Ch.9 CorrelationandRegression
9.1 Correlation
1 InterpretScatterPlotsandCorrelations
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Giventhelengthofahumanʹsfemur,x,andthelengthofahumanʹshumerus,y,wouldyouexpectapositive
correlation,anegativecorrelation,ornocorrelation?
A) positivecorrelation B) negativecorrelation C) nocorrelation
2) Giventhesupplyofacommodity,x,andthepriceofacommodity,y,wouldyouexpectapositivecorrelation,
anegativecorrelation,ornocorrelation?
A) negativecorrelation B) positivecorrelation C) nocorrelation
3) Giventhesizeofahumanʹsbrain,x,andtheirscoreonanIQtest,y,wouldyouexpectapositivecorrelation,a
negativecorrelation,ornocorrelation?
A) nocorrelation B) positivecorrelation C) negativecorrelation
2 IdentifytheExplanatoryandResponseVariables
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Identifytheexplanatoryvariableandtheresponsevariable.
1) Anagriculturalbusinesswantstodetermineiftherainfallininchescanbeusedtopredicttheyieldperacreon
awheatfarm.
2) Acollegecounselorwantstodetermineifthenumberofhoursspentstudyingforatestcanbeusedtopredict
thegradesonatest.
3 ConstructaScatterPlotandDetermineCorrelation
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Constructascatterplotforthedata.Determinewhetherthereisapositivelinearcorrelation,a
negativelinearcorrelation,ornolinearcorrelation.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
2) Constructascatterplotforthegivendata.Determinewhetherthereisapositivelinearcorrelation,negative
linearcorrelation,ornolinearcorrelation.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
Page201
3) Constructascatterplotforthegivendata.Determinewhetherthereisapositivelinearcorrelation,negative
linearcorrelation,ornolinearcorrelation.
x
y
–5
11
–3
–6
4
8
1
–3
–1
–2
–2
1
0
5
2
–5
3
6
–4
7
4) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Constructascatterplotforthedata.
Hours,x
Scores,y
3
65
5
80
2
60
8
88
2
66
4
78
4
85
5
90
6
90
3
71
5) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Constructascatterplotforthedata.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
6) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Constructascatterplotforthedata.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
7) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Constructascatterplotforthedata.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
8) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Constructascatterplotforthedata.
Milestraveled,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
9) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowtherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Construct
ascatterplotforthedata.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
Page202
10) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Constructascatterplotforthedata.
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
4 PerformaHypothesisTestforaPopulationCorrelationCoefficient
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
-1
0
1
2
8
19
5
11
3
8
2
4
4
9
6
13
7
16
0
2
A) 0.990 B) 0.881 C) 0.819 D) 0.792
2) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
1
1
3
–4
10
-16
7
-11
5
–7
4
–6
6
-9
8
-14
9
-15
2
–2
A) –0.995 B) –0.671 C) –0.778 D) –0.885
3) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
5
7
7
-10
14
4
11
-7
9
-6
8
-3
10
1
12
-9
13
2
6
3
A) –0.104 B) –0.132 C) –0.549 D) –0.581
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
4) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Calculatethecorrelationcoefficientr.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
5) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Calculatethecorrelationcoefficient,r.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
6) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Calculatethecorrelationcoefficientr.
Hours,x
Scores,y
2
68
4
83
1
63
7
91
1
69
3
81
3
88
4
93
5
93
2
74
A) 0.847 B) 0.991 C) 0.761 D) 0.654
Page203
7) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Calculatethecorrelationcoefficient,r.
Temperature,x
Numberofabsences,y
76
12
89
16
95
19
94
19
92
17
102
24
79
13
104
24
84
14
A) 0.980 B) 0.890 C) 0.881 D) 0.819
8) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Calculatethecorrelationcoefficient,r.
Age,x
Pressure,y
33
112
36
116
40
119
43
127
46
138
48
141
52
144
56
146
60
148
A) 0.960 B) 0.998 C) 0.890 D) 0.908
9) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Calculatethecorrelationcoefficient,r.
Numberofabsences,x
FinalGrade,y
0
93
3
81
6
75
4
77
9
66
2
87
15
50
8
71
5
77
A) –0.991 B) –0.888 C) –0.918 D) –0.899
10) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Calculatethecorrelationcoefficient,r.
