationtothenearestthousandth,giventhatthelinearcorrelationcoefficient,
r,is0.837.Whatdoesthistellyouabouttheexplainedvariationandtheunexplainedvariationofthedata
abouttheregressionline?
7) Calculatethecoefficientofdeterminationtothenearestthousandth,giventhatthelinearcorrelationcoefficient,
r,is–0.625.Whatdoesthistellyouabouttheexplainedvariationandtheunexplainedvariationofthedata
abouttheregressionline?
8) Calculatethecoefficientofdetermination,giventhatthelinearcorrelationcoefficient,r,is1.Whatdoesthistell
youabouttheexplainedvariationandtheunexplainedvariationofthedataabouttheregressionline?
Page117
9) Inastudyoffeedingbehavior,zoologistsrecordedthenumberofgruntsofawarthogfeedingbyalakeinthe
15minuteperiodfollowingtheadditionoffood.Thedatashowingtheweeklynumberofgruntsandtheageof
thewarthog(indays)arelistedbelow.FindandinterpretthevalueofR2.RoundR2tothenearestthousandth.
NumberofGrunts Age(days)
87 122
65 138
36 152
41 157
60 164
37 171
59 180
14 186
17 192
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
10) Inacomprehensiveroadtestonallnewcarmodels,onevariablemeasuredisthetimeittakesacarto
acceleratefrom0to60milesperhour.Tomodelaccelerationtime,aregressionanalysisisconductedona
randomsampleof129newcars.
TIME60: y=Elapsedtime(inseconds)from0mphto60mph
MAX: x1=Maximumspeedattained(milesperhour)
Initially,thesimplelinearmodelE(y)=β0+β1×1wasfittothedata.Computerprintoutsfortheanalysisare
givenbelow:
UNWEIGHTEDLEASTSQUARESLINEARREGRESSIONOFTIME60
PREDICTOR
VARIABLES COEFFICIENT STDERROR STUDENTʹSTP
CONSTANT 18.7171 0.63708 29.38 0.0000
MAX –0.08365 0.00491 –17.05 0.0000
R–SQUARED 0.6960 RESID.MEANSQUARE(MSE) 1.28695
ADJUSTEDR–SQUARED 0.6937 STANDARDDEVIATION 1.13444
SOURCE DF SS MS F P
REGRESSION 1374.285 374.285 290.83 0.0000
RESIDUAL 127 163.443 1.28695
TOTAL 128 537.728
CASESINCLUDED129MISSINGCASES0
Approximatelywhatpercentage,roundedtothenearestwholepercent,ofthesamplevariationinacceleration
timecanbeexplainedbythesimplelinearmodel?
A) 70% B) 0% C) –17% D) 8%
Page118
11) Amanufacturerofboilerdrumswantstouseregressiontopredictthenumberofman–hoursneededtoerect
drumsinthefuture.Themanufacturercollectedarandomsampleof35boilersandmeasuredthefollowing
twovariables:
MANHRS:y=Numberofman–hoursrequiredtoerectthedrum
PRESSURE:x1=Boilerdesignpressure(poundspersquareinch,i.e.,psi)
Initially,thesimplelinearmodelE(y)=β0+β1×1 wasfittothedata.Aprintoutfortheanalysisappearsbelow:
UNWEIGHTEDLEASTSQUARESLINEARREGRESSIONOFMANHRS
PREDICTOR
VARIABLES COEFFICIENT STDERROR STUDENTʹSTP
CONSTANT 1.88059 0.58380 3.22 0.0028
PRESSURE 0.00321 0.00163 2.17 0.0300
R–SQUARED 0.4342 RESID.MEANSQUARE(MSE) 4.25460
ADJUSTEDR–SQUARED 0.4176 STANDARDDEVIATION 2.06267
SOURCE DF SS MS F P
REGRESSION 1111.008 111.008 5.19 0.0300
RESIDUAL 34 144.656 4.25160
TOTAL 35 255.665
Giveapracticalinterpretationofthecoefficientofdetermination,R2.ExpressR2tothenearestwholepercent.
A) About43%ofthesamplevariationinnumberofman–hourscanbeexplainedbythesimplelinearmodel.
B) y
^
=1.88+0.00321xwillbecorrect43%ofthetime.
