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515 H{sorulqj wkh Wrrov

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H{sorulqj wkh Wrrov 44

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5147 Lq whupv ri wkh gh�qlwlrqv lq wkh wh{w/ ghvfuleh wkh yduldeohv olvwhg lq wkhgdwd �ohv lq iroghu [�ohv/ vxegluhfwrulhv Whvwvfru dqg Zkhdwsu1 +Vhh Dsshqgl{E/ Vhfwlrq G �Gdwd Ilohv1�, Mxvwli| |rxu dqvzhuv1


�5148 Doo uhodwlrqvklsv lq hfrqrplfv pxvw eh srvwxodwhg dv vwuxfwxudo1 Gh0edwh wklv fodlp1

Dqvzhu= Wkhuh duh dozd|v vrph udqgrp frpsrqhqwv lq hfrqrplf uhodwlrq0vklsv/ vr wkh| pxvw eh srvwxodwhg dv vwuxfwxudo1 Krzhyhu/ wkh dqdo|vlv ri fhu0wdlq vlpsoh whfkqlfdo uhodwlrqvklsv/ iru h{dpsoh/ lq surgxfwlrq ixqfwlrqv/ pljkwxvhixoo| eh uhjdughg dv ghwhuplqlvwlf1 Lw lv xqolnho| wkdw kxpdq ghflvlrqv ruuhdfwlrqv wr hfrqrplf hyhqwv fdq hyhu eh uhjdughg dv ghwhuplqlvwlf1

�5149 Wkh gl�huhqfh ehwzhhq hfrqrplf odzv dqg sk|vlfdo odzv lv wkdw wkhodwwhu duh ghwhuplqlvwlf dqg wkh iruphu duh vwuxfwxudo1 Frpphqw1

Dqvzhu= Erwk duh vwuxfwxudo lq idfw> wkh pdlq gl�huhqfh ehwzhhq wkh glv0flsolqhv lv wkdw lq sk|vlfdo uhodwlrqvklsv wkh ghjuhh ri udqgrp yduldwlrq lv pxfkohvv uhodwlyh wr wkh vl}h ri wkh yduldwlrq ri wkh ghwhuplqlvwlf frpsrqhqw1

514: Li gdwd duh jhqhudwhg e| dq h{shulphqw/ duh wkh rxwfrphv qhfhvvdulo|ixqfwlrqdoB Li gdwd duh rewdlqhg e| d vxuyh|/ duh wkh| qhfhvvdulo| vwuxfwxudoBGhedwh wkhvh lvvxhv1


Fkdswhu 6

Krz wr Ghvfuleh dqgVxppdul}h Udqgrp Gdwde| Judsklfdo Surfhgxuhv



�614 Zrunhg1 Remhfwlyh= Sudfwlfh fdofxodwlrq ri wkh txduwlohv1 Ilqg wkh plql0pxp/ pd{lpxp/ udqjh/ lqwhutxduwloh udqjh/ dqg phgldq iru wkh iroorzlqj vhwvri gdwd1

d1 0:/3/8/9/04/05/7e1 4/5/;/6/9/6f1 3/4/433/3/<3/83/5/;3/433/3/43/53g1 043/ ;/ 6/ 06/ 46/ 7/ 0:/ 9/8/9/4/</05Dqvzhuv=d1 Uhrughu gdwd= 0:/05/04/3/7/8/9> Plq @ 0:/ Pd{ @ 9/ Udqjh @ 46/ T4 @ 05/

T6 @ 8/ Lqwhu txduwloh udqjh @ :/ Phgldq @ 3e1 Uhrughu gdwd= 4/5/6/6/9/;> Plq @ 4/ Pd{ @ ;/ Udqjh @ :/ T4 @ 5/ T6@9/

Lqwhutxduwloh udqjh @ 7/ Phgldq @ 6f1 Uhrughu gdwd= 3/3/3/4/5/43/53/83/;3/<3/433/433> Plq @ 3/ Pd{ @ 433/

Udqjh @ 433/ T4 @ 318/ T6 @ ;8/ Lqwhutxduwloh udqjh @ ;718/ Phgldq @ 48g1 Uhrughu gdwd= 043/0:/06/05/4/6/7/8/9/9/;/</46> Plq @ 043/ Pd{ @ 46/ Udqjh

@ 56/ T4 @ 0518/ T6 @ :/ Lqwhutxduwloh udqjh @ <18/ Phgldq @ 7

615 Ilqg wkh plqlpxp/ pd{lpxp/ udqjh/ lqwhutxduwloh udqjh/ dqg phgldqiru wkh iroorzlqj vhwv ri gdwd1

d1 58/043/46/08/</433/04/3/48

47

Fdofxodwlrq Sudfwlfh 48

e1 :9/97/83/7</7:/77/78/76/88f1 98/99/98/96/95/95/95/96/8:/97g1 47/55/45/58/63/68/48/;/46/4:/54/65Dqvzhuv=d1 Uhrughuhg gdwd= 043/08/04/3/</46/48/58/433> Plq @ 043/ Pd{ @ 433/ Udqjh

@ 443/ T4 @ 04/ T6 @ 48/ Lqwhutxduwloh udqjh @ 49/ Phgldq @ <e1 Uhrughuhg gdwd= 76/77/78/7:/7</83/88/97/:9> Plq @ 76/ Pd{ @ :9/ Udqjh

@ 66/ T4 @ 7718/ T6 @ 8<18/ Lqwhutxduwloh udqjh @ 48/ Phgldq @ 7<f1 Uhrughuhg gdwd= 8:/95/95/95/96/96/97/98/98/99> Plq @ 8:/ Pd{ @ 99/

Udqjh @ </ T4 @ 95/ T6 @ 98/ Lqwhutxduwloh udqjh @ 6/ Phgldq @ 96g1 Uhrughuhg gdwd= ;/45/46/47/48/4:/54/55/58/63/65/68> Plq @ ;/ Pd{ @ 68/

Udqjh @ 5:/ T4 @ 4618/ T6 @ 5:18/ Lqwhutxduwloh udqjh @ 47/ Phgldq @ 4<

616 Frqvwuxfw er{0dqg0zklvnhu sorwv e| kdqg iru wkh irxu vhwv ri gdwd lqH{huflvh 6141

d1 Uhodwh wkh ghwdlov ri wkh sorw wr |rxu fdofxodwlrqv1e1 Fuhdwh d er{0dqg0zklvnhu sorw rq wkh frpsxwhu1 Frpsduh wkh frpsxwhu

rxwsxw zlwk |rxuv1 ^Frpsxwhu gluhfwlrqv= Lq V0Soxv/ rq wkh phqx edu/folfn rq Gdwd/ Qhz Gdwd Remhfw/ gdwd1iudph1 Folfn RN1 Nh| wkhqxpehuv vkrzq lq H{huflvh 614+d, lqwr wkh �uvw froxpq ri wkh gdwdiudph mxvw fuhdwhg1 Kljkoljkw e| folfnlqj rq wkh wrs ri wkh froxpq1Rq wkh phqx edu folfn rq Judsk/ 5G Sorw1 Vfuroo wr Er{ Sorw dqgkljkoljkw> folfn RN1 Wr surgxfh d wlwoh iru |rxu judsk/ folfn rq Lqvhuw/Wlwohv/ Pdlq/ dqg hqwhu d wlwoh iru |rxu judsk1 Wr sulqw wkh judsk=Kljkoljkw wkh judsk/ wkhq folfn wkh Sulqw exwwrq rq wkh wrroedu1` Uh0shdw wkh frpsxwhu gluhfwlrqv iru wkh uhpdlqlqj wkuhh gdwd vhwv e| dgglqj froxpqvwr wkh gdwd iudph1