Milestraveled,x
Sales,y
5
30
6
32
13
77
10
61
11
64
18
60
6
47
4
54
14
119
A) 0.632 B) 0.561 C) 0.717 D) 0.791
11) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Calculate
thecorrelationcoefficient,r.
Numberofyears,x
Gradesontest,y
5
52
6
59
6
66
7
73
5
64
8
81
4
49
9
84
5
63
A) 0.934 B) 0.911 C) 0.891 D) 0.902
12) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Calculatethecorrelationcoefficient,r.
Rainfall(ininches),x
Yield(bushelsperacre),y
9.5
45.5
7.8
41.2
12.4
53.8
11.5
54
17.8
77.4
9.3
44.2
6
26.9
14.6
71
15
73.8
A) 0.981 B) 0.998 C) 0.900 D) 0.899
13) Givenasamplewithr=0.823,n=10,andα =0.05,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) 4.098 B) 3.816 C) 2.891 D) 1.782
14) Givenasamplewithr=–0.541,n=20,andα =0.01,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) –2.729 B) –5.132 C) –4.671 D) –3.251
Page204
15) Givenasamplewithr=0.321,n=30,andα =0.10,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) 1.793 B) 3.198 C) 2.354 D) 2.561
16) Givenasamplewithr=–0.765,n=22,andα =0.02,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) –5.312 B) –4.392 C) –3.783 D) –2.653
17) Givenasamplewithr=0.823,n=10,andα =0.05,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±2.306 B) ±2.821 C) ±1.833 D) ±1.383
18) Givenasamplewithr=–0.541,n=20,andα =0.01,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±2.878 B) ±1.729 C) ±2.093 D) ±2.540
19) Givenasamplewithr=0.321,n=30,andα =0.10,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±1.701 B) ±1.311 C) ±2.462 D) ±0.683
20) Givenasamplewithr=–0.765,n=22,andα =0.02,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±2.528 B) ±2.080 C) ±2.831 D) ±1.721
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
21) Givenasamplewithr=0.823andn=10,testthesignificanceofthecorrelationrusingα=0.05andtheclaim
ρ=0.
22) Givenasamplewithr=–0.541,n=20,testthesignificanceofthecorrelationrusingα=0.01andtheclaim
ρ=0.
23) Givenasamplewithr=0.321andn=30,testthesignificanceofthecorrelationrusingα=0.10andtheclaim
ρ=0.
24) Givenasamplewithr=–0.765andn=22,testthesignificanceofthecorrelationrusingα=0.02 andtheclaim
ρ=0.
25) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.05andtheclaimρ =0.
x
y
-10
-2
-8
0
-1
17
-4
9
-6
6
-7
2
-5
7
-3
11
-2
14
-9
0
26) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.01andtheclaimρ =0.
x
y
-13
5
-11
0
-4
-12
-7
-7
-9
-3
-10
-2
-8
-5
-6
-10
-5
-11
-12
2
27) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.10andtheclaimρ =0.
x
y
-10
15
-8
-2
–1
12
–4
1
–6
2
–7
5
–5
9
–3
-1
–2
10
-9
11
Page205
28) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Testthesignificanceofthecorrelationcoefficientusingα=0.01andtheclaimρ>0.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
29) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Testthesignificanceofthecorrelationcoefficientusingα
=0.05andtheclaimρ=0.
Hours,x
Scores,y
4
67
6
82
3
62
9
90
3
68
5
80
5
87
6
92
7
92
4
73
30) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Testthesignificanceofthecorrelationcoefficientusingα=0.02,andtheclaimρ=0.
Temperature,x
Numberofabsences,y
71
12
84
16
90
19
89
19
87
17
97
24
74
13
99
24
79
14
31) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Testthesignificanceofthecorrelationcoefficientusingα=0.05andtheclaimρ=0.
Age,x
Pressure,y
43
114
46
118
50
121
53
129
56
140
58
143
62
146
66
148
70
150
32) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Testthesignificanceofthecorrelationcoefficientusingα=0.05andtheclaimρ=0.
Numberofabsences,x
FinalGrade,y
1
89
4
77
7
71
5
73
10
62
3
83
16
46
9
67
6
73
33) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Testthesignificanceofthecorrelationcoefficientusingα=0.01andtheclaimρ=0.
Milestraveled,x
Sales,y
5
33
6
35
13
80
10
64
11
67
18
63
6
50
4
57
14
122
34) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Testthe
significanceofthecorrelationcoefficientusingα=0.10andtheclaimρ=0.
