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Chapter 4: Linear Regression with One Regressor 1)Whent hees t i mat edsl opecoeffic i enti nt hes i mpl er egr es s i onmodel ,bet a_hat _one,i sz er o,t hen: Ans wer : R2 =0 2)Ther egr ess i on R2

ESS TSS

i sdefi nedas :

3)Thes t andar der r oroft her egr ess i on( SER)i sdefi nedasf ol l ows : 4)TSS=ESS+SSR. 5)Bi nar yv ar i abl escant akeonl yont woval ues. 6)Thef ol l owi ngar eal l s quar esas s umpt i onwi t ht heex c ept i onof : Ans wer :Theexpl anat or yvar i abl ei nr egr essi onmodeli snor mal l ydi st r i but ed. 7)Ther eas onwhyest i mat or shav eas ampl i ngdi s t r i but i oni st hatt heval uesoft heexpl anat or yvar i abl eandt he er r ort er m di fferacr osssampl es. 8)I nt hesi mpl el i nearr egr es si onmodel ,t her egr ess i ons l opei ndi cat esbyhow manyuni t sYi ncr eases, ,gi vena oneuni ti ncr easei nX. 9)TheOLSes t i mat ori sder i v edbymi ni mi z i ngt hesum ofsquar edr esi dual s. 10)I nt er pr et i ngt hei nt er c epti nas ampl er egr es s i onf unct i oni sr easonabl ei fyoursampl econt ai nsval uesofXi ar oundt heor i gi n. 11)Thev ar i anceofYi i sgi v enby :

( TSS=ESS+SSR) .

12)Thes ampl eav er ageoft heOLSr es i dual si sz er o. 13)TheOLSr es i dual s ,Ûi ,ar edefi nedasf ol l ows : 14)Thes l opees t i mat or ,bet a_one,hasas mal l ers t andar der r or ,ot hert hi ngsequal ,i ft her ei smor evar i at i oni nt he expl anat or yvar i abl e,X. 15)Ther egr es s i on R2

i sameas ur eoft hegoodnes soffitofy ourr egr es si onl i ne.

16)Thes ampl er egr es si onl i nees t i mat edbyOLSwi l lal waysr unt hr ought hepoi nt( X_hat ,Y_hat ) . 17)TheOLSr es i dual scanbecal cul at edbysubt r act i ngt hefit t edval uesf r om t heact ualval ues. 18)The nor malappr ox i mat i on t ot he s ampl i ng di s t r i but i on ofbet a_hat _one i s power f ulbec aus ei tal l ows economet r i ci anst odevel opmet hodsf orst at i st i cali nf er ence. 19) I ft he t hr ee l eas ts quar e as s umpt i ons hol d, t hen t he l ar ge nor mal di s t r i but i on of bet a_hat _one i s

20)I nt he s i mpl el i nearr egr es si on model f unct i on.

,b0 + b1Xir epr esent st he popul at i on r egr essi on

21)Toobt ai nt hes l opeoft hees t i mat orus i ngt hel eas ts quar espr i nc i pl e,y oudi v i det hesampl ecovar i anceofXand Ybyt hesampl evar i anceofX. 22)Todec i dewhet herornott hesl opec oeffic i enti sl ar geors mal l ,youshoul danal yzet heeconomi ci mpor t ance ofagi veni ncr easei nX. 23) mean.

s ay st hatt hecondi t i onaldi st r i but i on oft heer r orgi ven t heexpl anat or yvar i abl ehasaz er o

24)Mul t i pl y i ng t hedependentv ar i abl eby100 and t heex pl anat or yv ar i abl eby100, 000 l eav est he r egr essi on R squar edt hesame. 25)I nt her el at i ons hi pbet weent hechangei nt heunempl oy mentr at eandt hegr owt hofr at eofr ealGDP ( ‘ ’ Ok un’ s Law’ ’ ,t hei nt er cepthasar eal wor l di nt er pr et at i on. 26)TheOLSr es i dual s ,Ûiar es ampl ecount er par t soft hepopul at i oner r or s. 27)Changi ngt heuni t sofmeas ur ementwon’ tchanget hei nt er pr et at i onoft heeffect st hatachangei nXhason t hechangei nY. 28)T odec i dewhet hert hes l opec oeffic i enti ndi c at esa‘ ’ l ar geeffec t ’ ’ofX onY,y oul ookatt hesi z eoft hesl ope coeffici ent .

