Handout 7.docx
- 文档编号:14409596
- 上传时间:2023-06-23
- 格式:DOCX
- 页数:11
- 大小:72.29KB
Handout 7.docx
《Handout 7.docx》由会员分享,可在线阅读,更多相关《Handout 7.docx(11页珍藏版)》请在冰点文库上搜索。
Handout7
DepartmentofEconomics
NationalUniversityofIreland,Cork
BAIII
EC3121QuantitativeMethods:
Econometrics
Handout#7
AcademicYear:
2010/11Date:
16/11/2010
Lecturer:
RuthButlerTelephone:
(021)4901927E-mail:
ro.butler@ucc.ie
PART1:
REGRESSIONANALYSIS
3.HypothesisTesting
QUESTION1
WhatwouldbethetcriticalvaluesforthefollowingtestswithN=25,
Degreesoffreedom=24
A.Onesidedtestat5%levelofsignificance
B.Twosidedtestat10%levelofsignificance
C.Twosidedtestat1%levelofsignificance
QUESTION2
Createnullandalternativehypothesesforthefollowingcoefficients:
A.Theimpactofheightonweight
B.Theeffectofageonhealthstatus
C.TheeffectofGNPonroadfatalities
QUESTION3
Ŷi=520.4–5.82Xi
(20.4)(2.21)
n=100R2=0.08
Yi=AverageTestScores
Xi=ClassSize
(standarderrorsinbrackets)
A.Constructa95%confidenceintervalforβ1.
B.Testthesignificanceoftheslopecoefficientatthe5%levelofsignificance.Approximatethep-valueforthistest.
C.Testthenullhypothesisthatβ1=-5.6atthe5%levelofsignificance.Comparethisanswerwithyouranswerforpart(A).Whatcanyouinferfromyourcomparison?
QUESTION4
(0.3001)(0.0728)
n=240R2=0.471
(standarderrorsinbrackets)
rit=therateofreturnontheithsecurityintimet
rmt=therateofreturnonthemarketportfoliointimet.
Asecurity,whosebetacoefficient(ieβ1)isgreaterthanoneissaidtobeavolatileoraggressivesecurity.WasIBMavolatilesecurityinthetimeperiodunderstudy?
QUESTION5
Considerthefollowinghypotheticalequationforasampleofdivorcedmenwhofailedtomakeatleastonechildsupportpaymentinthelastfouryears(standarderrorsinparentheses).
(0.1)(20)
(1)(3)(0.05)
Where:
Pi=thenumberofmonthlychildsupportpaymentsthattheithmanmissedinthelastfouryears
Mi=thenumberofmonthstheithmanwasunemployedinthelastfouryears
Yi=thepercentageofdisposableincomethatgoestochildsupportpaymentsfortheithman
Ai=theageinyearsoftheithman
Bi=thereligiousbeliefsoftheithman(ascaleof1to4,with4beingthemostreligious)
Ci=thenumberofchildrentheithmanhasfathered
A.YourfriendexpectsthecoefficientsofMandYtobepositive.Testthesehypotheses.(Usethe5%levelatN=20)
B.TestthehypothesesthatthecoefficientofAisdifferentfromzero.(Usethe1%levelatN=25)
C.DevelopthetesthypothesesforthecoefficientsofBandC.(Usethe10%levelandN=17)
Answers
QUESTION1
WhatwouldbethetcriticalvaluesforthefollowingtestswithN=25andK=4?