Numberofyears,x
Gradesontest,y
2
58
3
65
3
72
4
79
2
70
5
87
1
55
6
90
2
69
35) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Testthesignificanceofthecorrelationcoefficientusingα=0.01andtheclaimρ=0.
Rainfall(ininches),x
Yield(bushelsperacre),y
11
51.5
9.3
47.2
13.9
59.8
13
60
19.3
83.4
10.8
50.2
7.5
32.9
16.1
77
16.5
79.8
Page206
36) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Testthesignificanceofthecorrelationcoefficientusingα
=0.05
andtheclaimρ<0.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
5 CalculatetheCorrelationCoefficientwithInterchangedxandy
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Calculatethecoefficientofcorrelation,r,lettingRow1representthex–valuesandRow2representthe
y–values.Nowcalculatethecoefficientofcorrelation,r,lettingRow2representthex–valuesandRow1
representthey–values.Whateffectdoesswitchingtheexplanatoryandresponsevariableshaveonthe
correlationcoefficient?
Row1
Row2
1
-7
3
11
10
12
7
4
5
1
4
-3
6
2
8
6
9
9
2
11
6 Concepts
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Explainthedifferencebetweenx2
∑andx
∑2.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) IfDataAhasacorrelationcoefficientofr= –0.991,andDataBhasacorrelationcoefficientofr=0.991,which
correlationiscorrect?
A) DataAandDataBhavethesamestrengthinlinearcorrelation.
B) DataAhasastrongerlinearcorrelationthanDataB.
C) DataAhasaweakerlinearcorrelationthanDataB.
3) Whichofthefollowingvaluescouldnotrepresentacorrelationcoefficient?
A) 1.032 B) 0 C) 0.927 D) –1
Page207
9.2 LinearRegression
1 FindtheEquationofaRegressionLine
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Matchtheregressionequationwiththeappropriategraph.(Notethatthex–andy–axesarebroken.)
y
^=0.00114x+0.57
A)
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
Coolingcapacity(inBTUs)
B)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
Age(inyears)
C)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
Protein(ingrams)
D)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
Worktime(hoursperweek)
Page208
2) Matchtheregressionequationwiththeappropriategraph.(Notethatthex–andy–axesarebroken.)
y
^=1.72x+84.99
A)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
Age(inyears)
B)
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
Coolingcapacity(inBTUs)
C)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
Protein(ingrams)
D)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
Worktime(hoursperweek)
Page209
3) Matchtheregressionequationwiththeappropriategraph.(Notethatthex–andy–axesarebroken.)
y
^=–1.1x+52.3
A)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
Protein(ingrams)
B)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
Age(inyears)
C)
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
Coolingcapacity(inBTUs)
D)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
Worktime(hoursperweek)
Page210
4) Matchtheregressionequationwiththeappropriategraph.(Notethatthex–andy–axesarebroken.)
y
^=–0.677x+52.3
A)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
x
40 41 42 43 44 45 46 47 48 49 50
y
28
26
24
22
20
18
Leisure time (hours per week)
Worktime(hoursperweek)
B)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
x
20 30 40 50 60 70
y
220
200
180
160
140
120
100
80
Systolic BP (in mm of mercury)
Age(inyears)
C)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
x
32 33 34 35 36 37 38
y
18
17
16
15
14
13
12
11
Fat (in grams)
Protein(ingrams)
D)
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
x
5800 6000 6200
y
11
10
9
8
Energy-efficiency rating
Coolingcapacity(inBTUs)
5) Findtheequationoftheregressionlineforthegivendata.
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
6) Findtheequationoftheregressionlineforthegivendata.
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
Page211
7) Findtheequationoftheregressionlineforthegivendata.
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
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
8) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Findtheequationoftheregressionlineforthegivendata.
Gestation,x8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
9) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Findtheequationoftheregressionlineforthegivendata.
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
^
=5.044x+56.113 B) y
^
=56.113x–5.044
C) y
^
^
=–56.113x–5.044 D) y
^
=–5.044x+56.113
10) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Findtheequationoftheregressionlineforthegivendata.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) y
^
=0.449x–30.27 B) y
^
=30.27x–0.449 C) y
^
=0.449x+30.27 D) y
^
=30.27x+0.449
11) Thedatabelowareagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Findtheequationoftheregressionlineforthegivendata.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) y
^
=1.488x+60.461 B) y
^
=60.461x–1.488
C) y
^
=1.448x–60.461 D) y
^
^
=60.461x+1.488
Page212
12) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Findtheequationoftheregressionlineforthegivendata.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) y
^
=–2.755x+96.139 B) y
^
=96.139x–2.755
C) y
^
=–2.755x–96.139 D) y
^
=–96.139x+2.755
13) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Findtheequationoftheregressionlineforthegivendata.
