1
V|VPV aV gVe
TheVNatureVofVEconometricsVandVEconomicVData
SOLUTIONVAMANUALVLATESTVEDITIONV2025/20
26
C1.1V(i)VTheVaverageVofVeducVisVaboutV12.6Vyears.VThereVareVtwoVpeopleVreportingVzeroVy
earsVofVeducationVandV19VpeopleVreportingV18VyearsVofVeducation.
(ii) TheVaverageVofVwageVinVtheVsampleVisVaboutV$5.90,VwhichVseemsVlow.
(iii) UsingVTableVB-
60VinVtheV2004VEconomicVReportVofVtheVPresident,VtheVCPIVwasV56.9VinV1976Vand
V233VinV2013.
(iv) ToVconvertV1976VdollarsVintoV2013Vdollars,VweVuseVtheVratioVofVtheVC
PIs,VwhichVisV233V/V56.9V≈V4.09.VTherefore,VtheVaverageVhourlyVwageVinV201
3VdollarsVisVroughlyV4.09($5.90)V≈V$24.13,VwhichVisVaVreasonableVfigure.
(v) TheVsampleVcontainsV252VwomenV(theVnumberVofVobservationsVwithVfemaleV=
V1)VandV274Vmen.
C1.3V(i)VTheVlargestVisV100,VtheVsmallestVisV0.
(ii) 289VoutVofV1,823,VorVaboutV15.85VpercentVofVtheVsample.
(iii) 17
(iv) TheVaverageVofVmath4VisVaboutV71.9VandVtheVaverageVofVread4VisVaboutV60.
1.VSo,VatVleastVinV2001,VtheVreadingVtestVwasVharderVtoVpass.
(v) TheVsampleVcorrelationVbetweenVmath4VandVread4VisVaboutV.843,VwhichVisVa
VveryVhighVdegreeVofV(linear)Vassociation.VNotVsurprisingly,VschoolsVthatVhaveVhigh
VpassVratesVonVoneVtestVhaveVaVstrongVtendencyVtoVhaveVhighVpassVratesVonVtheV
otherVtest.
,2
V|VPV aV gVe
(vi) TheVaverageVofVexpppVisVaboutV$5,194.87.VTheVstandardVdeviationVisV$1,091
.89,VwhichVshowsVratherVwideVvariationVinVspendingVperVpupil.V[TheVminimumVisV$
1,206.88VandVtheVmaximumVisV$11,957.64.]
(vii) TheVpercentageVbyVwhichVschoolVAVoutspendsVschoolVBVis
(vii)VTheVpercentageVbyVwhichVschoolVAVoutspendsVschoolVBVis
(6,000V−V5,500)
100V∙ 5,500 ≈V9.09%.
,3
V|VPV aV gVe
WhenVweVuseVtheVapproximationVbasedVonVtheVdifferenceVinVtheVnaturalVlogsVweVgetV
aVsomewhatVsmallerVnumber:
100V∙V[log(6,000)V−Vlog(5,500)]V≈V 8.71%.
C1.5V(i)VTheVsmallestVandVlargestVvaluesVofVchildrenVareV0VandV13,Vrespectively.VTh
eVaverageVisVaboutV2.27.
(ii) OutVofV4,358Vwomen,VonlyV611VhaveVelectricityVinVtheVhome,VorVaboutV14.02Vpercent.
(iii) TheVaverageVofVchildrenVforVwomenVwithoutVelectricityVisVaboutV2.33,VandVfo
rVthoseVwithVelectricityVitVisVaboutV1.90.VSo,VonVaverage,VwomenVwithVelectricityVha
veV.43VfewerVchildrenVthanVthoseVwhoVdoVnot.
(iv) WeVcannotVinferVcausalityVhere.VThereVareVmanyVconfoundingVfactorsVthatVm
ayVbeVrelatedVtoVtheVnumberVofVchildrenVandVtheVpresenceVofVelectricityVinVtheVho
me;VhouseholdV incomeVandVlevelVofVeducationVareVtwoVpossibilities.VForVexample,Vit
VcouldVbeVthatVwomenVwithVmoreVeducationVhaveVfewerVchildrenVandVareVmoreVlike
lyVtoVhaveVelectricityVinVtheVhomeV(theVlatterVdueVtoVanVincomeVeffect).
C1.7V(i)VTheVpercentageVofVmenVinVtheVsampleVreportVabusingValcoholVisV9.9.VTheVe
mploymentVrateVisV24.3.
(ii) TheVemploymentVrateVofVmenVwhoVabuseValcoholVisV22.6.
(iii) TheVemploymentVrateVwhoVdoVnotVabuseValcoholVisV24.5.
(iv) TheVemploymentVratesVofVmenVwhoVabuseValcoholVandVwhoVdoVnotVareV22.6Va
ndV24.5,Vrespectively.VTheVdifferenceVinVtheseVemploymentVratesVisVveryVless,Vwhich
VmeansVthatValcoholVabuseVdoesVnotVcauseVunemployment.
, 4
V|VPV aV gVe
CHAPTERV2
TheVSimpleVRegressionVModel
SOLUTIONSVTOVPROBLEMS
2.1V (i)VIncome,Vage,VandVfamilyVbackgroundV(suchVasVnumberVofVsiblings)VareVjustVaVfew
Vpossibilities.V ItVseemsVthatVeachVofVtheseVcouldVbeVcorrelatedVwithVyearsVofVeducation.