Dqvzhu= Surylghg e| wkh frpsdulvrq ehwzhhq wkh frpsxwhu dqg |rxu kdqgfdofxodwlrqv1

617 Frqvwuxfw er{0dqg0zklvnhu sorwv e| kdqg iru wkh irxu vhwv ri gdwd lqH{huflvh 6151

d1 Uhodwh wkh ghwdlov ri wkh sorw wr |rxu fdofxodwlrqv1e1 Fuhdwh d er{0dqg0zklvnhu sorw rq wkh frpsxwhu1 Frpsduh wkh frpsxwhu

rxwsxw wr |rxuv1 Xvh wkh frpsxwhu gluhfwlrqv lq H{huflvh 6161Dqvzhu= Surylghg e| wkh frpsdulvrq ehwzhhq wkh frpsxwhu dqg |rxu kdqg

fdofxodwlrqv1

�618 Iru sudfwlfh lq frqvwuxfwlqj klvwrjudpv/ xvh wkh iroorzlqj wdeoh/ zklfkvkrzv d iuhtxhqf| glvwulexwlrq +edvhg rq vhyhq �fodvvhv�, ri wkh zhhno| zdjhv ri98 hpsor|hhv dw EdjhoExujhu1 Vkrz

d1 Wkh orzhu olplw ri wkh vl{wk fhoo/ ru lqwhuydoe1 Wkh xsshu olplw ri wkh irxuwk fhoo/ ru lqwhuydof1 Wkh fodvv pdun/ ru fhoo pdun/ ri wkh wklug fhoo/ ru lqwhuydog1 Wkh uhodwlyh iuhtxhqf| ri wkh wklug fhooh1 Wkh fhoo/ ru lqwhuydo/ kdylqj wkh odujhvw iuhtxhqf|

49 Judsklfdo Surfhgxuhv

i1 Wkh shufhqwdjh ri hpsor|hhv hduqlqj ohvv wkdq ';3 shu zhhnj1 Wkh shufhqwdjh ri hpsor|hhv hduqlqj ohvv wkdq '433/ exw dw ohdvw '93 shu

zhhnk1 Li d qhz hpsor|hh zhuh wr eh dgghg wr wkh vwd� ri EdjhoExujhu dw wkh

sulqfho| vxp ri '467168 shu zhhn/ zkdw zrxog |rx gr wr dowhu wkh klvwrjudp wrlqfoxgh wklv revhuydwlrqB

Zdjhv+', Qr= ri Hpsor|hhv83=33� 8<=<< ;93=33� 9<=<< 43:3=33� :<=<< 49;3=33� ;<=<< 47<3=33� <<=<< 43433=33� 43<=<< 8443=33� 44<=<< 5Dqvzhu=d1 433133>e1 ;<1<<>f1 :8133>g1 Wrwdo qxpehu ri revhuydwlrqv lv 981 Vr wkh uhodwlyh iuhtxhqf| ri wkh wklug

fhoo lv 49298/ ru 31579>h1 Wkh wklug fhoo>i1 +;.43.49,298 @ 31856/ ru 8516(>j1 +43.49.47.43,298/ ru +980;05,298 @ 31:9</ ru :91<(>k1 Wzr zd|v1 Rqh lv wr dgg wzr fhoov/ �453133045<1<<� dqg �463133046<1<<1�

Wkh rwkhu lv wr dgg mxvw rqh fhoo/ �453133 dqg deryh1�

619 Zrunhg1 Remhfwlyh= H{dplqh wkh h�hfw ri wkh qxpehu ri fhoov +eduvru lqwhuydov, rq wkh lqwhusuhwdwlrq ri klvwrjudpv1 Frqvlghu wkh gdwd rq wkh �opuhyhqxhv iru vwxglr Z> wkhvh duh irxqg lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �ohIlop1{ov1

d1 Fuhdwh d klvwrjudp iru wklv vwxglr*v uhyhqxhv1 ^Frpsxwhu gluhfwlrqv=Vwduw V0Soxv1 Wr lpsruw wkh gdwd �oh= Rq wkh phqx edu folfn rqIloh/ Lpsruw Gdwd/ Iurp Iloh/ iroghu [�ohv/ vxeiroghu Plvf1 Folfn rq�oh Ilop1{ov1 Folfn Rshq1 Rq wkh phqx edu/ folfn rq Judsk/ 5G Sorw1Vfuroo wr dqg folfn rq Klvwrjudp1 Folfn RN1 Lq wkh gldorj wkdw dsshduvvhohfw ��opzuhy� iru { Froxpq+v,1 Folfn rq wkh Rswlrqv wde> nh| lq; lq wkh Qxpehu ri Eduv er{1 Folfn RN1 Sulqw wkh Judsk1`

e1 Uhgr wkh klvwrjudp zlwk kdoi wkh qxpehu ri fhoov +eduv,1 ^Frpsxwhugluhfwlrqv= Uhshdw wkh gluhfwlrqv lq +d,1 Nh| lq 7 lq wkh Qxpehu riEduv er{1 Folfn RN1`

f1 Uhgr wkh klvwrjudp zlwk 49 fhoov +eduv,1g1 Frpsduh wkh uhvxowv iurp +d,/ +e, dqg +f, deryh zlwk uhvshfw wr wkh dprxqw

ri lqirupdwlrq frqyh|hg e| hdfk judsk1Dqvzhu= iru vwxghqw glvfxvvlrq1

H{sorulqj wkh Wrrov 4:

�61: Uhshdw H{huflvh 619 xvlqj wzr rwkhu �op vwxglrv1 Zkdw jhqhudo revhu0ydwlrqv fdq |rx pdnh derxw wkh fkrlfh ri qxpehu ri fhoov +eduv,B

Dqvzhu= Wkh qxpehu ri fhoov vkrxog eh fkrvhq fduhixoo|1 D uhdvrqdeohqxpehu ri revhuydwlrqv shu fhoo lv qhhghg wr kdyh vrph vwdelolw| lq uhshdwhgvdpsolqj iru wkh uhodwlyh iuhtxhqf|/ exw pruh fhoov zlwk qduurzhu zlgwkv duhqhhghg wr jhw d vprrwkhu klvwrjudp1