C) Manhoursneededtoerectdrumswillbeassociatedwithboilerdesignpressure43%ofthetime.
D) About2.06%ofthesamplevariationinnumberofman–hourscanbeexplainedbythesimplelinear
model.
Page119
12) Civilengineersoftenusethestraight–lineequation,E(y)=β0+β1x,tomodeltherelationshipbetweenthe
meanshearstrengthE(y)ofmasonryjointsandprecompressionstress,x.Totestthistheory,aseriesofstress
testswereperformedonsolidbricksarrangedintripletsandjoinedwithmortar.Theprecompressionstress
wasvariedforeachtripletandtheultimateshearloadjustbeforefailure(calledtheshearstrength)was
recorded.Thestressresultsforn=7triplettestsisshownintheaccompanyingtablefollowedbyaSAS
printoutoftheregressionanalysis.
TripletTest 1234567
ShearStrength(tons),y1.00 2.18 2.24 2.41 2.59 2.82 3.06
Precomp.Stress(tons),x00.60 1.20 1.33 1.43 1.75 1.75
AnalysisofVariance
 Sumof Mean
Source DF Squares Square FValue Prob>F
Model 1 2.39555 2.39555 47.732 0.0010
Error 5 0.25094 0.05019
CTotal 6 2.64649
RootMSE 0.22403 R–square 0.9052
DepMean 2.32857 AdjR–sq 0.8862
C.V. 9.62073
ParameterEstimates
Parameter Standard TforHO:
Variable DF Estimate Error Parameter=0 Prob>|T|
INTERCEP 1 1.191930 0.18503093 6.442 0.0013
X 1 0.987157 0.14288331 6.909 0.0010
GiveapracticalinterpretationofR2,thecoefficientofdeterminationfortheleastsquaresmodel.ExpressR2to
thenearestwholepercent.
A) About91%ofthetotalvariationinthesampleofy–valuescanbeexplainedby(orattributedto)thelinear
relationshipbetweenshearstrengthandprecompressionstress.
B) Inrepeatedsampling,approximately91%ofallsimilarlyconstructedregressionlineswillaccurately
predictshearstrength.
C) Weexpecttopredicttheshearstrengthofatriplettesttowithinabout.91tonofitstruevalue.
D) Weexpectabout91%oftheobservedshearstrengthvaluestolieontheleastsquaresline.
13) ThedeanoftheBusinessSchoolatasmallFloridacollegewishestodeterminewhetherthegrade –point
average(GPA)ofagraduatingstudentcanbeusedtopredictthegraduateʹsstartingsalary.Morespecifically,
thedeanwantstoknowwhetherhigherGPAʹsleadtohigherstartingsalaries.Recordsfor23oflastyearʹs
BusinessSchoolgraduatesareselectedatrandom,anddataonGPA(x)andstartingsalary(y,in$thousands)
foreachgraduatewereusedtofitthemodel,E(y)=β0+β1x.Theresultsofthesimplelinearregressionare
providedbelow.
y
^=4.25+2.75x, SSxy=5.15,SSxx=1.87
SSyy=15.17,SSE=1.0075
Rangeofthex–values: 2.23–3.85
Rangeofthey–values: 9.3–15.6
CalculatethevalueofR2,thecoefficientofdetermination.
A) 0.934 B) 0.661 C) 0.872 D) 0.339
Page120
14) EachyearanationallyrecognizedpublicationconductsitsʺSurveyofAmericaʹsBestGraduateand
ProfessionalSchools.ʺAnacademicadvisorwantstopredictthetypicalstartingsalaryofagraduateatatop
businessschoolusingGMATscoreoftheschoolasapredictorvariable.AsimplelinearregressionofSALARY
versusGMATusing25datapointsshownbelow.
b0=–92040b1=228s=3213R2=0.66r=0.81df=23t=6.67
GiveapracticalinterpretationofR2=0.66.
A) 66%ofthesamplevariationinSALARYcanbeexplainedbyusingGMATinastraight –linemodel.
B) 66%ofthedifferencesinSALARYarecausedbydifferencesinGMATscores.
C) WeestimateSALARYtoincrease$.66forevery1–pointincreaseinGMAT.
D) WecanpredictSALARYcorrectly66%ofthetimeusingGMATinastraight –linemodel.
