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.
4) Anagriculturalbusinesswantstodetermineiftherainfallininchescanbeusedtopredicttheyieldperacreon
awheatfarm.
5) Acollegecounselorwantstodetermineifthenumberofhoursspentstudyingforatestcanbeusedtopredict
thegradesonatest.
3 ConstructaScatterPlotandDetermineCorrelation
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
6) 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
7) 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
Page179
8) 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
9) 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
10) 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
11) 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
12) 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
13) 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
14) 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
Page180
15) 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.
16) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
–14
–18
–12
–16
–5
1
–8
–7
–10
–10
–11
–14
–9
–9
–7
–5
–6
–2
–13
–16
A) 0.990 B) 0.881 C) 0.819 D) 0.792
17) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
–9
17
–7
12
0
0
–3
5
–5
9
–6
10
–4
7
–2
2
–1
1
–8
14
A) –0.995 B) –0.671 C) –0.778 D) –0.885
18) Calculatethecorrelationcoefficient,r,forthedatabelow.
x
y
1
8
3
–9
10
5
7
–6
5
–5
4
–2
6
2
8
–8
9
3
2
4
A) –0.104 B) –0.132 C) –0.549 D) –0.581
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
19) 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
20) 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.
21) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Calculatethecorrelationcoefficientr.
Hours,x
Scores,y
7
62
9
77
6
57
12
85
6
63
8
75
8
82
9
87
10
87
7
68
A) 0.847 B) 0.991 C) 0.761 D) 0.654
Page181
22) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Calculatethecorrelationcoefficient,r.
Temperature,x
Numberofabsences,y
77
10
90
14
96
17
95
17
93
15
103
22
80
11
105
22
85
12
A) 0.980 B) 0.890 C) 0.881 D) 0.819
23) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Calculatethecorrelationcoefficient,r.
Age,x
Pressure,y
35
121
38
125
42
128
45
136
48
147
50
150
54
153
58
155
62
157
A) 0.960 B) 0.998 C) 0.890 D) 0.908
24) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Calculatethecorrelationcoefficient,r.
Numberofabsences,x
FinalGrade,y
1
97
4
85
7
79
5
81
10
70
3
91
16
54
9
75
6
81
A) –0.991 B) –0.888 C) –0.918 D) –0.899
25) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Calculatethecorrelationcoefficient,r.
Milestraveled,x
Sales,y
4
35
5
37
12
82
9
66
10
69
17
65
5
52
3
59
13
124
A) 0.632 B) 0.561 C) 0.717 D) 0.791
26) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Calculate
thecorrelationcoefficient,r.
Numberofyears,x
Gradesontest,y
4
63
5
70
5
77
6
84
4
75
7
92
3
60
8
95
4
74
A) 0.934 B) 0.911 C) 0.891 D) 0.902
27) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Calculatethecorrelationcoefficient,r.
Rainfall(ininches),x
Yield(bushelsperacre),y
11.5
46.5
9.8
42.2
14.4
54.8
13.5
55
19.8
78.4
11.3
45.2
8
27.9
16.6
72
17
74.8
A) 0.981 B) 0.998 C) 0.900 D) 0.899
28) Givenasamplewithr=0.823,n=10,andα =0.05,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) 4.098 B) 3.816 C) 2.891 D) 1.782
29) Givenasamplewithr=–0.541,n=20,andα =0.01,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) –2.729 B) –5.132 C) –4.671 D) –3.251
Page182
30) Givenasamplewithr=0.321,n=30,andα =0.10,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) 1.793 B) 3.198 C) 2.354 D) 2.561
31) Givenasamplewithr=–0.765,n=22,andα =0.02,determinethestandardizedteststatistictnecessarytotest
theclaimρ=0.Roundanswerstothreedecimalplaces.
A) –5.312 B) –4.392 C) –3.783 D) –2.653
32) Givenasamplewithr=0.823,n=10,andα =0.05,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±2.306 B) ±2.821 C) ±1.833 D) ±1.383
33) Givenasamplewithr=–0.541,n=20,andα =0.01,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±2.878 B) ±1.729 C) ±2.093 D) ±2.540
34) Givenasamplewithr=0.321,n=30,andα =0.10,determinethecriticalvaluest0necessarytotesttheclaim
ρ=0.
A) ±1.701 B) ±1.311 C) ±2.462 D) ±0.683
35) 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.
36) Givenasamplewithr=0.823andn=10,testthesignificanceofthecorrelationrusingα=0.05andtheclaim
ρ=0.
37) Givenasamplewithr=–0.541,n=20,testthesignificanceofthecorrelationrusingα=0.01andtheclaim
ρ=0.
38) Givenasamplewithr=0.321andn=30,testthesignificanceofthecorrelationrusingα=0.10andtheclaim
ρ=0.
39) Givenasamplewithr=–0.765andn=22,testthesignificanceofthecorrelationrusingα=0.02 andtheclaim
ρ=0.
40) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.05andtheclaimρ =0.
x
y
0
–2
2
0
9
17
6
9
4
6
3
2
5
7
7
11
8
14
1
0
41) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.01andtheclaimρ =0.
x
y
5
4
7
–1
14
–13
11
–8
9
–4
8
–3
10
–6
12
–11
13
–12
6
1
42) Forthedatabelow,testthesignificanceofthecorrelationcoefficientusingα =0.10andtheclaimρ =0.
x
y
–11
17
–9
0
–2
14
–5
3
–7
4
–8
7
–6
11
–4
1
–3
12
–10
13
Page183
43) 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
44) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Testthesignificanceofthecorrelationcoefficientusingα
=0.05andtheclaimρ=0.
Hours,x
Scores,y
8
69
10
84
7
64
13
92
7
70
9
82
9
89
10
94
11
94
8
75
45) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Testthesignificanceofthecorrelationcoefficientusingα=0.02,andtheclaimρ=0.
Temperature,x
Numberofabsences,y
71
6
84
10
90
13
89
13
87
11
97
18
74
7
99
18
79
8
46) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Testthesignificanceofthecorrelationcoefficientusingα=0.05andtheclaimρ=0.
Age,x
Pressure,y
40
118
43
122
47
125
50
133
53
144
55
147
59
150
63
152
67
154
47) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Testthesignificanceofthecorrelationcoefficientusingα=0.05andtheclaimρ=0.
Numberofabsences,x
FinalGrade,y
2
90
5
78
8
72
6
74
11
63
4
84
17
47
10
68
7
74
48) Amanagerwishestodeterminetherelationshipbetweenthenumberofmiles(inhundredsofmiles)the
managerʹssalesrepresentativestravelpermonthandtheamountofsales(inthousandsofdollars)permonth.
Testthesignificanceofthecorrelationcoefficientusingα=0.01andtheclaimρ=0.
Milestraveled,x
Sales,y
4
35
5
37
12
82
9
66
10
69
17
65
5
52
3
59
13
124
49) Inorderforapplicantstoworkfortheforeign–servicedepartment,theymusttakeatestinthelanguageofthe
countrywheretheyplantowork.Thedatabelowshowstherelationshipbetweenthenumberofyearsthat
applicantshavestudiedaparticularlanguageandthegradestheyreceivedontheproficiencyexam.Testthe
significanceofthecorrelationcoefficientusingα=0.10andtheclaimρ=0.
Numberofyears,x
Gradesontest,y
5
54
6
61
6
68
7
75
5
66
8
83
4
51
9
86
5
65
50) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Testthesignificanceofthecorrelationcoefficientusingα=0.01andtheclaimρ=0.
Rainfall(ininches),x
Yield(bushelsperacre),y
9.9
54.5
8.2
50.2
12.8
62.8
11.9
63
18.2
86.4
9.7
53.2
6.4
35.9
15
80
15.4
82.8
Page184
51) 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.
52) Calculatethecoefficientofcorrelation,r,lettingRow1representthex–valuesandRow2representthe
y–values.Nowcalculatethecoefficientofcorrelation,r,lettingRow2representthex–valuesandRow1
representthey–values.Whateffectdoesswitchingtheexplanatoryandresponsevariableshaveonthe
correlationcoefficient?
Row1
Row2
–7
–3
–5
15
2
16
–1
8
–3
5
–4
1
–2
6
0
10
1
13
–6
15
6 Concepts
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
53) Explainthedifferencebetweenx2
∑andx
∑2.
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
54) IfDataAhasacorrelationcoefficientofr= –0.991,andDataBhasacorrelationcoefficientofr=0.991,which
correlationiscorrect?
A) DataAandDataBhavethesamestrengthinlinearcorrelation.
B) DataAhasastrongerlinearcorrelationthanDataB.
C) DataAhasaweakerlinearcorrelationthanDataB.
55) Whichofthefollowingvaluescouldnotrepresentacorrelationcoefficient?
A) 1.032 B) 0 C) 0.927 D) –1
9.2 LinearRegression
1 FindtheEquationofaRegressionLine
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) 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
Page185
2) 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
3) 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.
4) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Findtheequationoftheregressionlineforthegivendata.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
5) 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
6) 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
Page186
7) 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
8) 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
9) 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
10) 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
11) 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
Page187
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
12) 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
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
13) Giventheequationofaregressionlineisy
^
=2x–5,whatisthebestpredictedvalueforygivenx=10?
Assumethatthevariablesxandyhaveasignificantcorrelation.
A) 15 B) 25 C) 48 D) 7
14) Giventheequationofaregressionlineisy
^
=–5.5x–9.4,whatisthebestpredictedvalueforygivenx=–2.8?
Assumethatthevariablesxandyhaveasignificantcorrelation.
A) 6.00 B) 24.80 C) –24.80 D) –6.00
15) Giventheequationofaregressionlineisy
^
=3.5x–5.4,whatisthebestpredictedvalueforygivenx=–1.2?
Assumethatthevariablesxandyhaveasignificantcorrelation.
