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,/ FErdz.*.+.1..t*{*-*g./ AEAIt t o\ oJEC 1I7 - INTRODUCTION TO ECONOMETRICSDEPARTMENT OF ECONOMICSEXAM # 1, January 7,2009AII answersshouldbe written on the blue book. If calculations reneeded, e sure oclearlyshowhowyouobtained ouranswer Thepointvalue of eachquestion s givenafterthequestion. he otalscores 100.Gooduck!1. Statewhetherhe ollowingstatementsre rueor false.Giveabrief explanation nly fyouranswers false. 3 points)a) TheMaximum Likelihood andLeastSquaresmethods ield different formulas oestimateheparametersf amultiple inear egression odel.b) Thenormalityassumption n heresiduals f a inear egtessionmodel s not requiredwhen atest of hypothesiss conducted.

c) WhenR-squareds zero,calculated -statistics alsozero.d) If yourejectedhenull hypotheseshat hecoefficientofthe independentariablen asimple inearregressionmodel s not statisticallydiflerentfrom zerousing he teststatisticapproach,henit is possible o accep the samenull hypothesis singtheconfidencentervalaPProach.e) In an OrdinaryLeastSquaresegressionstimation,t ispossible hatall theactualYivalueswould lie abovehe estimated imple egressionine.2. A residential uildingcontractorwisheso relatehomesize X, in hundreds f squareeet)to his materialcost(Y, in thousand esos).The ANOVA tableshowsheresultsafterarandom ample f completedobsarcanalyzed.

SOURCERegressionErrorTotal

SS df2049.23 191.24 . 902140.47 2la)How manyhouseswere n the sample?2points)b) Computeheteststatistichatwouldbeused o evaluatehehypothesishatX andYarenot inearly elated,5 points)c) What s theestimatedalueof d? (5 points)d-)Whatpercentagef the otalvariation n materialcost s due o the nfluenceof homesize n the egression odel? 3points)

3. Considerhesimple inear egression t: cr+ FXt+ ul whichsatisfies ll theassumptionsf theclassicalinearmodel. s theestimatorb:Vf; for Bunbiased?5points)4. A researcherlans o estimatehe ollowingmodelvia ordinaryeast quares:Yi:a+b*Xi +c*Zif ei where:1,2,3,. . . tr

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Theresearchers concernedhatXi andeimiSt To decidewhether or notthere s aproblem, he proposes o do the foa) Runordinary Leastsquares ols) on themultipleregressionmodelandcalculatetheresiduals r effortermfromtheequation'b) Regresshe calculated esidualson Xi (i.e. the calculate{ residualswill be the' dependentvariable triletheXi will be he ndependentvariable)If the slopecoefficient n thesecondegressions significantlydifferent rom zeroatthe0.05 evel, heresearcher ill conclude-that i andei are inearly elatedTd fut OLS sinappropriaten tt emultipleregression.sthissuggestedrocedure orrect?Whyorwhynot? 10Points)

5. Considerhe ollowing egressionutput:Yi =0'2033+0'6560Xs.E.0.0e76)0.1e61)R.squared:0.397 RSS:0.0544 ESS:0.0358 n:19cities

whereY=labor orceparticipationate LFPR)of womennI972 . i:X:LFPRofwomenin 1968'Test hehypothesishatHo: Fz:l vsHa: Bz>1' 5 points)

, ' " ,4 ,, .J---* -_ ' .. a- '* >+---: - - .-"= .+ .:- .- -

Thefollowing estimateaq*Uo" wasobtained singqtffiWo^Aata rom 1960o 1979Y :2.20- 0.104 l + 3'48X2 + 0'34X3 esE (3.4) (0,00s) Q,2) (0'1s)

Y= quantitydemandedf goodl (kilogram)X1 i priceof good1(pesos/kilogram)X2: monthlyncome Pesos)X3 : priceof good2 (pesos/kilogram)standardeffors are in parentheses,he explainedsumof squareswas 112'5' andtheresidual umof squares as19'5

6.

a)b)c)d)e)D

Interpretall theparametersf themultipleregressionmodel'(10points)Are goodl andgood2substitutes r compleirents?Briefly explainyour answer' 5points)which of thepartial egressionoefficients resignificantlydifferent rom zeroatthe95%significanceevel? 15Points)Makea oint test tratall i#.f regressionoefficientsarenot significantlydifferentfromzero. 10Points)CalculateheR-squareor this regression'5points)CalculateheadjustedR-square'5points)

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ta.s5,2[- .725to.ozs,zo:2.086

SelectedTabulated -valuesFo.orr,zo)8.10Fo.osr,zo)4.35

to.os,z 1.740to.azs,tt2.110

Fo.or:,ro5.29Fo.osr,rz) 5.18

tb.os,o I.746to.ozs,ro2.120

Fo.or+,ro)4.77Fo.os+,rz)2.96