Milestraveled,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
A) y
^
=3.529x+37.916 B) y
^
=37.916x–3.529
C) y
^
^
=3.529x–37.916 D) y
^
=37.916x+3.529
14) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Findthe
equationoftheregressionlineforthegivendata.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) y
^
=6.910x+46.261 B) y
^
=6.910x–46.261
C) y
^
=46.261x–6.910 D) y
^
=46.261x+6.910
15) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Findtheequationoftheregressionlineforthegivendata.
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.
16) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Findtheequationoftheregressionlineforthegivendata.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
Page213
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
17) Giventheequationofaregressionlineisy
^
=3x–1,whatisthebestpredictedvalueforygivenx=4?Assume
thatthevariablesxandyhaveasignificantcorrelation.
A) 11 B) 13 C) 1 D) 6
18) Giventheequationofaregressionlineisy
^
=-2.5x+ 5.3,whatisthebestpredictedvalueforygivenx=4.9?
Assumethatthevariablesxandyhaveasignificantcorrelation.
A) -6.95 B) -17.55 C) 17.55 D) 6.95
19) Giventheequationofaregressionlineisy
^
=3.5x–5.4,whatisthebestpredictedvalueforygivenx=–1.2?
Assumethatthevariablesxandyhaveasignificantcorrelation.
A) –9.6 B) 12.3 C) –6.9 D) –12.3
20) Usetheregressionequationtopredictthevalueofyforx=-2.8.Assumethatthevariablesxandyhavea
significantcorrelation.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) -6.424 B) -5.320 C) 3.643 D) 0.551
21) Usetheregressionequationtopredictthevalueofyforx=-0.2.Assumethatthevariablesxandyhavea
significantcorrelation.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
A) 1.135 B) 0.381 C) -2.037 D) 1.733
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
22) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Usetheregressionequationtopredictthelifespan,y,foragestationperiodof6months,x.
Assumethevariablesxandyhaveasignificantcorrelation.
Gestation,x82.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
23) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Whatisthebestpredictedvalueforygivenx=3?Assumethatthevariablesxandy
haveasignificantcorrelation.
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) 71 B) 70 C) 69 D) 72
Page214
24) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Whatisthebestpredictedvalueforygivenx=84?Assumethatthevariablesxandy
haveasignificantcorrelation.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) 7 B) 8 C) 9 D) 10
25) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Whatisthebestpredictedvalueforygivenx=41?Assumethatthevariablesxandyhavea
significantcorrelation.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) 121 B) 123 C) 119 D) 117
26) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Whatisthebestpredictedvalueforygivenx=10?Assumethatthevariablesxandyhavea
significantcorrelation.
.Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) 69 B) 70 C) 71 D) 68
27) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowtherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Whatis
thebestpredictedvalueforygivenx=5.5?Assumethatthevariablesxandyhaveasignificantcorrelation.
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
28) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Whichisthebestpredictedvalueforygivenx=7.3?Assumethatthevariablesx
andyhaveasignificantcorrelation.
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) 36.2 B) 36.5 C) 36.0 D) 36.7
Page215
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
29) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Whatisthebest–predictedvalueforthegasconsumption,y,
givenx=50°F?Assumethatthevariablesxandyhaveasignificantcorrelation.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
30) 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)Graphascatterplotofthedata.
b)Findanequationoftheregressionline.
c)Determineifthereisasignificantcorrelationbetweenthedata.Useα
=0.01.
d)PredictaCalculusIIexamscoreforastudentwhoreceivesan80inCalculusI.Isyouransweravalid
prediction?
2 FindtheEquationofaRegressionLinewithInterchangedxandy
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) 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
3 Concepts
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Giventheequationofaregressionlineisy
^
=–1.04x+50.3,determinewhetherthereisapositivelinear
correlationoranegativelinearcorrelation.
A) negativelinearcorrelation B) positivelinearcorrelation
2) Giventheequationofaregressionlineisy
^
=0.00014x+2.53,determinewhetherthereisapositivelinear
correlationoranegativelinearcorrelation.