15) Arealestatemagazinereportedtheresultsofaregressionanalysisdesignedtopredicttheprice(y),measured
indollars,ofresidentialpropertiesrecentlysoldinanorthernVirginiasubdivision.Oneindependentvariable
usedtopredictsalepriceisGLA,grosslivingarea(x),measuredinsquarefeet.Datafor157propertieswere
usedtofitthemodel,E(y)=β0+β1x.Theresultsofthesimplelinearregressionareprovidedbelow.
y=96,600+22.5xs=6500R2=0.77t=6.1(fortestingβ1)
Interpretthevalueofthecoefficientofdetermination,R2.
A) 77%ofthetotalvariationinthesamplesalepricescanbeattributedtothelinearrelationshipbetween
GLA(x)and(y).
B) GLA(x)islinearlyrelatedtosaleprice(y)77%ofthetime.
C) 77%oftheobservedsaleprices(yʹs)willfallwithin2standarddeviationsoftheleastsquaresline.
D) Thereisamoderatelystrongpositivecorrelationbetweensaleprice(y)andGLA(x).
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
16) Acompanykeepsextensiverecordsonitsnewsalespeopleonthepremisethatsalesshouldincreasewith
experience.Arandomsampleofsevennewsalespeopleproducedthedataonexperienceandsalesshownin
thetable.
MonthsonJob MonthlySales
y($thousands)
22.4
47.0
8 11.3
12 15.0
10.8
53.7
9 12.0
SummarystatisticsyieldSSxx=94.8571,SSxy=124.7571,SSyy=176.5171,x=5.8571,andy=7.4571.Findand
interpretthecoefficientofdetermination.RoundR2tothenearesthundredthofapercent.
17) Toinvestigatetherelationshipbetweenyieldofpotatoes,y,andleveloffertilizerapplication,x,an
experimenterdividesafieldintoeightplotsofequalsizeandappliesdifferingamountsoffertilizertoeach.
Theyieldofpotatoes(inpounds)andthefertilizerapplication(inpounds)arerecordedforeachplot.Thedata
areasfollows:
x11.5 2 2.5 3 3.5 4 4.5
y25 31 27 28 36 35 32 34
SummarystatisticsyieldSSxx=10.5,SSyy=112,andSSxy=25.Calculatethecoefficientofdetermination
roundedtothenearestten–thousandth.
Page121
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
18) Thecoefficientofcorrelationbetweenxandyisr=0.59.CalculatethecoefficientofdeterminationR2.Round
R2tothenearesthundredth.
A) 0.35 B) 0.59 C) 0.41 D) 0.65
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
19) Thecoefficientofdeterminationforastraight–linemodelrelatingsellingpriceytomanufacturingcostxfora
particularitemisR2=0.83.Interpretthisvalue.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
20) Themeasuresthepercentageoftotalvariationintheresponsevariablethatisexplained
bytheleastsquaresregressionline.
A) coefficientofdetermination B) coefficientoflinearcorrelation
C) sumoftheresidualssquared D) slopeoftheregressionline
21) Ifthecoefficientofdeterminationiscloseto1,then
A) theleastsquaresregressionlineequationexplainsmostofthevariationintheresponsevariable.
B) theleastsquaresregressionlineequationhasnoexplanatoryvalue.
C) thesumofthesquareresidualsislargecomparedtothetotalvariation.
D) thelinearcorrelationcoefficientisclosetozero.
22) Thecoefficientofdeterminationistheofthelinearcorrelationcoefficient.
A) square B) squareroot C) opposite D) reciprocal
2 Performresidualanalysisonaregressionmodel.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Analyzetheresiduallotbelow.Doesitviolateanyoftheconditionsforanadequatelinearmodel?
1)
A) No,theplotofresidualsisrandom.
B) Yes,thereisadiscernablepatternintheresiduals.
C) Yes,theresidualsdonotdisplayconstanterrorvariance.
Page122
2)
A) Yes,theresidualsdonotdisplayconstanterrorvariance.
B) Yes,thereisadiscernablepatternintheresiduals.
C) No,theplotofresidualsisrandom.
3)
A) Yes,thereisadiscernablepatternintheresiduals.
B) Yes,theresidualsdonotdisplayconstanterrorvariance.
C) No,theplotofresidualsisrandom.
Provideanappropriateresponse.