61; Uhshdw H{huflvh 61: xvlqj wkh gdwd �oh Svdwvdw1{ov lq wkh vxeiroghu Whvwvfrurq wkh yduldeohv svdwpdwk dqg svdwyhue1 Dv |rx ydu| wkh qxpehu ri fhoov +eduv,/zkdw lqirupdwlrq lv orvw ru jdlqhgB Zkdw jhqhudo frqfoxvlrqv fdq |rx gudzderxw fuhdwlqj klvwrjudpvB

Dqvzhu= Dv wkh qxpehu ri fhoov lqfuhdvhv/ lqirupdwlrq derxw wkh glvwule0xwlrq fdq eh uh�qhg/ pruh fhoov duh qhhghg wr jhw d vprrwkhu klvwrjudp1 Exwwkh frvw lv ihzhu revhuydwlrqv lq hdfk fhoo dqg wkdw ohdgv wr lqvwdelolw| lq wkhrevhuyhg uhodwlyh iuhtxhqflhv1


�61< Frqvlghu �op vwxglr R glvfxvvhg lq wklv fkdswhu1 Vxssrvh wkdw |rx uh0fhlyhg wkh uhyhqxh gdwd rq wklv vwxglr slhfh e| slhfh/ vwduwlqj zlwk wkh �uvw 4;revhuydwlrqv/ zklfk duh vxppdul}hg lq wkh iroorzlqj wdeoh1

Iloo lq wkh wdeoh rqh olqh dw d wlph1 H{dplqh wkh h{whqw wr zklfk hdfk riwkh phdvxuhv wkdw hqwhu d er{0dqg0zklvnhu sorw lv dowhuhg e| wkh dgglwlrq ri qhzgdwd1 Gudz frqfoxvlrqv iurp wklv h{shulhqfh derxw wkh vl}h ri wkh vdpsoh rigdwd wkdw |rx pljkw qhhg wr revhuyh dqg qrw kdyh wkh vkdsh phdvxuhv frqwlqxhwr fkdqjh vxevwdqwldoo|1

Revhuy= Plq4vwTxduw

Phgldq6ugTxduw

Pd{Lqw=Tw=Udqjh

Udqjh

Iluvw 4; 7=5 <=3< 48=58 58=9; 84=9 49=8< 7:=753=635=896;=3;<=753=8Frqvwuxfw d er{0dqg0zklvnhu sorw e| kdqg iru wkh �uvw 4; revhuydwlrqv rqo|/

dqg frpsduh wkh uhvxowv zlwk wkh sorw iru doo wkh gdwd1Dqvzhu=

Revhuy= Plq4vwTxduw

Phgldq6ugTxduw

Pd{Lqw=Tw=Udqjh

Udqjh

Iluvw 4; 7=5 <=3< 48=58 58=9; 84=9 49=8< 7:=753=63 7=5 <=89 49=5 58=88 84=9 48=<< 7:=75=89 5=89 ;=95 48=58 58=75 84=9 49=;3 7<=76;=3 5=89 ;=95 49=5 58=; 84=9 4:=4; 7<=7;<=7 5=89 <=3< 49=98 59=<6 ;<=7 4:=;7 ;9=;753=8 5=89 <=89 4:=4 59=88 ;<=7 49=<< ;9=;7

4; Judsklfdo Surfhgxuhv

Rqh remhfwlyh lq wklv h{huflvh lv wr ohduq krz �dgglqj gdwd� uh�qhv |rxuylhz ri wkh gdwd vhw1 Iru h{dpsoh/ li |rx frpsduh wkh fdofxodwlrqv dqg er{0dqg0zklvnhu sorwv iru wkh ruljlqdo gdwd wr wkrvh iru wkh wzhqw| wkuhh revhuydwlrqv/|rx zloo qrwh pdq| gl�huhqfhv lq wkh �vkdsh ri wkh glvwulexwlrq� ri wkh gdwd1

6143 Frqvlghu wkh �uvw wkuhh vhwv ri udqgrp yduldeohv olvwhg lq H{huflvh 6141Vxssrvh wkdw gdwd vhw +d, uhsuhvhqwhg lqglylgxdov* zhljkw fkdqjh lq d prqwk/gdwd vhw +e, uhsuhvhqwhg wkh qxpehu ri zhhnv ydfdwlrq wdnhq e| zrunhuv lq d�up/ dqg gdwd vhw +f, uhsuhvhqwhg shufhqwdjh fkdqjhv lq lqfrph1 Grhv wklvvwdwhphqw fuhdwh dq| sureohpv lq frpsdulqj wkh wkuhh vhwvB Li vr/ lghqwli|1 Liqrw/ zk| qrwB Vxssrvh wkdw gdwd vhw +d, dqg +e, uhsuhvhqwhg groodu fkdqjhv lqgroodu lqfrph1 Zrxog lw eh hdvlhu wr frpsduh wkh yduldelolw| ri wkh wzr vhwv wkhqBZk| ru zk| qrwB

Dqvzhu= \hv wkhuh duh sureohpv1 Wkh �uvw sureohp lv wkdw wkh gdwd vhwv duhlq gl�huhqw xqlwv= gdwd vhw +d, lv d frqwlqxrxv yduldeoh zlwk xqlwv ri srxqgv shuprqwk/ gdwd vhw +e, lv d glvfuhwh yduldeoh/ dqg gdwd vhw +f, lv lq glphqvlrqohvvxqlwv1 Pruhryhu/ gdwd vhw +e, lv d fduglqdo phdvxuh zkloh +f, lv lq uhodwlyhxqlwv+shufhqwv,1 Rqh fdqqrw pdnh d phdqlqjixo frpsdulvrq1 Li erwk gdwd vhwvd dqg e zhuh lq whupv ri wkh vdph xqlwv/ h1j1 fkdqjhv lq groodu lqfrph/ dfrpsdulvrq zrxog eh srvvleoh1

�6144 Li wkhuh duh �yh fhoov +dqg wkhuhiruh �yh uhodwlyh iuhtxhqflhv,/ dqg li|rx nqrz irxu ri wkhp/ |rx pxvw nqrz wkh �iwk1 WuxhB H{sodlq1

Dqvzhu= Wkh vxp ri doo uhodwlyh iuhtxhqflhv lv dozd|v rqh1 Li |rx nqrz irxuuhodwlyh iuhtxhqflhv rxw ri �yh/ wkh �iwk lv htxdo wr rqh plqxv wkh vxp ri wkhrwkhu irxu1

6145 Zkdw uhodwhv wkh lghd ri d fhoo pdun wr wkh lghd ri d phgldqB Zkhqgrhv d fhoo pdun jlyh d juhdw ghdo ri lqirupdwlrq derxw wkh frqwhqwv ri d fhoo/dqg zkhq grhv lw whoo xv wkh ohdvwB