A) positivelinearcorrelation B) negativelinearcorrelation
Page216
9.3 MeasuresofRegressionandPredictionIntervals
1 FindTypesofVariationsandtheCoefficientofDetermination
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Calculatethecoefficientofdetermination,giventhatthelinearcorrelationcoefficient,r,is0.837.Whatdoesthis
tellyouabouttheexplainedvariationandtheunexplainedvariationofthedataabouttheregressionline?
2) Calculatethecoefficientofdetermination,giventhatthelinearcorrelationcoefficient,r,is–0.625.Whatdoes
thistellyouabouttheexplainedvariationandtheunexplainedvariationofthedataabouttheregressionline?
3) Calculatethecoefficientofdetermination,giventhatthelinearcorrelationcoefficient,r,is1.Whatdoesthistell
youabouttheexplainedvariationandtheunexplainedvariationofthedataabouttheregressionline?
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
4) Findthestandarderrorofestimate,se,forthedatabelow,giventhaty
^
=2x+1.
x
y
1
3
2
5
3
7
4
9
A) 0 B) 1 C) 2 D) 3
5) Findthestandarderrorofestimate,se,forthedatabelow,giventhaty
^
=–2.5x.
x
y
–1
2
–2
6
–3
7
–4
10
A) 0.866 B) 0.675 C) 0.532 D) 0.349
6) Findthestandarderrorofestimate,se,forthedatabelow,giventhaty
^
=2.097x–0.552.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) 0.976 B) 0.990 C) –0.990 D) 0.980
7) Findthestandarderrorofestimate,se,forthedatabelow,giventhaty
^
=–1.885x+0.758.
x
y
–5
11
–3
6
4
–6
1
–1
–1
3
–2
4
0
1
2
–4
3
–5
–4
8
A) 0.613 B) 0.981 C) 0.312 D) 0.011
8) Findthestandarderrorofestimate,se,forthedatabelow,giventhaty
^
=–0.206x+2.097.
x
y
–5
11
–3
–6
4
8
1
–3
–1
–2
–2
1
0
5
2
–5
3
6
–4
7
A) 6.306 B) 3.203 C) 5.918 D) 8.214
Page217
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
9) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Findthestandarderrorofestimate,se,giventhaty
^=1.523x+6.343.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
10) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Findthestandarderrorofestimate,se,giventhaty
^=5.044x+56.11.
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) 6.305 B) 7.913 C) 8.912 D) 9.875
11) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Findthestandarderrorofestimate,se,giventhaty
^=0.449x–30.27.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) 0.935 B) 1.162 C) 1.007 D) 0.815
12) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Findthestandarderrorofestimate,se,giventhaty
^=1.488x+60.46.
Age,x
Pressure,y
38
116
41
120
45
123
48
131
51
142
53
145
57
148
61
150
65
152
A) 4.199 B) 6.981 C) 5.572 D) 3.099
13) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Findthestandarderrorofestimate,se,giventhaty
^=–2.75X+96.14.
Numberofabsences,x
Finalgrade,y
0
98
3
86
6
80
4
82
9
71
2
92
15
55
8
76
5
82
A) 1.799 B) 4.531 C) 3.876 D) 2.160
14) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Findthestandarderrorofestimate,se,giventhaty
^=3.53x+37.92.
Milestraveled,x
Sales,y
2
31
3
33
10
78
7
62
8
65
15
61
3
48
1
55
11
120
A) 22.062 B) 15.951 C) 10.569 D) 5.122
Page218
15) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Findthe
standardofestimate,se,giventhaty
^=6.91x+46.26.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) 4.578 B) 3.412 C) 5.192 D) 6.713
16) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Findthestandarderrorofestimate,se,giventhaty
^=4.379x+4.267.