4) TrueorFalse:Residualanalysiscannotbeusedtocheckforoutliers.
A) False B) True
5) TrueorFalse:Ifaresidualplotshowsanalmoststraightlinethenalinearmodelisappropriate.
A) False B) True
6) Todetermineifthereareoutliersinaleastsquaresregressionmodelʹsdataset,wecouldconstructaboxplotof
the
A) residuals. B) responsevariables.
C) predictorvariables. D) lurkingvariables.
Page123
3 Identifyinfluentialobservations.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
AscatterdiagramisgivenwithoneofthepointslabeledʺA.ʺInaddition,therearetwoleast –squaresregressionlines
drawn.ThesolidlineexcludesthepointA.ThedashedlineincludesthepointA.Basedonthegraph,isthepointA
influential?
1)
x
12345678910
y
10
9
8
7
6
5
4
3
2
1
A
x
12345678910
y
10
9
8
7
6
5
4
3
2
1
A
A) yes B) no
2)
x
12345678910
y
10
9
8
7
6
5
4
3
2
1
A
x
12345678910
y
10
9
8
7
6
5
4
3
2
1
A
A) no B) yes
Provideanappropriateresponse.
3) Aninfluentialobservationisanobservationthatsignificantlyaffectsthevalueofthe
A) theslopeoftheleastsquaresregressionline. B) themeanoftheresponsevariable.
C) themedianofthepredictorvariable. D) themedianoftheresponsevariable.
4) Whateffectwillaninfluentialobservationhaveuponthegraphoftheleastsquaresregressionline?
A) Itwillpullthegraphtowardtheobservation.
B) Itwillhavenoeffect.
C) Itwillpushthegraphawayfromtheobservation.
D) Itwilllowerthevalueofthecorrelationcoefficienttomakefurtheranalysismeaningless.
Page124
4.4 ContingencyTablesandAssociation
1 Computethemarginaldistributionofavariable.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Thefollowingdatarepresentthelivingsituationofnewlywedsinalargemetropolitanareaandtheirannual
householdincome.Findthemarginalfrequencyfornewlywedswhorenttheirhome.
<$20,000 $20–35,000 $35–50,000 $50–75,000 >$75,000
Ownhome 31 52 202 355 524
Renthome 67 66 52 23 11
Livew/family 89 69 30 4 2
A) 219 B) 67 C) 11 D) 52
2) Thefollowingdatarepresentthelivingsituationofnewlywedsinalargemetropolitanareaandtheirannual
householdincome.Findthemarginalfrequencyfornewlywedswhomakebetween$20,000and$35,000per
year.
<$20,000 $20–35,000 $35–50,000 $50–75,000 >$75,000
Ownhome 31 52 202 355 524
Renthome 67 66 52 23 11
Livew/family 89 69 30 4 2
A) 187 B) 69 C) 52 D) 66
3) Thefollowingdatarepresentthelivingsituationofnewlywedsinalargemetropolitanareaandtheirannual
householdincome.Whatpercentofpeoplewhomakebetween$20,000and$35,000peryearowntheirown
home?Roundtothenearesttenthofapercent.
<$20,000 $20–35,000 $35–50,000 $50–75,000 >$75,000
Ownhome 31 52 202 355 524
Renthome 67 66 52 23 11
Livew/family 89 69 30 4 2
A) 27.8% B) 35.3% C) 36.9% D) 4.5%
4) Thefollowingdatarepresentthelivingsituationofnewlywedsinalargemetropolitanareaandtheirannual
householdincome.Whatpercentofpeoplewhoowntheirownhomemakebetween$35,000and$50,000per
year?Roundtothenearesttenthofapercent.