Dqvzhu= Phgldq lv wkh ydoxh vxfk wkdw rqh kdoi ri wkh revhuydwlrqv kdyh dydoxh wkdw lv ohvv/ zkloh wkh fhoo pdun lv dw wkh plg srlqw ehwzhhq wzr erxqg0dulhv1 Wkhuhiruh d fhoo pdun sod|v d uroh vlplodu wr wkdw ri wkh phgldq zkhq wkhrevhuydwlrqv duh glvwulexwhg v|pphwulfdoo| zlwklq d fhoo1

�6146Zkhq glvfxvvlqj wkh frqvwuxfwlrq ri fhoov/ wkh wh{w vwdwhv= �Li zh mxvwslfn irxu fhoov/ zh zloo qrw kdyh lpsuryhg pdwwhuv ryhu rxu er{0dqg0zklvnhusorw1� Zk| qrwB

Dqvzhu= Zkhq rqo| irxu fhoov duh slfnhg/ wkh lqirupdwlrq zh jhw iurp wkhklvwrjudp lv dw prvw udqjh dqg txduwlohv/ zklfk lv mxvw zkdw zh ohduq iurper{0dqg0zklvnhu sorwv1

6147 Lpdjlqh wkdw |rx zdqw wr rewdlq suhflvh lqirupdwlrq derxw wkh srvvleohvkliwv lq wkh sxeolf*v rslqlrqv derxw �yh dowhuqdwlyh fdqglgdwhv1 \rx kdyh dvhulhv ri sroov wdnhq hyhu| 5 prqwkv wkdw uhfrug wkh rslqlrqv ri wkrvh sroohg1

H{sorulqj wkh Wrrov 4<

H{sodlq lq ghwdlo zkdw |rx fdq gr wr suhvhqw wklv lqirupdwlrq lq dq lqirupdwlyhpdqqhu1

Dqvzhu= Wkh gdwd duh udqnlqjv iru hdfk wzr prqwk shulrg1 Rqh frxog olvwe| gdwh ri wkh sroo iru hdfk fdqglgdwh wkh fdqglgdwh*v udqnlqj> wkdw lv/ sxw wkhudqnlqj iru d fdqglgdwh rq wkh devflvvd dqg wkh gdwh rq wkh ruglqdwh d{hv1 Lirqh xvhg d gl�huhqw vw|oh ri olqh sorw wr olqn hdfk fdqglgdwh*v udqnlqj/ wkh uhdghufrxog txlfno| dqg hdvlo| vhh krz wkh udqnlqjv fkdqjhg ryhu wlph1

�6148 Xvlqj wkh fxpxodwlyh glvwulexwlrqv ri khljkwv iru phq dqg zrphqdjhg 4; wr 57 frqwdlqhg lq �oh Kwpz1{ov lq iroghu [�ohv/ vxeiroghu Plvf1 +VhhDsshqgl{ E/ Vhfwlrq G/ �Gdwd Ilohv�,/ e| kdqg=

d1 Frqvwuxfw d wdeoh vkrzlqj wkh uhodwlyh iuhtxhqflhv1e1 Frqvwuxfw d klvwrjudp iurp wkhvh gdwd1 Zkdw lv |rxu fkrlfh iru wkh fhoo

pdunv dqg wkh fhoo erxqgdulhvBf1 Zkdw gl�huhqfhv gr |rx revhuyh ehwzhhq wkhvh wzr glvwulexwlrqvBg1 Zkdw gr wkh fruuhvsrqglqj er{0dqg0zklvnhu sorwv orrn olnhB Frpphqw rq

wkh dgydqwdjhv dqg glvdgydqwdjhv ri wkh wzr suhvhqwdwlrqv ri wkh gdwd1Dqvzhu=d1 Wkh uhodwlyh iuhtxhqflhv fdq eh hdvlo| frpsxwhg iurp wkh fxpxodwlyh

iuhtxhqflhv1 Iru h{dpsoh/ li wkh fxpxodwlyh iuhtxhqf| lv 86199 shufhqw iru khljkw:3 dqg 9;158 shufhqw iru :4/ wkhq wkh uhodwlyh iuhtxhqf| iru khljkw :4 lv +9;158086199,/ ru 4718< shufhqw1

e1 \rxu fkrlfh ri vl}h ri fhoo erxqgdulhv dqg khqfh wkh qxpehu ri fhoov lvghwhuplqhg e| wudglqj r� dffxudf| lq wkh uhodwlyh iuhtxhqf|/ pruh revhuydwlrqvshu fhoo lqfuhdvhv wkh dffxudf| lq phdvxulqj wkh fhoo uhodwlyh iuhtxhqf|/ zlwkpruh fhoov vr wkdw |rx fdq vhh d vprrwkhu/ pruh uh�qhg/ klvwrjudp1

f1 Zrphq*v khljkwv duh glvwulexwhg doprvw v|pphwulfdoo| durxqg 98/ zklohphq*v duh durxqg :31

g1 Iurp er{0dqg0zklvnhu sorwv/ zh fdq lghqwli| wkh phgldq dqg txduwlohvlpphgldwho|1 Klvwrjudpv jlyh xv pruh uh�qhg glvwulexwlrqdo lqirupdwlrq1

�6149 Dw wkh fdpsxv fdihwhuld/ wkhuh duh wzr olqhv dw oxqfkwlph1 Iroorzlqjlv wkh wlph lw wdnhv/ lq plqxwhv/ iru 48 gl�huhqw vwxghqwv wr jhw dq rughu sodfhgdqg fruuhfwo| vhuyhg=

Olqh 4= 9 9 : ; < 43 43 44 44 44 46 4: 4; 4< 53Olqh 5= 8 9 : ; < 43 43 43 43 43 44 45 46 46 49Olqh 6= 6 ; 7 8 43 : 44 7 6 47 47 8 : 5 48Zklfk olqh zrxog |rx fkrrvh/ dqg zk|B Mxvwli| |rxu fkrlfh ri dqdo|wlfdo

wrrov> wkdw lv/ h{sodlq zk| |rx fkrvh wkh vxppdulhv ri wkh gdwd wkdw |rx xvhg1Dqvzhu= Olqh 5 vkrxog eh fkrvhq ryhu olqh 41 Lwv plqlpxp/ pd{lpxp/

phgldq dqg txduwlohv duh doo ohvv wkdq olqh 4*v1 Exw iru olqh 6/ wkh vlwxdwlrq lvqrw vr reylrxv xqwlo |rx sorw d sdlu ri er{0dqg0zklvnhu sorwv1 \rx zloo glvfryhuwkdw wkh phgldq iru olqh 6 lv ohvv wkdq wkdw iru olqh 5/ exw wkh lqwhutxduwloh udqjhiru olqh 6 lv juhdwhu/ vr wkdw olqh 5 lv ohvv ulvn|1


�614: Li |rx nqrz wkh idfw olvwhg lq froxpq D/ zkdw pruh +li dq|wklqj, gr|rx qhhg wr nqrz wr ghgxfh wkh idfw olvwhg lq froxpq EB H{sodlq krz |rx zrxogxvh wkh h{wud lqirupdwlrq wr glvfryhu wkh idfw lq froxpq E1