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) 3.529 B) 4.759 C) 2.813 D) 1.332
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
17) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Findthestandarderrorofestimate,se,giventhat
y
^=–4.310x+296.352.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
2 ConstructandInterpretPredictionIntervals
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Constructa95%predictionintervalforygivenx=2.5,y
^
=2x+4andse=0.
x
y
1
6
2
8
3
10
4
12
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
2) Constructa95%predictionintervalforygivenx=2.5,y
^
=–2.5xandse=0.866.Roundintervaltothree
decimalplaces.
x
y
–1
2
–2
6
–3
7
–4
10
A) –15.566<y<3.066 B) –12.594<y<0.094
C) –16.156<y<3.656 D) –8.244<y< –4.256
Page219
3) Constructa95%predictionintervalforygivenx=–3.5,y
^
=2.097x–0.552andse=0.976.Roundintervalto
twodecimalplaces.
x
y
–5
–10
–3
–8
4
9
1
1
–1
–2
–2
–6
0
–1
2
3
3
6
–4
–8
A) –10.31<y<–5.47 B) –3.19<y< –2.15 C) –4.60<y< –1.99 D) –12.14<y< –6.48
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
4) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Constructa95%predictionintervalfory,thelifespan,givenx=10months,y
^=1.523x+6.343,
andse=5.618.Roundintervaltotwodecimalplaces.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
5) Thedatabelowarethescoresof10randomlyselectedstudentsfromastatisticsclassandthenumberofhours
theystudiedfortheexam.Constructa95%predictionintervalfory,thescoreonthefinalexam,givenx=7
hours,y
^=5.044x+56.11andse=6.305.Roundintervaltotwodecimalplaces.
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) 74.54<y<108.30 B) 55.43<y<78.19 C) 77.21<y<110.45 D) 79.16<y<112.34
6) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Constructa95%predictionintervalfory,thenumberofdaysabsent,givenx=95
degrees,y
^=0.449x–30.27andse=0.934.Roundintervaltothreedecimalplaces.
Temperature,x
Numberofabsences,y
72
3
85
7
91
10
90
10
88
8
98
15
75
4
100
15
80
5
A) 9.957<y<14.813 B) 3.176<y<5.341 C) 4.321<y<6.913 D) 6.345<y<8.912
7) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Construct
a95%predictionintervalforygivenx=2.5,y
^
^
=6.91x+46.26,andse=4.578.Roundintervaltotwodecimal
places.
Numberofyears,x
Gradesontest,y
3
61
4
68
4
75
5
82
3
73
6
90
2
58
7
93
3
72
A) 51.50<y<75.57 B) 60.23<y<91.42 C) 55.12<y<87.34 D) 47.32<y<72.13
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8) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Constructa95%predictionintervalfory,theyield,givenx=11inches,
y
^=4.379x+4.267andse=3.529.Roundintervaltotwodecimalplaces.
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) 43.56<y<61.32 B) 41.68<y<63.21 C) 40.54<y<64.15 D) 39.86<y<65.98
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
9) Thedatabelowaretheaveragemonthlytemperatures,in°F,andthemonthlynaturalgasconsumption,inccf,
forahouseholdinnorthwesternPennsylvania.Constructa90%predictionintervalfory,themonthlygas
consumption,givenx=50°F.Roundintervaltotwodecimalplaces.
Temperature 47 35 21 27 39 48 61 65 70
Consumption 34 169 248 134 137 100 19 34 12
10) Aprivateorganizationconductedasurveyin9regionsofthecountrytodeterminetheaverageweekly
spendingindollarsperpersonontobaccoproductsandalcoholicbeverages.Thedataarelistedbelow.
Region
Alcoholspending,x
Tobaccospending,y
1
$12.80
$8.50
2
$13.20
$7.60
3
$9.50
$6.90
4
$10.30
$6.80
5
$9.80
$6.80
6
$11.70
$5.70
7
$10.00
$6.50
8
$8.90
$4.90
9
$11.60
$7.00
a)Constructascatterplotofthedatalettingxrepresentspendingonalcoholandyrepresentspendingon
tobacco.
b)Findtheregressionline.
c)Findthecoefficientofdetermination.Whatcanyouconclude?
d)Findthestandarderrorofestimate,se.
e)Constructa95%predictionintervalfortheweeklyspendingontobaccowhentheamountspentonalcoholis
$9.50.
9.4 MultipleRegression
1 UseaMultipleRegressionEquationtoPredicty–values
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Amultipleregressionequationisy
^
=–35,000+130x1+20,000x2,wherex1isapersonʹsage,x2isthepersonʹs
gradepointaverageincollege,andyisthepersonʹsincome.Predicttheincomeforapersonwhois26years
oldandhadacollegegradepointaverageof3.8.
A) $44,380 B) $114,380 C) $79,380 D) $485,494
2) AresearcherfoundasignificantrelationshipbetweenastudentʹsIQ,x1
,
gradepointaverage,x2
,
andthescore,
y,ontheverbalsectionoftheSATtest.Therelationshipcanberepresentedbythemultipleregressionequation
y
^=250+1.5x1+80x2.PredicttheSATverbalscoreofastudentwhoseIQis112andgradepointaverageis3.4.