<$20,000 $20–35,000 $35–50,000 $50–75,000 >$75,000
Ownhome 31 52 202 355 524
Renthome 67 66 52 23 11
Livew/family 89 69 30 4 2
A) 17.4% B) 4.5% C) 30.5% D) 71.1%
Page125
5) Constructafrequencymarginaldistributionforthegivencontingencytable.
x1x2x3
y140 25 30
y265 60 60
A)
x1x2x3MarginalDistribution
y140 25 30 95
y265 60 60 185
MarginalDistribution 105 85 90 280
B)
x1x2x3MarginalDistribution
y140 25 30 95
y265 60 60 185
MarginalDistribution 105 85 90 560
C)
x1x2x3MarginalDistribution
y140 25 30 95
y265 60 60 185
MarginalDistribution 25 35 30 560
D)
x1x2x3MarginalDistribution
y140 25 30 105v
y265 60 60 85
MarginalDistribution 95 185 90 560
Page126
6) Constructarelativefrequencymarginaldistributionforthegivencontingencytable.Roundvaluesetothe
nearestthousandth.
x1x2x3
y120 25 25
y255 50 50
A)
x1x2x3
RelativeFrequency
MarginalDistribution
y120 25 25 0.311
y255 50 50 0.689
RelativeFrequency
MarginalDistribution 0.333 0.333 0.333 1
B)
x1x2x3
RelativeFrequency
MarginalDistribution
y120 25 25 0.311
y255 50 50 0.689
RelativeFrequency
MarginalDistribution 0.156 0.111 0.111 1
C)
x1x2x3
RelativeFrequency
MarginalDistribution
y120 25 25 0.70
y255 50 50 1.55
RelativeFrequency
MarginalDistribution 0.75 0.75 0.75 1
D)
RelativeFrequency
MarginalDistribution x1x2x3
y10.089 0.111 0.111
y20.244 0.222 0.222
Page127
7) Constructaconditionaldistributionbyxforthegivencontingencytable.Roundvaluesetothenearest
thousandth.
x1x2x3
y125 25 35
y275 75 70
A)
x1x2x3
y10.250 0.250 0.333
y20.750 0.750 0.667
Total 111
B)
x1x2x3
y10.250 0.250 0.333
y20.341 0.341 0.318
Total 111
C)
x1x2x3
y10.082 0.082 0.115
y20.246 0.246 0.230
D)
x1x2x3Total
y10.294 0.294 0.412 1
y20.341 0.341 0.318 1
8) Acontingencytablerelates
A) twocategoriesofdata.
B) thedifferenceinthemeansoftworandomvariables.
C) aparticularresponsewithorderinwhichthatresponseshouldbeapplied.
D) onlycontinuousrandomvariables.
9) Toeliminatetheeffectsofeithertheroworthecolumnvariablesinacontingencytable,a
distributioniscreated.
A) marginal B) normalized C) χ2D) Studentʹst
2 Usetheconditionaldistributiontoidentifyassociationamongcategoricaldata.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Thedatabelowshowtheageandfavoritetypeofmusicof779randomlyselectedpeople.Useα=0.05. What,if
any,associationexistsbetweenfavoritemusicandage?Discusstheassociation.
Age Country Rock Pop Classical
15–21 21 45 90 33
21–30 60 55 42 48
30–40 65 47 31 57
40–50 68 39 25 53
2) Thefollowingdatarepresentthelivingsituationofnewlywedsinalargemetropolitanareaandtheirannual
householdincome.What,ifany,associationexistsbetweenlivingsituationandhouseholdincome?Discussthe
association.
<$20,000 $20–35,000 $35–50,000 $50–75,000 >$75,000
Ownhome 31 52 202 355 524
Renthome 67 66 52 23 11
Livew/family 89 69 30 4 2
Page128
3 ExplainSimpsonʹsParadox.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Researchersconductedastudytodeterminewhichoftwodifferenttreatments,AorB,ismoreeffectiveinthe
treatmentofatherosclerosis.Theresultsoftheirexperimentaregiveninthetable.(a)Whichtreatmentappears
tobemoreeffective?Why?
TreatmentA TreatmentB
Effective 420 435
Noteffective 130 140
Thedatainthetabledonottakeintoaccounttheseriousnessofthecase.Thedatashowninthenexttable
showtheeffectivenessofeachtreatmentforbothmildandadvancedcasesofatherosclerosis.
Mild Advanced
atherosclerosis atherosclerosis
TreatmentATreatmentBTreatmentATreatmentB
Effective 31095 110340
Noteffective 8020 50120
(b)DeterminetheproportionofmildcasesofatherosclerosisthatwereeffectivelydealtwithusingtreatmentA.
DeterminetheproportionofmildcasesofatherosclerosisthatwereeffectivelydealtwithusingtreatmentB.
(c)Repeatpart(b)foradvancedcasesofatherosclerosistocreateaconditionaldistributionofeffectivenessby
treatmentforeachcategoryofthedisease.