A.Onesidedtestat5%levelofsignificance
DegreesofFreedom=21
@5%α=0.05for1tailedtest
t-crit=1.721
DegreesofFreedom=24
@5%α=0.05for1-tailedtest
t-crit=1.711
B.Twosidedtestat10%levelofsignificance
DegreesofFreedom=21
@10%α=0.1
tcrit=1.721
DegreesofFreedom=24
@10%α=0.1
t-crit=1.711
C.Twosidedtestat1%levelofsignificance
D.F=21
@1%α=0.01
tcrit=2.831
D.F=24
@1%α=0.01
t-crit=2.797
QUESTION2
Createnullandalternativehypothesesforthefollowingcoefficients:
A.Theimpactofheightonweight
(1-TailedTest)
B.TheeffectofAgeonHealthStatus
(1-TailedTest)
C.TheeffectofGNPonRoadFatalities
(2-TailedTest)
QUESTION3
A.Constructa95%confidenceintervalforβ1.
ConfidenceInterval=
±tcrit*
Criticalvalue:
1)Twosidedtestforconfidenceinterval
2)Levelofsignificance:
95%confidenceinterval→α=0.05
3)Degreesoffreedom:
n–k=100–2=98
Therefore,t-criticalvalueis1.984(approx)
95%ConfidenceInterval=–5.82±1.984*2.21
=–5.82±4.38464
Thereforetheconfidenceintervalis:
–10.2046≤β1≤–1.43536
Thisinterpretedasmeaningthetruepopulationcoefficientwouldlieintheaboveintervalsin95outof100repeatedsamples.
B.Testthesignificanceoftheslopecoefficientatthe5%levelofsignificance.Approximatethep-valueforthistest.
H0:
Ha:
t-statistic=
=
=-2.63348=|-2.63348|
Criticalvalue:
1)Twotailedtest
2)Levelofsignificance:
5%→α=0.05
3)Degreesoffreedom:
n-k=100–2=98
Therefore,thet-criticalvalueis1.984(approx)
Asthet-statisticexceedsthet-criticalvalue,wecanrejectthenullhypothesisatthe5%levelofsignificanceandconcludethat
isstatisticallydifferentfromzero,thereforetheestimateoftheslopecoefficientissignificant.
Astheestimatefortheslopecoefficientissignificant,theapproximatep-valueforthistestwouldbealittleunder0.01.
C.Testthenullhypothesisthatβ1=-5.6atthe5%levelofsignificance.Comparethisanswerwithyouranswerforpart(A).Whatcanyouinferfromyourcomparison?
H0:
Ha:
t-statistic=
=
=-0.09955=|-0.09955|
Criticalvalue:
1)Twotailedtest
2)Levelofsignificance:
5%→α=0.05
3)Degreesoffreedom:
n-k=100–2=98
Therefore,thet-criticalvalueis1.984(approx)
Asthet-statisticdoesNOTexceedthet-criticalvalue,wecannotrejectthenullhypothesisatthe5%levelofsignificanceandtherebyconcludethat
isnotstatisticallydifferentfrom–5.6.Wewouldexpectthisanswersince–5.6liesintheconfidenceintervalcalculatedinpartA.
QUESTION4
(0.3001)(0.0728)
n=240R2=0.471
(standarderrorsinbrackets)
rit=therateofreturnontheithsecurityintimet
rmt=therateofreturnonthemarketportfoliointimet.
Asecurity,whosebetacoefficient(i.e.β1)isgreaterthanoneissaidtobeavolatileoraggressivesecurity.WasIBMavolatilesecurityinthetimeperiodunderstudy?
H0:
Ha:
t-statistic=
=
=0.821
Criticalvalue:
1)One-tailedtest
2)Levelsofsignificance:
1%,5%10%→α=0.01,0.05,0.1
3)Degreesoffreedom:
n-k=240–2=238
Therefore,thet-criticalvaluesare2.364,1.660,and1.290(approx)
Asthet-statisticdoesnotexceedthet-criticalvaluewecannotrejectthenullhypothesisatanyofthelevelsofsignificance.WecantherebyconcludethatIBMwasnotavolatilesecurityoverthesampleperiod,astheassociatedbetawasnotgreaterthan1.
