1g|gPgaggge
ThegNaturegofgEconometricsgandgEconomicgData
SOLUTIONgAMANUALgLATESTgEDITIONg2025/202
6
C1.1g(i)gThegaveragegofgeducgisgaboutg12.6gyears.gTheregaregtwogpeoplegreportinggzerogyearsgofged
ucationgandg19gpeoplegreportingg18gyearsgofgeducation.
(ii) Thegaveragegofgwagegingthegsamplegisgaboutg$5.90,gwhichgseemsglow.
(iii) UsinggTablegB-
60gingtheg2004gEconomicgReportgofgthegPresident,gthegCPIgwasg56.9ging1976gandg233ging
2013.
(iv) Togconvertg1976gdollarsgintog2013gdollars,gwegusegthegratiogofgthegCPIs,gwhi
chgisg233g/g56.9g≈g4.09.gTherefore,gthegaverageghourlygwageging2013gdollarsgisgroug
hlyg4.09($5.90)g≈g$24.13,gwhichgisgagreasonablegfigure.
(v) Thegsamplegcontainsg252gwomeng(thegnumbergofgobservationsgwithgfemaleg=g1)gand
g274gmen.
C1.3g(i)gTheglargestgisg100,gthegsmallestgisg0.
(ii) 289goutgofg1,823,gorgaboutg15.85gpercentgofgthegsample.
(iii) 17
(iv) Thegaveragegofgmath4gisgaboutg71.9gandgthegaveragegofgread4gisgaboutg60.1.gSo,gat
gleastging2001,gthegreadinggtestgwasghardergtogpass.
(v) Thegsamplegcorrelationgbetweengmath4gandgread4gisgaboutg.843,gwhichgisgagveryg
highgdegreegofg(linear)gassociation.gNotgsurprisingly,gschoolsgthatghaveghighgpassgratesgon
gonegtestghavegagstronggtendencygtoghaveghighgpassgratesgongthegothergtest.
,2g|gPgaggge
(vi) Thegaveragegofgexpppgisgaboutg$5,194.87.gThegstandardgdeviationgisg$1,091.89,gw
hichgshowsgrathergwidegvariationgingspendinggpergpupil.g[Thegminimumgisg$1,206.88gandg
thegmaximumgisg$11,957.64.]
(vii) ThegpercentagegbygwhichgschoolgAgoutspendsgschoolgBgis
(vii)gThegpercentagegbygwhichgschoolgAgoutspendsgschoolgBgis
(6,000g−g5,500)
100g∙ 5,500 ≈g9.09%.
,3g|gPgaggge
Whengwegusegthegapproximationgbasedgongthegdifferencegingthegnaturalglogsgweggetgagsomewh
atgsmallergnumber:
100g∙g[log(6,000)g−glog(5,500)]g≈g 8.71%.
C1.5g(i)gThegsmallestgandglargestgvaluesgofgchildrengareg0gandg13,grespectively.gThegaverag
egisgaboutg2.27.
(ii) Outgofg4,358gwomen,gonlyg611ghavegelectricitygingtheghome,gorgaboutg14.02gpercent.
(iii) Thegaveragegofgchildrengforgwomengwithoutgelectricitygisgaboutg2.33,gandgforgthoseg
withgelectricitygitgisgaboutg1.90.gSo,gongaverage,gwomengwithgelectricityghaveg.43gfewergchi
ldrengthangthosegwhogdognot.
(iv) Wegcannotginfergcausalityghere.gTheregaregmanygconfoundinggfactorsgthatgmaygbegr
elatedgtogthegnumbergofgchildrengandgthegpresencegofgelectricitygingtheghome;ghouseholdg in
comegandglevelgofgeducationgaregtwogpossibilities.gForgexample,gitgcouldgbegthatgwomengwi
thgmoregeducationghavegfewergchildrengandgaregmoreglikelygtoghavegelectricitygingtheghome
g(theglattergduegtogangincomegeffect).
C1.7g(i)gThegpercentagegofgmengingthegsamplegreportgabusinggalcoholgisg9.9.gThegemployme
ntgrategisg24.3.
(ii) Thegemploymentgrategofgmengwhogabusegalcoholgisg22.6.
(iii) Thegemploymentgrategwhogdognotgabusegalcoholgisg24.5.
(iv) Thegemploymentgratesgofgmengwhogabusegalcoholgandgwhogdognotgareg22.6gandg24.5,g
respectively.gThegdifferencegingthesegemploymentgratesgisgverygless,gwhichgmeansgthatgalco
holgabusegdoesgnotgcausegunemployment.
, 4g|gPgaggge
CHAPTERg2
ThegSimplegRegressiongModel
SOLUTIONSgTOgPROBLEMS
2.1g (i)gIncome,gage,gandgfamilygbackgroundg(suchgasgnumbergofgsiblings)garegjustgagfewgposs
ibilities.g Itgseemsgthatgeachgofgthesegcouldgbegcorrelatedgwithgyearsgofgeducation.g (Incomeg
andgeducationgaregprobablygpositivelygcorrelated;gagegandgeducationgmaygbegnegatively
ThegNaturegofgEconometricsgandgEconomicgData
SOLUTIONgAMANUALgLATESTgEDITIONg2025/202
6
C1.1g(i)gThegaveragegofgeducgisgaboutg12.6gyears.gTheregaregtwogpeoplegreportinggzerogyearsgofged
ucationgandg19gpeoplegreportingg18gyearsgofgeducation.