(d)Writeashortreportdetailingandexplainingyourfindings.
2) Acompanyencouragesapplicationsfromminoritygroupswhotheyfeelareunder–representedinthe
company.Thetableshowsthenumberofapplicationsthatwereacceptedlastyearfrompeoplebelongingto
minoritygroupsandthenumberofapplicationsthatwereacceptedfrompeoplenotbelongingtominority
groups.Onlyapplicationsfromwellqualifiedapplicantsareincludedintheanalysis.(a)Doestheacceptance
rateappeartobehigherforthosebelongingtominoritygroupsorforthosenotbelongingtominoritygroups?
Why?
Minority Notminority
Accepted 70 79
Rejected 460 500
Thedatainthetabledonottakeintoaccountthedepartmentofthecompany.Thedatashowninthenexttable
showthenumberofapplicationsacceptedfromeachgroupwithineachdepartment.
DepartmentA DepartmentB DepartmentC
MinorityNotminority MinorityNotminority MinorityNotminority
Accepted 2710 2234 2135
Rejected 260110 80150 120240
(b)DeterminetheproportionofminorityapplicationsthatwereacceptedwithindepartmentA.Determinethe
proportionofnon–minorityapplicationsthatwereacceptedwithindepartmentA.
(c)Repeatpart(b)fordepartmentsBandCtocreateaconditionaldistributionofacceptanceratebygroupfor
eachdepartmentofthecompany.
(d)Writeashortreportdetailingandexplainingyourfindings.
Page129
4.5 NonlinearRegression:Transformations(onCD)
1 Convertbetweenexponentialandlogarithmicexpressions.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Changetheexponentialexpressiontoanequivalentexpressioninvolvingalogarithm.
1) 23=8
A) log28=3 B) log82=3 C) log38=2 D) log23=8
2) 23=x
A) log2x=3 B) logx2=3 C) log3x=2 D) log23=x
3) 83=y
A) log8y=3 B) log3y=8 C) logy8=3 D) logy3=8
4) 7x=49
A) log749=x B) logx49 =7 C) log497=x D) log49x=7
5) 2x=279
A) log2279=x B) log2792=x C) log279x=2 D) log2x=279
Changethelogarithmicexpressiontoanequivalentexpressioninvolvinganexponent.
6) log39=2
A) 32=9B)2
3=9C)3
9=2D)9
2=3
7) log4x=3
A) 43=xB)3
4=xC)4
x=3D)x
3=4
8) logb32=5
A) b5=32 B) 5
b
=32 C) 325=bD)32
b
=5
9) log464=x
A) 4x=64 B) x4=64 C) 64x=4D)64
4=x
2 Simplifylogarithmicexpressions.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Writetheexpressionasasumoflogs.Expresspowersasfactors.
1) log10xy
A) log10x+log10y B) log10x–log10y C) log5x+log5y D) log5x–log5y
2) log7x2
A) 2log7x B) 7log2xC)7logx D) 2log7x2
3) logbyz2
A) logby+2logbz B) 2logby+2logbz C) 2logbyz D) logby+logb2z
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4) logby7z3
A) 7logby+3logbz B) 21logbyz C) logb(yz)21 D) logb21yz
Useacalculatortoevaluatetheexpression.Roundyouranswertothreedecimalplaces.
5) log111
A) 2.045 B) 4.710 C) 2.049 D) 2.041
6) log2.99
A) 0.476 B) 1.095 C) 0.490 D) 0.461
7) 101.4
A) 25.119 B) 31.623 C) 4.055 D) 39.811
8) 100.5826
A) 3.825 B) 0.261 C) 0.558 D) 1.144
3 Uselogarithmictransformationstolinearizeexponentialrelations.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Thefollowingdatarepresentthebacteriapopulationinalaboratoryexperiment.Theresearcherssuspectthat
thepopulationisgrowingexponentially.Determinethelogarithmofthey–valuessothatY=logy.
Day,x Population,y
0 1828
1 4982
2 13,494
3 36,784
4 100,058
5 272,152
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) Thefollowingdatarepresentthebacteriapopulationinalaboratoryexperiment.Theresearcherssuspectthat
thepopulationisgrowingexponentially.Findtheexponentialequationofbestfit.