QUESTION5
Considerthefollowinghypotheticalequationforasampleofdivorcedmenwhofailedtomakeatleastonechildsupportpaymentinthelastfouryears(standarderrorsinparentheses)
(0.1)(20)
(1)(3)(0.05)
Where:
Pi=thenumberofmonthlychildsupportpaymentsthattheithmanmissedinthelastfouryears
Mi=thenumberofmonthstheithmanwasunemployedinthelastfouryears
Yi=thepercentageofdisposableincomethatgoestochildsupportpaymentsfortheithman
Ai=theageinyearsoftheithman
Bi=thereligiousbeliefsoftheithman(ascaleof1to4,with4beingthemostreligious)
Ci=thenumberofchildrentheithmanhasfathered
A.YourfriendexpectsthecoefficientsofMandYtobepositive.Testthesehypotheses.(Usethe5%levelatN=20)
itisa1tailedtest
DecisionRule:
Ifthetstatisticisgreaterthanthecriticalvalue,youcanrejectthenullhypothesis.
Findtstat:
=
=5
Findtcrit:
@5%alpha=0.05andd.f=n-k=20-6=14
Sincetheabsolutevalueofthetstatisticdoesexceedthecriticalvalueoft=1.761atthe5%level(one-tailedtest)andn-k=20-6=14df,weconcludethatβmisstatisticallygreaterthanzeroatthe5%levelandissignificant.(i.ewerejectthenullhypothesisthatβm=0)
itisa1tailedtest
DecisionRule:
Ifthetstatisticisgreaterthanthecriticalvalue,youcanrejectthenullhypothesis.
Findtstat:
=
=1.25
Findtcrit:
@5%alpha=0.05andd.f=n-k=20-6=14
Sincetheabsolutevalueofthetstatisticdoesnotexceedthecriticalvalueoft=1.761atthe5%level(one-tailedtest)andn-k=20-6=14df,wecannotrejectthenullhypothesisandconcludethatbyisnotstatisticallygreaterthanzeroatthe5%levelandisinsignificant.
B.TestthehypothesesthatthecoefficientofAisdifferentfromzero.(Usethe1%levelatN=25)
itisa2tailedtest
DecisionRule:
Ifthetstatisticisgreaterthanthecriticalvalue,youcanrejectthenullhypothesis.
Findtstat:
=
=.8
Findtcrit:
@1%alpha=0.01andd.f=n-k=25-6=19
Sincetheabsolutevalueofthetstatisticdoesnotexceedthecriticalvalueoft=2.861atthe1%level(two-tailedtest)andn-k=25-6=19df,wecannotrejectthenullhypothesisandconcludethatbAisnotstatisticallydifferentfromzeroatthe1%levelandisinsignificant.
C.
DevelopthetesthypothesesforthecoefficientsofBandC.(Usethe10%levelandN=17)
H0:
Ha:
itisa1tailedtest
DecisionRule:
Ifthetstatisticisgreaterthanthecriticalvalue,youcanrejectthenullhypothesis.
Findtstat:
=
=1
Findtcrit:
@10%alpha=0.1andd.f=n-k=17-6=11
Sincetheabsolutevalueofthetstatisticdoesnotexceedthecriticalvalueoft=1.363atthe10%level(one-tailedtest)andn-k=17-6=11df,wecannotrejectthenullhypothesisandconcludethatbbisnotstatisticallygreaterthanzeroatthe10%levelandisinsignificant.
itisa1tailedtest
DecisionRule:
Ifthetstatisticisgreaterthanthecriticalvalue,youcanrejectthenullhypothesis.
Findtstat:
=
=-3
Findtcrit:
@10%alpha=0.1andd.f=n-k=17-6=11
Eventhough|-3|isgreaterthanthet-criticalvalueof1.363,wecannotrejectthenullhypothesisasthet-statisticisnotpositiveasstatedinthealternativehypothesis.Therefore,wecannotrejectthenullhypothesisatthe5%levelofsignificanceandconcludethattheslopeco
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- Handout