1j|jPj aj gje
ThejNaturejofjEconometricsjandjEconomicjData
SOLUTIONjAMANUALjLATESTjEDITIONj2025/2026
C1.1j(i)jThejaveragejofjeducjisjaboutj12.6jyears.jTherejarejtwojpeoplejreportingjzerojyearsjofjeducation
jandj19jpeoplejreportingj18jyearsjofjeducation.
(ii) Thejaveragejofjwagejinjthejsamplejisjaboutj$5.90,jwhichjseemsjlow.
(iii) UsingjTablejB-
60jinjthej2004jEconomicjReportjofjthejPresident,jthejCPIjwasj56.9jinj1976jandj233jinj2013.
(iv) Tojconvertj1976jdollarsjintoj2013jdollars,jwejusejthejratiojofjthejCPIs,jwhichjisj2
33j/j56.9j≈j4.09.jTherefore,jthejaveragejhourlyjwagejinj2013jdollarsjisjroughlyj4.09($5.9
0)j≈j$24.13,jwhichjisjajreasonablejfigure.
(v) Thejsamplejcontainsj252jwomenj(thejnumberjofjobservationsjwithjfemalej=j1)jandj274j
men.
C1.3j(i)jThejlargestjisj100,jthejsmallestjisj0.
(ii) 289joutjofj1,823,jorjaboutj15.85jpercentjofjthejsample.
(iii) 17
(iv) Thejaveragejofjmath4jisjaboutj71.9jandjthejaveragejofjread4jisjaboutj60.1.jSo,jatjleastji
nj2001,jthejreadingjtestjwasjharderjtojpass.
(v) Thejsamplejcorrelationjbetweenjmath4jandjread4jisjaboutj.843,jwhichjisjajveryjhighjd
egreejofj(linear)jassociation.jNotjsurprisingly,jschoolsjthatjhavejhighjpassjratesjonjonejtestjha
vejajstrongjtendencyjtojhavejhighjpassjratesjonjthejotherjtest.
,2j|jPj aj gje
(vi) Thejaveragejofjexpppjisjaboutj$5,194.87.jThejstandardjdeviationjisj$1,091.89,jwhichjs
howsjratherjwidejvariationjinjspendingjperjpupil.j[Thejminimumjisj$1,206.88jandjthejmaximu
mjisj$11,957.64.]
(vii) ThejpercentagejbyjwhichjschooljAjoutspendsjschooljBjis
(vii)jThejpercentagejbyjwhichjschooljAjoutspendsjschooljBjis
(6,000j−j5,500)
100j∙ 5,500 ≈j9.09%.
,3j|jPj aj gje
Whenjwejusejthejapproximationjbasedjonjthejdifferencejinjthejnaturaljlogsjwejgetjajsomewhatjsma
llerjnumber:
100j∙j[log(6,000)j−jlog(5,500)]j≈j 8.71%.
C1.5j(i)jThejsmallestjandjlargestjvaluesjofjchildrenjarej0jandj13,jrespectively.jThejaveragejisjab
outj2.27.
(ii) Outjofj4,358jwomen,jonlyj611jhavejelectricityjinjthejhome,jorjaboutj14.02jpercent.
(iii) Thejaveragejofjchildrenjforjwomenjwithoutjelectricityjisjaboutj2.33,jandjforjthosejwithje
lectricityjitjisjaboutj1.90.jSo,jonjaverage,jwomenjwithjelectricityjhavej.43jfewerjchildrenjthanjth
osejwhojdojnot.
(iv) Wejcannotjinferjcausalityjhere.jTherejarejmanyjconfoundingjfactorsjthatjmayjbejrelated
jtojthejnumberjofjchildrenjandjthejpresencejofjelectricityjinjthejhome;jhouseholdj incomejandjle
veljofjeducationjarejtwojpossibilities.jForjexample,jitjcouldjbejthatjwomenjwithjmorejeducation
jhavejfewerjchildrenjandjarejmorejlikelyjtojhavejelectricityjinjthejhomej(thejlatterjduejtojanjinco
mejeffect).
C1.7j(i)jThejpercentagejofjmenjinjthejsamplejreportjabusingjalcoholjisj9.9.jThejemploymentjrate
jisj24.3.
(ii) Thejemploymentjratejofjmenjwhojabusejalcoholjisj22.6.
(iii) Thejemploymentjratejwhojdojnotjabusejalcoholjisj24.5.
(iv) Thejemploymentjratesjofjmenjwhojabusejalcoholjandjwhojdojnotjarej22.6jandj24.5,jrespect
ively.jThejdifferencejinjthesejemploymentjratesjisjveryjless,jwhichjmeansjthatjalcoholjabusejdo
esjnotjcausejunemployment.
, 4j|jPj aj gje
CHAPTERj2
ThejSimplejRegressionjModel
SOLUTIONSjTOjPROBLEMS
2.1j (i)jIncome,jage,jandjfamilyjbackgroundj(suchjasjnumberjofjsiblings)jarejjustjajfewjpossibilities
.j Itjseemsjthatjeachjofjthesejcouldjbejcorrelatedjwithjyearsjofjeducation.j (Incomejandjeducationj
arejprobablyjpositivelyjcorrelated;jagejandjeducationjmayjbejnegatively
ThejNaturejofjEconometricsjandjEconomicjData
SOLUTIONjAMANUALjLATESTjEDITIONj2025/2026
C1.1j(i)jThejaveragejofjeducjisjaboutj12.6jyears.jTherejarejtwojpeoplejreportingjzerojyearsjofjeducation
jandj19jpeoplejreportingj18jyearsjofjeducation.