A) 690 B) 440 C) 590 D) 640
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3) Aresearcherfoundasignificantrelationshipbetweenapersonʹsage,x1
,
thenumberofhoursapersonworks
perweek,x2,andthenumberofaccidents,y,thepersonhasperyear.Therelationshipcanberepresentedby
themultipleregressionequationy
^=–3.2+0.012x1+0.23x2.Predictthenumberofaccidentsperyear(tothe
nearestwholenumber)forapersonwhoseageis50andwhoworks38hoursperweek.
A) 6accidents B) 7accidents C) 8 accidents D) 5accidents
2 FindaMultipleRegressionEquation,StandardErrorofEstimate,andCoefficientofDetermination
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Aresearcheratalocallawuniversitywishestoseewhetherastudentʹsgradepointaverageandagearerelated
toastudentʹsscoreonthestatebarexam.Sixstudentsarerandomlyselected.Thedataaregivenbelow.
Student GPA Age Score
1 3.5 23 530
2 2.8 28 550
3 3.9 22 690
4 3.4 27 620
5 2.3 21 430
6 3.3 26 580
a)Findamultipleregressionequationforthedata.
b)Whatisthestandarderrorofestimate?
c)Whatisthecoefficientofdetermination?
d)Interprettheresultsin(c).
e)Predictthestatebarexamscorefora25–year–oldstudentwithagradepointaverageof3.0.
2) Amedicalresearcherwishestoseewhetherthereisarelationshipbetweenapersonʹsage,cholesterollevel,
andsystolicbloodpressure.Eightpeoplearerandomlyselected.Thedataarelistedbelow.
Person Age
Cholesterol
level
Blood
Pressure
138 220 116
2 41 225 120
3 45 200 123
4 48 190 131
5 51 250 142
6 53 215 145
7 57 200 148
8 61 170 150
a)Findamultipleregressionequationforthedata.
b)Whatisthestandarderrorofestimate?
c)Whatisthecoefficientofdetermination?
d)Interprettheresultsin(c).
e)Ifaperson50yearsoldwithacholesterolreadingof220isselected,whatisthatpersonʹspredictedblood
pressurereading?
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3 FindtheAdjustedCoefficientofDetermination
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
1) Aresearcheratalocallawuniversitywishestoseewhetherastudentʹsgradepointaverageandagearerelated
toastudentʹsscoreonthestatebarexam.Sixstudentsarerandomlyselected.Thedataaregivenbelow.
Student GPA Age Score
1 3.5 23 530
2 2.8 28 550
3 3.9 22 690
4 3.4 27 620
5 2.3 21 430
6 3.3 26 580
Calculatetheadjustedcoefficientofdetermination,r2adj.
2) Amedicalresearcherwishestoseewhetherthereisarelationshipbetweenapersonʹsage,cholesterollevel,
andsystolicbloodpressure.Eightpeoplearerandomlyselected.Thedataarelistedbelow.
Person Age
Cholesterol
level
Blood
Pressure
1 38 220 116
2 41 225 120
3 45 200 123
4 48 190 131
5 51 250 142
6 53 215 145
7 57 200 148
8 61 170 150
Calculatetheadjustedcoefficientofdetermination,r2adj.
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Ch.9 CorrelationandRegression
AnswerKey
9.1 Correlation
1 InterpretScatterPlotsandCorrelations
2 IdentifytheExplanatoryandResponseVariables
3 ConstructaScatterPlotandDetermineCorrelation
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4 PerformaHypothesisTestforaPopulationCorrelationCoefficient
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5 CalculatetheCorrelationCoefficientwithInterchangedxandy
6 Concepts
9.2 LinearRegression
1 FindtheEquationofaRegressionLine
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2 FindtheEquationofaRegressionLinewithInterchangedxandy
3 Concepts
9.3 MeasuresofRegressionandPredictionIntervals
1 FindTypesofVariationsandtheCoefficientofDetermination
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2 ConstructandInterpretPredictionIntervals
9.4 MultipleRegression
1 UseaMultipleRegressionEquationtoPredicty–values
2 FindaMultipleRegressionEquation,StandardErrorofEstimate,andCoefficientofDetermination
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3 FindtheAdjustedCoefficientofDetermination
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