Day,x Population,y
0 1952
1 5319
2 14410
3 39279
4 106845
5 290613
A) y
^
=3.291+0.435x B) y
^
=3.458+1.151x
C) y
^
=–7.537+2.301x D) y
^
=–50,222.143+50,650.057x
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4 Uselogarithmictransformationstolinearizepowerrelations.
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Thefollowingdatarepresenttheperiods(inseconds)ofsimplependulumsofvariouslengths(infeet).
Determinethelogarithmofboththex–andy–valuessothatX=logxandY=logy.
Length,x Period,y
1 1.3
2 1.8
3 2.3
4 2.6
5 2.9
6 3.2
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) Thefollowingdatarepresenttheperiods(inseconds)ofsimplependulumsofvariouslengths(infeet).Findthe
powerequationofbestfit.
Length,x Period,y
1 1.3
2 1.9
3 2.3
4 2.7
5 3.0
6 3.3
A) y
^
=0.1171+0.5176x B) y
^
=–0.2258+1.9309x
C) y
^
=0.0948+0.0768x D) y
^
=1.0467+0.3914x
3) Thefollowingdatarepresenttheinfectionrateforaparticulardiseaseinathirdworldcountryxyearsaftera
vaccinebecamewidelyavailable.Determinetheʺbestʺmodeltodescribetherelationshipbetweenyearspast
andinfectionrate.
YearsAfterVaccine,x InfectionRate(%),y
132
211
35
42
5 0.5
A) exponentialmodel:y
^
=1.955–0.435x B) powermodel:y
^
=1.648–2.402x
C) linearmodel:y
^
=31.7–7.2x D) linearmodel:y
^
=31.7+7.2x
4) Thefollowingdatarepresentthecompoundyieldingramsforachemicalreactionforvarioustemperaturesof
thereaction.Determinetheʺbestʺmodeltodescribetherelationshipbetweentemperatureandcompound
yield.
Temperature(°C),x CompoundYield(grams),y
50 4
60 12
70 14
80 21
90 26
A) linearmodel:y
^
=–21.7+0.53x B) exponentialmodel:y
^
=–0.195+0.019x
C) powermodel:y
^
=–4.392+2.999x D) powermodel:y
^
=4.392+2.999x
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5) Thefollowingdatarepresenttheheight(relativetotheground)ofaprojectileshotintotheairafterxseconds
oftravel.Determinetheʺbestʺmodeltodescribetherelationshipbetweentraveltimeandheight.
TravelTime(seconds),x Height(feet),y
8 890
9 869
10 798
11 708
12 571
A) powermodel:y
^
=3.930–1.056x B) exponentialmodel:y
^
=3.354–0.047x
C) linearmodel:y
^
=1566.2–79.9x D) exponentialmodel:y
^
=3.354+0.047x
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Ch.4 DescribingtheRelationbetweenTwoVariables
AnswerKey
4.1 ScatterDiagramsandCorrelation
1 Drawandinterpretscatterdiagrams.
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2 Describethepropertiesofthelinearcorrelationcoefficient.
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3 Computeandinterpretthelinearcorrelationcoefficient.
4 Determinewhetheralinearrelationexistsbetweentwovariables.
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5 Explainthedifferencebetweencorrelationandcausation.
4.2 Least–SquaresRegression
1 Findtheleast–squaresregressionlineandusethelinetomakepredictions.
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2 Interprettheslopeandthey–interceptoftheleast–squaresregressionline.
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3 Computethesumofsquaredresiduals.
4.3 DiagnosticsontheLeast–SquaresRegressionLine
1 Computeandinterpretthecoefficientofdetermination.
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2 Performresidualanalysisonaregressionmodel.
3 Identifyinfluentialobservations.
4.4 ContingencyTablesandAssociation
1 Computethemarginaldistributionofavariable.
2 Usetheconditionaldistributiontoidentifyassociationamongcategoricaldata.
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3 ExplainSimpsonʹsParadox.
4.5 NonlinearRegression:Transformations(onCD)
1 Convertbetweenexponentialandlogarithmicexpressions.
2 Simplifylogarithmicexpressions.
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3 Uselogarithmictransformationstolinearizeexponentialrelations.
4 Uselogarithmictransformationstolinearizepowerrelations.
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