Chapter 5: Simple Regression: Hypothesis Testing and Confidence Intervals 1)Het er os k edas t i ci t ymeanst hatt hevar i anceoft heer r ort er mi snotconst ant . 2)Wi t hhet er osk edas t i cer r or s ,t hewei ght edl eas ts quar eses t i mat ori sBLUE.Yous houl dOLSwi t hhet er osk edas t i c t y r obusts t andar der r or sbec aus et heexactf or m oft hecondi t i onalvar i ancei sr ar el yknow. 3)Whenes t i mat i ngademandf unc t i onf oragoodwher equant i t ydemandedi sal i nearf unct i onoft hepr i ce,y ou s houl duseaonesi dedal t er nat i vehypot hesi st ocheckt hei nfluenceofpr i ceonquant i t y . 4)Thet s t at i s t i ci sc al c ul at edbydi vi di ngt heest i mat ormi nusi t shypot hesi z edval uebyt heSEoft heest i mat or . 5)The c onfidenc ei nt er v alf ort he s ampl er egr es s i on f unc t i on s l ope can be used t o conducta t estabouta hypot hesi z edpopul at i onr egr essi onf unct i onsl ope. 6)I ft heabs ol ut ev al ueofy ourcal c ul at edt s t at i st i cex ceedst hec r i t i cal v al uef r om t hes t andar dnor mal i z eddi s t r i but i on, t heny oucanr ej ectt henul lhypot hesi s. 7)Undert hel eas ts quar esas s umpt i ons ,t heOLSes t i mat orf ort hes l opeandi nt er cepti sunbi ased. 8)Thecons t r uc t i onoft het s t at i s t i cf oraone-andat wosi dedhy pot hes i si st hesame. 9)95% confi denc ei nt er v al f ort hepr edi ct edeffec tofagener al changei nXi s :

10)Thehomoes k edas t i c i t y onl yes t i mat orf ort hev ar i anceofbet a_one_hati s :

12)Fi ndi ngasmal l v al ueoft hepv al ue( l es st han5%)i ndi cat esevi denceagai nstt henul lhypot hesi s. 13)Theonl ydi ffer enc ebet weenaone-andat wos i dedhypot hes i st es ti show youi nt er pr ett het st at i st i c. 14)Abi nar yv ar i abl ei sof t enc al l edadummyvar i abl e. 15)Theer r ort er mi shomos k edas t i ci f 16)I nt he pr es enc e ofhet er os k edas t i c i t y ,and ass umi ng t hatt he us uall eas ts quar esas s umpt i on hol d,t he OLS est i mat ori sunbi asedandconsi st ent . 17)Thepr ooft hatOLSi sBLUEr equi r esal l oft hef ol l owi ngas s umpt i onswi t ht heex c ept i onsoft heer r or sar enor mal l y di s t r i but ed. 18)The homosk edas t i c nor malr egr es s i on as s umes t hatt he er r or s ar e homoskedast i c,t hatt he er r or s ar e nor mal l ydi st r i but edandt hatt her ear enoout l i er s.I tdoes n’ tas s umet hatt her ei satl eas t10obs er v at i ons ,f or i ns t anc e. 19)Thehet er ok edas t i ci t yr obus tf or mul ai sr ecommendedwhencal c ul at i ngt het s t at i s t i c .

Chapter 6: Linear Regression with Multiple Regressors 1)I nt he mul t i pl er egr es s i on model ,t he adj us t ed R squar ed,R s quar ed_hat ,wi l lneverbe gr eat ert han t he r egr essi onR_squar ed. 2)Underi mper f ec tmul t i col l i near i t y ,t woormor eoft her egr essor sar ehi ghl ycor r el at ed. 3)Whent her ear eomi t t edv ar i abl esi nt her egr es si on,whi char edet er mi nant soft hedependentv ar i abl e,t hen,t he OLSest i mat ori sbi asedi ft heomi t t edvar i abl ei scor r el at ewi t ht hei ncl udedvar i abl e. 4)I magi ney our egr es s edear ni ngsofi ndi v i dual sonac ons t ant ,abi nar yv ar i abl e( ‘ ’ Mal e’ ’ )whi c ht ak esont hev al ues1 f ormal esandi s0ot her wi se,andanot herbi nar yv ar i abl e( ‘ ’ Femal e’ ’ )whi cht ak esont hev al ue1f orf emal esandi s0 ot her wi s e.Bec aus ef emal est y pi cal l year nl es st hanmal es ,y ouwoul dex pectnoneoft heOLSest i mat or st oexi st becauset her ei sper f ectmul t i col l i near i t y. 5)Wheny ouhav eanomi t t edv ar i abl epr obl em,t heas s umpt i ont hat est i mat ori snol ongerconsi st ent .