(ii) Thejaveragejofjwagejinjthejsamplejisjaboutj$5.90,jwhichjseemsjlow.
(iii) UsingjTablejB-
60jinjthej2004jEconomicjReportjofjthejPresident,jthejCPIjwasj56.9jinj1976jandj233jinj2013.
(iv) Tojconvertj1976jdollarsjintoj2013jdollars,jwejusejthejratiojofjthejCPIs,jwhichjisj2
33j/j56.9j≈j4.09.jTherefore,jthejaveragejhourlyjwagejinj2013jdollarsjisjroughlyj4.09($5.9
0)j≈j$24.13,jwhichjisjajreasonablejfigure.
(v) Thejsamplejcontainsj252jwomenj(thejnumberjofjobservationsjwithjfemalej=j1)jandj274j
men.
C1.3j(i)jThejlargestjisj100,jthejsmallestjisj0.
(ii) 289joutjofj1,823,jorjaboutj15.85jpercentjofjthejsample.
(iii) 17
(iv) Thejaveragejofjmath4jisjaboutj71.9jandjthejaveragejofjread4jisjaboutj60.1.jSo,jatjleastji
nj2001,jthejreadingjtestjwasjharderjtojpass.
(v) Thejsamplejcorrelationjbetweenjmath4jandjread4jisjaboutj.843,jwhichjisjajveryjhighjd
egreejofj(linear)jassociation.jNotjsurprisingly,jschoolsjthatjhavejhighjpassjratesjonjonejtestjha
vejajstrongjtendencyjtojhavejhighjpassjratesjonjthejotherjtest.
,2j|jPj aj gje
(vi) Thejaveragejofjexpppjisjaboutj$5,194.87.jThejstandardjdeviationjisj$1,091.89,jwhichjs
howsjratherjwidejvariationjinjspendingjperjpupil.j[Thejminimumjisj$1,206.88jandjthejmaximu
mjisj$11,957.64.]
(vii) ThejpercentagejbyjwhichjschooljAjoutspendsjschooljBjis
(vii)jThejpercentagejbyjwhichjschooljAjoutspendsjschooljBjis
(6,000j−j5,500)
100j∙ 5,500 ≈j9.09%.
,3j|jPj aj gje
Whenjwejusejthejapproximationjbasedjonjthejdifferencejinjthejnaturaljlogsjwejgetjajsomewhatjsma
llerjnumber:
100j∙j[log(6,000)j−jlog(5,500)]j≈j 8.71%.
C1.5j(i)jThejsmallestjandjlargestjvaluesjofjchildrenjarej0jandj13,jrespectively.jThejaveragejisjab
outj2.27.
(ii) Outjofj4,358jwomen,jonlyj611jhavejelectricityjinjthejhome,jorjaboutj14.02jpercent.
(iii) Thejaveragejofjchildrenjforjwomenjwithoutjelectricityjisjaboutj2.33,jandjforjthosejwithje
lectricityjitjisjaboutj1.90.jSo,jonjaverage,jwomenjwithjelectricityjhavej.43jfewerjchildrenjthanjth
osejwhojdojnot.
(iv) Wejcannotjinferjcausalityjhere.jTherejarejmanyjconfoundingjfactorsjthatjmayjbejrelated
jtojthejnumberjofjchildrenjandjthejpresencejofjelectricityjinjthejhome;jhouseholdj incomejandjle
veljofjeducationjarejtwojpossibilities.jForjexample,jitjcouldjbejthatjwomenjwithjmorejeducation
jhavejfewerjchildrenjandjarejmorejlikelyjtojhavejelectricityjinjthejhomej(thejlatterjduejtojanjinco
mejeffect).
C1.7j(i)jThejpercentagejofjmenjinjthejsamplejreportjabusingjalcoholjisj9.9.jThejemploymentjrate
jisj24.3.
(ii) Thejemploymentjratejofjmenjwhojabusejalcoholjisj22.6.
(iii) Thejemploymentjratejwhojdojnotjabusejalcoholjisj24.5.
(iv) Thejemploymentjratesjofjmenjwhojabusejalcoholjandjwhojdojnotjarej22.6jandj24.5,jrespect
ively.jThejdifferencejinjthesejemploymentjratesjisjveryjless,jwhichjmeansjthatjalcoholjabusejdo
esjnotjcausejunemployment.
, 4j|jPj aj gje
CHAPTERj2
ThejSimplejRegressionjModel
SOLUTIONSjTOjPROBLEMS
2.1j (i)jIncome,jage,jandjfamilyjbackgroundj(suchjasjnumberjofjsiblings)jarejjustjajfewjpossibilities
.j Itjseemsjthatjeachjofjthesejcouldjbejcorrelatedjwithjyearsjofjeducation.j (Incomejandjeducationj
arejprobablyjpositivelyjcorrelated;jagejandjeducationjmayjbejnegatively