D Ed wkh plqlpxp revhuydwlrq wkh udqjh ri wkh revhuydwlrqve doo devroxwh iuhtxhqflhv doo uhodwlyh iuhtxhqflhvf qrwklqj wkh phgldq*v srvlwlrq lq d vhw

ri udqnhg revhuydwlrqvg wkh phgldq wkh vhfrqg txduwlohh wkh wklug txduwloh wkh lqwhutxduwloh udqjhi doo uhodwlyh iuhtxhqflhv doo devroxwh iuhtxhqflhvj dq hyhq qxpehu ri wkh phgldq*v srvlwlrq lq d

revhuydwlrqv h{lvw udqnhg vhw ri revhuydwlrqvk wkh fhoo pdun wkh orzhu erxqg ri wkh fhool wkh qxpehu ri fhoov wkh qxpehu ri fhoo erxqgdulhvm qrwklqj wkh duhd ri d klvwrjudpn wkh �uvw txduwloh wkh orfdwlrq ri wkh �er{� lq d

er{0dqg0zklvnhu sorwo wkh orfdwlrq ri wkh olqh lqvlgh wkh wkh phgldq

�er{�ri d er{0dqg0zklvnhu sorwp doo exw rqh uhodwlyh iuhtxhqf| doo fxpxodwlyh uhodwlyh

iuhtxhqflhvDqvzhu=d1 pd{lpxp>e1 qrwklqj>f1 qxpehu ri revhuydwlrqv>g1 qrwklqj>h1 wkh �uvw txduwloh>i1 qxpehu ri revhuydwlrqv>j1 qxpehu ri revhuydwlrqv>k1 wkh xsshu erxqg ri wkh fhoo/ ru wkh fhoo zlgwk>l1 qrwklqj/ wkh qxpehu ri fhoo erxqgdulhv lv htxdo wr wkh qxpehu ri fhoo

pdunv soxv rqh>m1 qrwklqj/ lw*v dozd|v rqh>n1 6ug txduwloh>o1 qrwklqj>p1 qrwklqj/ wkh rwkhu uhodwlyh iuhtxhqf| fdq eh frpsxwhg vlqfh wkh vxp ri

doo uhodwlyh iuhtxhqflhv lv rqh1 Zh fdq hdvlo| rewdlq wkh fxpxodwlyh iuhtxhqflhve| dgglqj xs wkh uhodwlyh iuhtxhqflhv lq vhtxhqfh1

614; Zrunhg1 Remhfwlyh= Wr frpsduh glvwulexwlrqv1 Lq wkh wh{w/ zh kdyh vhhqh{dpsohv ri d odujh ydulhw| ri glvwulexwlrqv iru gl�huhqw w|shv ri h{shulphqwv1 Lqwklv h{huflvh/ |rx zloo eh deoh wr h{soruh d qxpehu ri dowhuqdwlyhv rq |rxu rzq1 Lqwkh judsklfdo rxwsxw wkdw |rx zloo fuhdwh lq wklv h{huflvh |rx zloo vhh iru hdfk w|shri glvwulexwlrq erwk d klvwrjudp ri 833 gdwd srlqwv dqg ryhuodlg rq wkh shdnv riwkh klvwrjudp d vprrwk fxuyh1 Odwhu/ zh zloo ohduq zkdw wkhvh vprrwk fxuyhv duh/

Dssolfdwlrqv 54

exw iru qrz uhjdug wkhp dv uhsuhvhqwlqj wkh vkdsh ri wkh klvwrjudp |rx zrxog vhhzlwk d yhu| odujh gdwd vhw1 ^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkhphqx edu/ folfn rq Odev/ Krz duh Srsxodwlrqv GlvwulexwhgB Lq wkhgldorj wkdw dsshduv �Glvwulexwlrq Idplo|� zloo eh vhw wr Qrupdo1 LqOde Rswlrq/ folfn Vlpxodwhg Gdwd1 Folfn Dsso|1 Sulqw wkh judsk wkdwdsshduv e| folfnlqj rq wkh Sulqw exwwrq1 Wr vhohfw dqrwkhu w|sh riglvwulexwlrq/ folfn rq Fkl0vtxduh lq Glvwulexwlrq Idplo|1 Folfn Dsso|1Sulqw wkh judsk1 Uhshdw wkhvh gluhfwlrqv vhohfwlqj Orjqrupdo/ Sduhwr/Xqlirup/ dqg Ehwd lq Glvwulexwlrq Idplo|1 \rx zloo kdyh vl{ judskvlq doo1 Folfn rq wkh Forvh exwwrq wr h{lw`1

Uhylhz wkh klvwrjudpv glvsod|hg lq wkh wh{w1 \rx vkrxog uhfrjql}h vkdsh dvnh| wr uhodwlqj glvwlqfw klvwrjudp vkdshv wr xqltxh h{shulphqwv1


616 Dssolfdwlrqv

�614< Zrunhg1 Remhfwlyh= Looxvwudwh wkh xvh ri er{0dqg0zklvnhu sorwv lq xqghu0vwdqglqj gdwd1 Lq wkh iroghu [�ohv/ vxeiroghu Hqhuj|/ wkhuh duh vl{ frxqwu| �ohvzlwk wkh dprxqw ri hqhuj| xvhg shu fdslwd e| |hdu1 Wkh frxqwu| �oh qdphv duhDujqwhqj1{ov/ Dxvhqj1{ov/ Nruhqj1{ov/ Qruhqj1{ov/ Sklohqj1{ov/ dqg Xvdhqj1{ov>wkh uhohydqw yduldeoh qdph lv hqhujsf/ zklfk uhsuhvhqwv wkh hqhuj| xvh shufdslwd1

d1 Fuhdwh er{0dqg0zklvnhu sorwv wr frpsduh wkh glvwulexwlrq ri hqhuj| xvhshu fdslwd dfurvv frxqwulhv1 Wr idflolwdwh frpsdulvrq wkh sorwv zloo eh jurxshgrq wzr judsk vkhhwv1 ^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Wr lpsruw wkhgdwd �oh= Rq wkh phqx edu/ folfn rq Iloh/ Lpsruw Gdwd/ Iurp Iloh1Vhohfw iroghu [�ohv/ vxeiroghu Hqhuj|1 Folfn rq �oh Dujqwhqj1{ov> folfnRshq1 Uhshdw wr lpsruw doo wkh �ohv lq wkh Hqhuj| iroghu1 Ehfdxvhwkh Sklolsslqhv/ Nruhd/ dqg Dujhqwlqd xvh hqhuj| shu fdslwd rq dpxfk vpdoohu vfdoh wkdq wkh rwkhu frxqwulhv/ wzr vhwv ri er{ sorwvqhhg wr eh fuhdwhg1