(ii) Thegaveragegofgwagegingthegsamplegisgaboutg$5.90,gwhichgseemsglow.
(iii) UsinggTablegB-
60gingtheg2004gEconomicgReportgofgthegPresident,gthegCPIgwasg56.9ging1976gandg233ging
2013.
(iv) Togconvertg1976gdollarsgintog2013gdollars,gwegusegthegratiogofgthegCPIs,gwhi
chgisg233g/g56.9g≈g4.09.gTherefore,gthegaverageghourlygwageging2013gdollarsgisgroug
hlyg4.09($5.90)g≈g$24.13,gwhichgisgagreasonablegfigure.
(v) Thegsamplegcontainsg252gwomeng(thegnumbergofgobservationsgwithgfemaleg=g1)gand
g274gmen.
C1.3g(i)gTheglargestgisg100,gthegsmallestgisg0.
(ii) 289goutgofg1,823,gorgaboutg15.85gpercentgofgthegsample.
(iii) 17
(iv) Thegaveragegofgmath4gisgaboutg71.9gandgthegaveragegofgread4gisgaboutg60.1.gSo,gat
gleastging2001,gthegreadinggtestgwasghardergtogpass.
(v) Thegsamplegcorrelationgbetweengmath4gandgread4gisgaboutg.843,gwhichgisgagveryg
highgdegreegofg(linear)gassociation.gNotgsurprisingly,gschoolsgthatghaveghighgpassgratesgon
gonegtestghavegagstronggtendencygtoghaveghighgpassgratesgongthegothergtest.
,2g|gPgaggge
(vi) Thegaveragegofgexpppgisgaboutg$5,194.87.gThegstandardgdeviationgisg$1,091.89,gw
hichgshowsgrathergwidegvariationgingspendinggpergpupil.g[Thegminimumgisg$1,206.88gandg
thegmaximumgisg$11,957.64.]
(vii) ThegpercentagegbygwhichgschoolgAgoutspendsgschoolgBgis
(vii)gThegpercentagegbygwhichgschoolgAgoutspendsgschoolgBgis
(6,000g−g5,500)
100g∙ 5,500 ≈g9.09%.
,3g|gPgaggge
Whengwegusegthegapproximationgbasedgongthegdifferencegingthegnaturalglogsgweggetgagsomewh
atgsmallergnumber:
100g∙g[log(6,000)g−glog(5,500)]g≈g 8.71%.
C1.5g(i)gThegsmallestgandglargestgvaluesgofgchildrengareg0gandg13,grespectively.gThegaverag
egisgaboutg2.27.
(ii) Outgofg4,358gwomen,gonlyg611ghavegelectricitygingtheghome,gorgaboutg14.02gpercent.
(iii) Thegaveragegofgchildrengforgwomengwithoutgelectricitygisgaboutg2.33,gandgforgthoseg
withgelectricitygitgisgaboutg1.90.gSo,gongaverage,gwomengwithgelectricityghaveg.43gfewergchi
ldrengthangthosegwhogdognot.
(iv) Wegcannotginfergcausalityghere.gTheregaregmanygconfoundinggfactorsgthatgmaygbegr
elatedgtogthegnumbergofgchildrengandgthegpresencegofgelectricitygingtheghome;ghouseholdg in
comegandglevelgofgeducationgaregtwogpossibilities.gForgexample,gitgcouldgbegthatgwomengwi
thgmoregeducationghavegfewergchildrengandgaregmoreglikelygtoghavegelectricitygingtheghome
g(theglattergduegtogangincomegeffect).
C1.7g(i)gThegpercentagegofgmengingthegsamplegreportgabusinggalcoholgisg9.9.gThegemployme
ntgrategisg24.3.
(ii) Thegemploymentgrategofgmengwhogabusegalcoholgisg22.6.
(iii) Thegemploymentgrategwhogdognotgabusegalcoholgisg24.5.
(iv) Thegemploymentgratesgofgmengwhogabusegalcoholgandgwhogdognotgareg22.6gandg24.5,g
respectively.gThegdifferencegingthesegemploymentgratesgisgverygless,gwhichgmeansgthatgalco
holgabusegdoesgnotgcausegunemployment.
, 4g|gPgaggge
CHAPTERg2
ThegSimplegRegressiongModel
SOLUTIONSgTOgPROBLEMS
2.1g (i)gIncome,gage,gandgfamilygbackgroundg(suchgasgnumbergofgsiblings)garegjustgagfewgposs
ibilities.g Itgseemsgthatgeachgofgthesegcouldgbegcorrelatedgwithgyearsgofgeducation.g (Incomeg
andgeducationgaregprobablygpositivelygcorrelated;gagegandgeducationgmaygbegnegatively