A) –9.6 B) 12.3 C) –6.9 D) –12.3
16) Usetheregressionequationtopredictthevalueofyforx=2.2.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) 4.061 B) 5.165 C) 0.883 D) 3.311
17) Usetheregressionequationtopredictthevalueofyforx= –1.5.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) 3.586 B) –2.069 C) –3.022 D) 0.748
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
18) Thedatabelowarethegestationperiods,inmonths,ofrandomlyselectedanimalsandtheircorrespondinglife
spans,inyears.Usetheregressionequationtopredictthelifespan,y,foragestationperiodof6months,x.
Assumethevariablesxandyhaveasignificantcorrelation.
Gestation,x 8 2.1 1.3 1 11.5 5.3 3.8 24.3
Lifespan,y 30126 325 121040
Page188
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
19) Thedatabelowarethefinalexamscoresof10randomlyselectedstatisticsstudentsandthenumberofhours
theystudiedfortheexam.Whatisthebestpredictedvalueforygivenx=2?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) 66 B) 65 C) 64 D) 67
20) Thedatabelowarethetemperaturesonrandomlychosendaysduringasummerclassandthenumberof
absencesonthosedays.Whatisthebestpredictedvalueforygivenx=91?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) 11 B) 12 C) 13 D) 14
21) Thedatabelowaretheagesandsystolicbloodpressures(measuredinmillimetersofmercury)of9randomly
selectedadults.Whatisthebestpredictedvalueforygivenx=64?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) 156 B) 158 C) 154 D) 152
22) Thedatabelowarethenumberofabsencesandthefinalgradesof9randomlyselectedstudentsfroma
statisticsclass.Whatisthebestpredictedvalueforygivenx=11?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) 66 B) 67 C) 68 D) 65
23) 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
Page189
24) InanareaoftheMidwest,recordswerekeptontherelationshipbetweentherainfall(ininches)andtheyield
ofwheat(bushelsperacre).Whichisthebestpredictedvalueforygivenx=7.1?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) 35.4 B) 35.7 C) 35.2 D) 35.9
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
25) 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
26) 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.
27) 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.
28) Giventheequationofaregressionlineisy
^
=–1.04x+50.3,determinewhetherthereisapositivelinear
correlationoranegativelinearcorrelation.
A) negativelinearcorrelation B) positivelinearcorrelation
Page190
29) Giventheequationofaregressionlineisy
^
=0.00014x+2.53,determinewhetherthereisapositivelinear
correlationoranegativelinearcorrelation.
A) positivelinearcorrelation B) negativelinearcorrelation
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
Page191
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
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
Page192
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
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.
18) Constructa95%predictionintervalforygivenx=2.5,y
^
=2x+4andse=0.
x
y
1
6
2
8
3
10
4
12
Page193
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
19) 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
20) 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.
21) 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.
22) 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
23) 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
Page194
24) 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
25) 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.
26) 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
27) 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.
Page195
9.4 MultipleRegression
1 UseaMultipleRegressionEquationtoPredicty–values
MULTIPLECHOICE.Choosetheonealternativethatbestcompletesthestatementoranswersthequestion.
Provideanappropriateresponse.
1) Amultipleregressionequationisy
^
=–35,000+130x1+20,000x2,wherex1isapersonʹsage,x2isthepersonʹs
gradepointaverageincollege,andyisthepersonʹsincome.Predicttheincomeforapersonwhois34years
oldandhadacollegegradepointaverageof2.5.
A) $19,420 B) $89,420 C) $54,420 D) $645,325
2) AresearcherfoundasignificantrelationshipbetweenastudentʹsIQ,x1
,
gradepointaverage,x2
,
andthescore,
y,ontheverbalsectionoftheSATtest.Therelationshipcanberepresentedbythemultipleregressionequation
y
^=250+1.5x1+80x2.PredicttheSATverbalscoreofastudentwhoseIQis129andgradepointaverageis3.8.
A) 748 B) 498 C) 648 D) 698
3) Aresearcherfoundasignificantrelationshipbetweenapersonʹsage,x1
,
thenumberofhoursapersonworks
perweek,x2,andthenumberofaccidents,y,thepersonhasperyear.Therelationshipcanberepresentedby
themultipleregressionequationy
^=–3.2+0.012x1+0.23x2.Predictthenumberofaccidentsperyear(tothe
nearestwholenumber)forapersonwhoseageis47andwhoworks46hoursperweek.
A) 8accidents B) 9accidents C) 10 accidents D) 7accidents
2 FindaMultipleRegressionEquation,StandardErrorofEstimate,andCoefficientofDetermination
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
4) 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.
Page196
5) 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
a)Findamultipleregressionequationforthedata.
b)Whatisthestandarderrorofestimate?
c)Whatisthecoefficientofdetermination?
d)Interprettheresultsin(c).
e)Ifaperson50yearsoldwithacholesterolreadingof220isselected,whatisthatpersonʹspredictedblood
pressurereading?
3 FindtheAdjustedCoefficientofDetermination
SHORTANSWER.Writethewordorphrasethatbestcompleteseachstatementoranswersthequestion.
Provideanappropriateresponse.
6) 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.
7) 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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