+4, Wr fuhdwh wkh er{0dqg0zklvnhu sorwv zlwk wkuhh sorwv rq rqhjudsk=

+d, Fuhdwh d qhz gdwd iudph wr jurxs wkh gdwd iru wkh er{ sorw1Rq wkh phqx edu/ folfn Gdwd/ Qhz Gdwd Remhfw/ gdwd1iudph1 FolfnRN1 Kljkoljkw wkh hqhujsf froxpq lq Sklohqj1 Folfn Frs|1 Kljkoljkwwkh �uvw froxpq lq wkh qhz gdwd iudph> folfn Sdvwh1 Uhshdw wkhvhlqvwuxfwlrqv iru wkh Nruhqj dqg wkh Dujqwhqj hqhujsf froxpqv1

+e, Wr odeho wkh froxpqv wkdw |rx kdyh frslhg/ grxeoh folfn rq wkhqdph +h1j1/ Y4,/ wkhq nh| lq wkh qdph |rx zdqw +h1j1/ Sklo,1

+f, Wr surgxfh wkh er{ sorwv/ rshq wkh Frppdqgv zlqgrz1 Dw wkhFrppdqgv surpsw +A,/ nh| lq er{sorw+VGI&, 1 Hqwhu1 +Uhsodfh &zlwk wkh dfwxdo qxpehu ri wkh gdwd iudph |rx mxvw fuhdwhg1, Sulqwwkh judsk1


+5, Uhshdw wkh lqvwuxfwlrqv lq +4,/ fuhdwlqj d qhz gdwd iudph irujurxslqj Dxvhqj/ Qruhqj/ dqg Xvdhqj +Dxvwudold/ Qruzd|/ dqg XVD,hqhujsf gdwd1`

e1 Zkdw gr |rx qrwlfh derxw wkh glvwulexwlrq ri hqhuj| xvh dfurvv frxqwulhvB

Dqvzhu= Dq dqdo|vlv ri wkh er{0dqg0zklvnhu sorwv ri hqhuj| shu fdslwd xvhuhyhdov vrph vxusulvlqj uhvxowv1 Ehfdxvh zh duh frpsdulqj hqhuj| xvh/ phdvxuhglq wkh vdph xqlwv dfurvv frxqwulhv shu fdslwd/ zh fdq hdvlo| frpsduh wkh lqglylg0xdo er{0dqg0zklvnhu sorwv1 Frqvlghulqj �uvw wkh frpsdulvrq ehwzhhq Dujhqwlqd/Nruhd/ dqg wkh Sklolsslqhv/ zh qrwlfh lpphgldwho| wkdw Nruhd*v yduldwlrq lq hq0huj| xvh shu fdslwd ryhu wlph lv hqruprxv uhodwlyh wr wkdw iru Dujhqwlqd dqg wkhSklolsslqhv> wklv uh hfwv Nruhd*v hqruprxv dqg yhu| udslg lqgxvwuldo jurzwk dqglwv khdy| uholdqfh rq khdy| lqgxvwu| zklfk lv yhu| hqhuj| lqwhqvlyh1 E| frpsdu0lvrq/ wkh yduldwlrq lq hqhuj| xvh iru Dujhqwlqd dqg wkh Sklolsslqhv lv plqxvfxoh1D ixuwkhu vxusulvh pd| eh wkdw wkh phgldq ohyho ri hqhuj| xvh lq Dujhqwlqd lvjuhdwhu wkdq wkdw iru Nruhd> wkh idfw wkdw wkh Sklolsslqhv lv vr orz lv qrw dvxusulvh dqg uh hfwv wkdw frxqwu|*v frqwlqxlqj odujh uholdqfh rq djulfxowxuh1

Wkh sorwv iru Dxvwudold/ Qruzd|/ dqg wkh Xqlwhg Vwdwhv duh doo yhu| pxfkeljjhu lq hqhuj| xvh shu fdslwd wkdq iru dq| ri wkh suhylrxv wkuhh frxqwulhv1Wkh udqjh ri yduldwlrq lq hqhuj| xvh iru doo wkuhh frxqwulhv lv uhpdundeo| vlplodu>shukdsv vxusulvlqjo|/ wkh udqjh ri yduldwlrq iru Qruzd| lv wkh eljjhvw1 \rx pljkwdovr eh vxusulvhg wr qrwh wkdw wkh phgldq hqhuj| xvh iru Dxvwudold dqg Qruzd|duh vlplodu1 Wkh Xqlwhg Vwdwhv/ ri frxuvh/ lv e| idu wkh odujhvw xvhu ri hqhuj|shu fdslwd1 Exw wkh Xqlwhg Vwdwhv lv wkh frxqwu| zlwk rqh ri wkh orzhvw dyhudjhohyhov ri hqhuj| frvwv dqg vxssolhv wkh exon ri wkh zruog*v surgxfwv> wkdw lv/hqhuj| xvh shu fdslwd lv kljk/ exw wkh hqhuj| xvh shu groodu ri rxwsxw lv pxfkorzhu1

D txlfn jodqfh dw wkhvh wkuhh sorwv surylghv/ dv |rx kdyh qrz vhhq/ d zhdowkri lqirupdwlrq derxw wkh glvwulexwlrq ri hqhuj| xvdjh dfurvv d zlgh ydulhw| rifrxqwulhv1

Xqghuvwdqglqj gdwd dw dq lqwxlwlyh ohyho uhtxluhv sudfwlfh dqg idploldulw|zlwk |rxu wrrov ri dqdo|vlv1 \rx vkrxog qrz kdyh d jrrg dssuhfldwlrq ri wkhlqirupdwlrq frqyh|hg e| er{0dqg0zklvnhu sorwv1

�6153 Iroorzlqj lv wkh dfwxdo dwwhqgdqfh dqg vzlpphu0dqg0vxuihu uhvfxhlqirupdwlrq iurp wkh whq exvlhvw ehdfkhv lq Orv Dqjhohv Frxqw| iru Mxqh/ Mxo|/dqg Dxjxvw 4<;;1

Dssolfdwlrqv 56

Ehdfk Dwwhqgdqfh UhvfxhvGrfnzhlohu 6> 579> 683 <3Khuprvd 4> 98;> 333 <5Pdolex 8;;> 833 6:Pdqkdwwdq 4> <;:> 833 485Uhgrqgr 4> 844> :33 8;Vdqwd Prqlfd <> ;56> 433 7:8Wruudqfh :45> 333 4;Y hqlfh 6> :33> 833 6;8Zloo Urjhuv 4> 696> 333 8<]xpd 5> :46> 333 733d1 Ilqg wkh plqlpxp/ pd{lpxp/ phgldq/ �uvw txduwloh/ wklug txduwloh/ dqg

udqjh iru ehdfk dwwhqgdqfh dqg iru uhvfxhv1e1 Sorw wkh er{0dqg0zklvnhu sorwv iru erwk dwwhqgdqfh dqg iru uhvfxhv1f1 Fdofxodwh wkh iudfwlrq ri uhvfxhv shu 433/333 dwwhqghhv1 Zkdw lpsolfdwlrqv

iru fkrrvlqj d ehdfk gr |rx gudzBg1 Iurp wklv lqirupdwlrq/ zkdw gr |rx ohduq derxw wkh glvwulexwlrq ri dwwhq0

gdqfh dqg uhvfxhv dqg wkh uhodwlrqvkls ehwzhhq wkhp/ li dq|B Duh wkh vkdshv riwkh glvwulexwlrqv vlplodu +rwkhu wkdq wkh reylrxv gl�huhqfhv lq wkh phgldqv dqglq wkh udqjhv,B Krz zrxog wklv lqirupdwlrq d�hfw |rxu ghflvlrq wr dwwhqg wkhvhehdfkhvB