V (IncomeVandVeducationVareVprobablyVpositivelyVcorrelated;VageVandVeducationVmayVbeV
negatively
V|VPV aV gVe
TheVNatureVofVEconometricsVandVEconomicVData
SOLUTIONVAMANUALVLATESTVEDITIONV2025/20
26
C1.1V(i)VTheVaverageVofVeducVisVaboutV12.6Vyears.VThereVareVtwoVpeopleVreportingVzeroVy
earsVofVeducationVandV19VpeopleVreportingV18VyearsVofVeducation.
(ii) TheVaverageVofVwageVinVtheVsampleVisVaboutV$5.90,VwhichVseemsVlow.
(iii) UsingVTableVB-
60VinVtheV2004VEconomicVReportVofVtheVPresident,VtheVCPIVwasV56.9VinV1976Vand
V233VinV2013.
(iv) ToVconvertV1976VdollarsVintoV2013Vdollars,VweVuseVtheVratioVofVtheVC
PIs,VwhichVisV233V/V56.9V≈V4.09.VTherefore,VtheVaverageVhourlyVwageVinV201
3VdollarsVisVroughlyV4.09($5.90)V≈V$24.13,VwhichVisVaVreasonableVfigure.
(v) TheVsampleVcontainsV252VwomenV(theVnumberVofVobservationsVwithVfemaleV=
V1)VandV274Vmen.
C1.3V(i)VTheVlargestVisV100,VtheVsmallestVisV0.
(ii) 289VoutVofV1,823,VorVaboutV15.85VpercentVofVtheVsample.
(iii) 17
(iv) TheVaverageVofVmath4VisVaboutV71.9VandVtheVaverageVofVread4VisVaboutV60.
1.VSo,VatVleastVinV2001,VtheVreadingVtestVwasVharderVtoVpass.
(v) TheVsampleVcorrelationVbetweenVmath4VandVread4VisVaboutV.843,VwhichVisVa
VveryVhighVdegreeVofV(linear)Vassociation.VNotVsurprisingly,VschoolsVthatVhaveVhigh
VpassVratesVonVoneVtestVhaveVaVstrongVtendencyVtoVhaveVhighVpassVratesVonVtheV
otherVtest.
,2
V|VPV aV gVe
(vi) TheVaverageVofVexpppVisVaboutV$5,194.87.VTheVstandardVdeviationVisV$1,091
.89,VwhichVshowsVratherVwideVvariationVinVspendingVperVpupil.V[TheVminimumVisV$
1,206.88VandVtheVmaximumVisV$11,957.64.]
(vii) TheVpercentageVbyVwhichVschoolVAVoutspendsVschoolVBVis
(vii)VTheVpercentageVbyVwhichVschoolVAVoutspendsVschoolVBVis
(6,000V−V5,500)
100V∙ 5,500 ≈V9.09%.
,3
V|VPV aV gVe
WhenVweVuseVtheVapproximationVbasedVonVtheVdifferenceVinVtheVnaturalVlogsVweVgetV
aVsomewhatVsmallerVnumber:
100V∙V[log(6,000)V−Vlog(5,500)]V≈V 8.71%.
C1.5V(i)VTheVsmallestVandVlargestVvaluesVofVchildrenVareV0VandV13,Vrespectively.VTh
eVaverageVisVaboutV2.27.
(ii) OutVofV4,358Vwomen,VonlyV611VhaveVelectricityVinVtheVhome,VorVaboutV14.02Vpercent.
(iii) TheVaverageVofVchildrenVforVwomenVwithoutVelectricityVisVaboutV2.33,VandVfo
rVthoseVwithVelectricityVitVisVaboutV1.90.VSo,VonVaverage,VwomenVwithVelectricityVha
veV.43VfewerVchildrenVthanVthoseVwhoVdoVnot.
(iv) WeVcannotVinferVcausalityVhere.VThereVareVmanyVconfoundingVfactorsVthatVm
ayVbeVrelatedVtoVtheVnumberVofVchildrenVandVtheVpresenceVofVelectricityVinVtheVho
me;VhouseholdV incomeVandVlevelVofVeducationVareVtwoVpossibilities.VForVexample,Vit
VcouldVbeVthatVwomenVwithVmoreVeducationVhaveVfewerVchildrenVandVareVmoreVlike
lyVtoVhaveVelectricityVinVtheVhomeV(theVlatterVdueVtoVanVincomeVeffect).
C1.7V(i)VTheVpercentageVofVmenVinVtheVsampleVreportVabusingValcoholVisV9.9.VTheVe
mploymentVrateVisV24.3.
(ii) TheVemploymentVrateVofVmenVwhoVabuseValcoholVisV22.6.
(iii) TheVemploymentVrateVwhoVdoVnotVabuseValcoholVisV24.5.
(iv) TheVemploymentVratesVofVmenVwhoVabuseValcoholVandVwhoVdoVnotVareV22.6Va
ndV24.5,Vrespectively.VTheVdifferenceVinVtheseVemploymentVratesVisVveryVless,Vwhich
VmeansVthatValcoholVabuseVdoesVnotVcauseVunemployment.
, 4
V|VPV aV gVe
CHAPTERV2
TheVSimpleVRegressionVModel
SOLUTIONSVTOVPROBLEMS
2.1V (i)VIncome,Vage,VandVfamilyVbackgroundV(suchVasVnumberVofVsiblings)VareVjustVaVfew
Vpossibilities.V ItVseemsVthatVeachVofVtheseVcouldVbeVcorrelatedVwithVyearsVofVeducation.
V (IncomeVandVeducationVareVprobablyVpositivelyVcorrelated;VageVandVeducationVmayVbeV
negatively