i sv i ol at ed.Thi si mpl i est hatt heOLS

6)I fy ouhadat wor egr es sorr egr es si onmodel ,t henomi t t i ngonev ar i abl ewhi chi sr el ev antcanr esul ti nanegat i ve val uef ort hecoeffici entoft hei ncl udedvar i abl e,event hought hecoeffici entwi l lhaveasi gni ficantposi t effectonYi ft heomi t t edvar i abl ewer ei ncl uded. 7)I nt hemul t i pl er egr es si onmodely oues t i mat et heeffectonYiofauni tc hangei noneoft heXiwhi l ehol di ngal l ot herr egr ess or scons t ant .Thi scor r espondst ot aki ngapar t i alder i vat i vei nmat hemat i cs. 8)I n at wo r egr ess orr egr es s i on model ,i fy ou ex cl ude one oft he r el ev antv ar i abl es ,t hen you ar e notl onger cont r ol l i ngf ort hei nfluenceoft heot hervar i abl e.

9)Youhav et owor r yaboutper f ectmul t i col l i near i t yi nt hemul t i pl er egr es s i onmodelbec aus et he OLS est i mat or cannotbecomput edi nt hi ssi t uat i on. 10)Thei nt er c epti nt hemul t i pl er egr es si onmodel det er mi nest hehei ghtoft her egr essi onl i ne. 11)I nt hemul t i pl er egr es s i on model ,t he l eas ts quar eses t i mat ori sder i v ed bymi ni mi z i ng t hesum ofsquar ed pr edi ct i onmi st akes. 12)The s ampl er egr es si on l i ne es t i mat ed byOLS i st he l i ne t hatmi ni mi zes t he sum ofsquar ed pr edi ct i on mi st akes. 13)TheOLSr es i dual si nt hemul t i pl er egr es s i onmodel canbecal cul at edbysubt r act i ngt hefit t edval uesf r om t he act ualval ues. 14)Undert heLSA,t heOLSes t i mat or sf ort hes l opesandi nt er ceptar eunbi asedandconsi st ent . 15)Themai nadv ant ageofus i ngmul t i pl er egr ess i onanal y s i sov erdi ffer enc esi nmeanst es t i ngi st hatt her egr es si on t ec hni quegi vesyouquant i t at i veest i mat esofauni tchangei nX. 16)I namul t i pl er egr es si onf r amewor k ,t hes l opec oeffici entont her egr es sorX2i i smeas ur edi nt heuni t sofYidi vi des byuni t sofX2i . 17)Oneoft hel eas ts quar esas s umpt i onsi nt hemul t i pl er egr es s i onmodeli st haty ouhav er andom v ar i abl eswhi c h ar e‘ ’ i . i . d’ ’ .Thi sst andsf ori ndependent l yandi dent i cal l ydi st r i but ed. 18)OVB exi st si ft heomi t t edvar i abl ei scor r el at edwi t ht hei ncl udedr egr essorandi sadet er mi nantoft he dependentvar i abl e. 19)Thef ol l owi ngOLSas s umpt i oni smos tl i k el yvi ol at edbyOVB:Meanofugi v enXi =0.

21)I nt hemul t i pl er egr es s i onmodel ,t heOLSes t i mat or sar eobt ai nedbymi ni mi z i ngt hes um of :

22)I nt hemul t i pl er egr es s i onmodel ,t heSERi sgi v enby : 23)I nt hemul t i pl er egr ees i on,R^ 2i nc r eas eswhenev erar egr es s ori naddedunl esst hecoeffici entont headded r egr essori sexact l yzer o.

24)R2_hati sgi v enby : 25)Dummyv ar i abl et r api sanex ampl eofper f ectmul t i col l i near i t y. 26)I mper f ec tmul t i col l i near i t yi mpl i est hati twi l lbedi fficul tt oest i mat epr eci sel yoneormor eoft hepar ci al effect susi ngt hedat aathand.

27)Cons i dert hemul t i pl er egr es si onmodelwi t ht wor egr es s or s ,X1andX2,wher ebot hv ar i abl esar edet er mi nant sof t hedependentv ar i abl eYoufi r s tr egr es sYonX1onl yandfi ndnor el at i ons hi p.Howev er ,whenr egr es si ngYonX1and X2,t hes l opec oeffic i entbet a_one_hatchangesbyal ar geamount .Thi ss ugges t st haty ourfi r str egr es si ons uffer s f r om omi t t edvar i abl ebi as....