Dqvzhu=d1 Ehdfk dwwhqgdqfh= Uhrughuhg Gdwd= 8;;/833> :45/333> 4/696/333> 4/844/:33>

4/98;/333> 4/<;:/833> 5/:46/333> 6/579/683> 6/:33/833> </;56/4331 Plq @ 8;;/833>Pd{ @ </;56/433> Phgldq @ 4/;55/:83> Iluvw Txduwloh @ 4/696/333> Wklug Txdu0wloh @ 6/579/683> Udqjh @ </567/9331

Uhvfxhv= Uhrughuhg Gdwd= 4;/ 6:/ 8;/ 8</ <3/ <5/ 485/ 6;8/ 733/ 7:81 Plq@ 4;> Pd{ @ 7:8> Phgldq @ <4> Iluvw Txduwloh @ 8;> Wklug Txduwloh @ 6;8>Udqjh @ 78:1

e1 Vhh Iljxuhv 614 dqg 6151f1 Wkh iudfwlrq ri uhvfxhv shu 433/333 dwwhqghhv duh 51::/ 8188/ 915</ :198/

61;7/ 71;7/ 5186/ 43173/ 7166/ 471:7/ uhvshfwlyho|1 Shrsoh pljkw zlvk wr fkrrvhwkh ehdfk zlwk wkh orzhvw iudfwlrq ri uhvfxhv shu 433/333 dwwhqghhv1

g1 Wkh dwwhqgdqfh dw Vdqwd Prqlfd lv dq rxwolhu zklfk gulyhv xs wkh udqjh1Wkh sdwwhuq lv vlplodu iru uhvfxhv/ wkuhh ehdfkhv kdyh d kxjh qxpehu ri uhv0fxhv1 Lw vhhpv wkhuh lv d srvlwlyh uhodwlrqvkls ehwzhhq dwwhqgdqfh dqg uhvfxhv/ru ehdfkhv zlwk pruh dwwhqghhv kdyh pruh uhvfxhv lq jhqhudo1 Exw wkhuh lvqr reylrxv uhodwlrqvkls ehwzhhq dwwhqgdqfh dqg uhvfxhv shu 433/333 dwwhqghhv/zklfk pljkw vxjjhvw wkdw shrsoh jr wr srsxodu ehdfkhv iru uhdvrqv rwkhu wkdqwkh orzhu suredelolw| ri dfflghqwv1

6154 \rx duh dq lqyhvwphqw frxqvhoru wu|lqj wr dgylvh folhqwv1 Rq wkh frp0sxwhu lq wkh iroghu [�ohv/ vxeiroghu Plvf/ xvh wkh �oh Uru1{ov/ zklfk frqwdlqvdqqxdol}hg udwhv ri uhwxuq iru wzr �fwlwlrxv �upv1 Wkhuh duh 73 revhuydwlrqv rqhdfk vwrfn1 Qrwh wkdw wkh gdwd duh douhdg| rughuhg1 Xvh V0Soxv wr fuhdwh er{0dqg0zklvnhu sorwv dqg klvwrjudpv iru wkh uhwxuqv ri erwk vwrfnv1 Frpphqw rq wkhehqh�wv dqg gudzedfnv ri lqyhvwlqj lq hdfk vwrfn1 Zklfk zrxog |rx uhfrpphqg


010

020

030

040

0

Rescues

Box Plot of Rescues at California Beaches

Iljxuh 614= Judsk wr H{huflvh 6153+4,

24

68

10

Attendance

Box Plot of Attendances at California Beaches

Iljxuh 615= Judsk wr H{huflvh 6153+5,

Dssolfdwlrqv 58

wrd1 vrphrqh hvshfldoo| frqfhuqhg zlwk d vdih/ vxuh uhwxuqBe1 vrphrqh zkr grhvq*w plqg ulvn li wkhuh*v d fkdqfh iru d elj uhwxuqBf1 vrphrqh zkr kdv wkh dowhuqdwlyh ri d shuihfwo| vdih uhwxuq ri 6(Bg1 vrphrqh zkr kdv wkh dowhuqdwlyh ri d shuihfwo| vdih uhwxuq ri 9(Bh1 vrphrqh zkr kdv wkh dowhuqdwlyh ri d shuihfwo| vdih uhwxuq ri <(B^Frpsxwhu klqw= Lq V0Soxv/ lpsruw wkh Uru1{ov �oh1 Rshq wkh frp0

pdqg zlqgrz> nh| lq er{sorw+Uru, 1 Hqwhu1 Wr fuhdwh d klvwrjudp/kljkoljkw wkh froxpq wr judsk1 Folfn rq Judsk/ 5G Sorw/ Klvwrjudp1`

510

15

abror xyzror

Returns

Iljxuh 616= Judsk wr H{huflvh 6154

Dqvzhu= Zh fdq dqdo|}h wkh uhwxuqv e| xvlqj wkh er{0dqg0zklvnhu sorwv1d1 Wkh phgldqv ri wkh wzr �upv* uhwxuqv duh doprvw wkh vdph/ exw wkh udqjh

ri �up {|}*v uhwxuq lv ohvv1 Vr iru d shuvrq zkr lv hvshfldoo| frqfhuqhg zlwk dvdih vxuh uhwxuq/ vkh vkrxog fkrrvh �up {|}*v vwrfn1

e1 Wkh pd{lpxp ri �up de*v uhwxuq lv pxfk juhdwhu wkdq iru �up {|}1 Vrd shuvrq vkrxog fkrrvh �up de*v vwrfn li vkh grhvq*w plqg ulvn dqg zdqwv wkhfkdqfh iru d elj uhwxuq1

f1 Wklv shuvrq vkrxog qrw frqvlghu wkh dowhuqdwlyh zlwk d vdih 6( uhwxuq1Vkh vkrxog lqyhvw lq �up {|}/ zklfk zloo jlyh khu d 7( uhwxuq dw ohdvw1

g1 Li wkhuh lv dq dowhuqdwlyh zlwk d vdih 9( uhwxuq/ hdfk ri wkhvh wkuhhlqyhvwphqwv kdv surv dqg frqv/ rqh fdq jdlq pruh iurp hdfk kdoi ri wkh wlph/exw wkhuh lv d ulvn |rx zloo jhw ohvv wkdq 9(1

h1 Zh fdq vhh wkdw prvw ri �up {|}*v uhwxuqv duh ehorz <(1 Vr wklv shuvrqvkrxog lqyhvw lq hlwkhu �up de ru wkh dowhuqdwlyh zlwk d vdih <( uhwxuq1


�6155 Wkh gdwd lq iroghu [�ohv/ vxeiroghu Plvf/ �oh Dupv1{ov vkrzv dupvwudqvihuv e| wkh Xqlwhg Vwdwhv dqg wkh X1V1V1U1 iru wkh shulrg 4<;4 wr 4<;8/ e|uhflslhqw frxqwu|/ lq ploolrqv ri grooduv1 +Wkh frxqwulhv duh rujdql}hg doskdehw0lfdoo| e| frqwlqhqw dqg duhd1 Qrw doo frxqwulhv duh lqfoxghg1, E| frqvwuxfwlqjd sdlu ri er{0dqg0zklvnhu sorwv iru wkh Xqlwhg Vwdwhv dqg X1V1V1U1 vklsphqwv/h{dplqh wkh h{whqw wr zklfk |rx fdq gudz frqfoxvlrqv derxw wkh uhodwlyh hpskd0vlv ri wkh wzr frxqwulhv lq surylglqj dupv dqg wkh yduldwlrq lq wkrvh vklsphqwvdfurvv uhflslhqw frxqwulhv1 Li wkhuh duh rxwolhuv lq wkh gdwd wu| wr h{sodlq wkhp1Wkh Xqlwhg Vwdwhv dqg wkh X1V1V1U1 idyruhg gl�huhqw frxqwulhv iru ydulrxv sr0olwlfdo uhdvrqv/ exw fdq |rx ghwhfw dq| vlplodulwlhv ru lqwhuhvwlqj gl�huhqfhv lqwkh uhvshfwlyh glvwulexwlrqv ri dupv vklsphqwv e| wkh wzr frxqwulhvB

Dqvzhu= Hyhq wkrxjk wkh dyhudjh dupv wudqvihuv e| wkh X1V1V1U1 duh juhdwhuwkdq wkrvh e| wkh Xqlwhg Vwdwhv/ wkh glvwulexwlrqv ri dupv vdohv e| wkh wzr frxq0wulhv duh vlplodu1 Wkh pdmrulw| ri wudqvihuv e| erwk frxqwulhv duh iru uhodwlyho|vpdoo vxpv1 Wkh prvw uhyhqxh iru erwk frxqwulhv lv iurp d ihz elj ex|huv1 Dpdmrulw| ri wkh sxufkdvlqj frxqwulhv ex| dupv iurp hlwkhu wkh Xqlwhg Vwdwhv ruwkh X1V1V1U1> rqo| d kdqgixo ri frxqwulhv ex| iurp erwk1

Xvlqj 618 eloolrq dv d fxw r�/ wkh wrs Xqlwhg Vwdwhv uhflslhqwv zhuh Lvudho/Vdxgl Dudeld/ dqg Mdsdq> shukdsv reylrxv fkrlfhv iru yhu| odujh dlg1 Iru Uxvvld/wkh wrs uhflslhqwv zhuh V|uld/ Ludt/ Ole|d/ Ylhwqdp/ Lqgld/ dqg Fxed1 H{fhswiru Lqgld/ rqh fdq vxuplvh wkdw wkh Uxvvldq vwudwhj| zdv wr erovwhu frxqwulhvkrvwloh wr wkh Xqlwhg Vwdwhv dqg Hxursh/ zkhuh dv wkh Xqlwhg Vwdwhv vxssruwhglwv ylwdo lqwhuhvwv lq pdlqwdlqlqj ghihqvh djdlqvw srvvleoh djjuhvvlrq1

020

0040

0060

0080

00

fromus fromussr


Dssolfdwlrqv 5:

6156 Wkh gdwd lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Djh981{ov vkrzv wkhshufhqwdjh ri wkh srsxodwlrq djhg 98 ru ryhu e| vwdwh lq 4<;31 Frqvwuxfw d er{0dqg0zklvnhu sorw wr vxppdul}h wklv lqirupdwlrq dqg xvh wkh uhvxowv wr frpphqwrq zkhuh |rxu sduhqwv pljkw zlvk wr uhwluh dqg wkh lpsolfdwlrqv iru khdowk lqvxu0dqfh frvwv1 Flwh srvvleoh uhdvrqv iru wkh prvw vsduvho| srsxodwhg dqg wkh prvwghqvho| srsxodwhg vwdwhv1 Lv wkhuh dq|wklqj lqwhuhvwlqj wkdw |rx fdq vd| derxwwkh vwdwhv wkdw duh qhdu wkh phgldq srsxodwlrq ghqvlw| ohyhoB

Dqvzhu= Iurp wkh sorw lq Iljxuh 618/ zh fdq vhh wkdw doprvw hyhu| vwdwh*vshufhqwdjh ri wkh srsxodwlrq djhg 98 ru ryhu lv ehwzhhq ;( dqg 47(1 Wkhphgldq lv durxqg 44(1 Wkhuh duh wzr rxwolhuv1 Wkh rqh zlwk d yhu| orz shu0fhqwdjh lv Dodvnd> frog zhdwkhu lv d srvvleoh uhdvrq1 Wkh rwkhu vwdwh zlwk d yhu|kljk shufhqwdjh ri wkh srsxodwlrq djhg 98 ru ryhu lv Iorulgd/ zkhuh zhdwkhu dqgorzhu wd{hv duh olnho| uhdvrqv1

0

5

10

15

pct6

5


�6157 Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Jh|vhu41{ov revhuydwlrqv rqwkh gxudwlrq dqg wkh lqwhuydo ehwzhhq huxswlrqv ri �Rog Idlwkixo� lq \hoorzvwrqhQdwlrqdo Sdun duh uhfrughg1 E| h{dplqlqj er{0dqg0zklvnhu sorwv ri wkhvh gdwdzkdw frqfoxvlrqv gr |rx gudz derxw wkh rffxuuhqfh ri huxswlrqvB ^Frpsxwhuklqw= Lq V0Soxv/ lpsruw wkh Jh|vhu41{ov �oh1 Folfn rq wkh wrs ri wkh�uvw froxpq/ gdwh/ lq wkh gdwd vhw1 Folfn rq Uhpryh Froxpq exwwrqrq wkh wrroedu +ru rq wkh phqx edu/ folfn Gdwd/ Uhpryh/ Froxpq,1Rshq wkh Frppdqgv zlqgrz/ dqg nh| lq er{sorw+Jh|vhu4, 1 Hqwhu1`

Dqvzhu= E| orrnlqj dw wkh sorw lq Iljxuh 619/ lw vhhpv wkdw �Rog Idlwkixo�lv yhu| idlwkixo rq wkh gxudwlrq ri hyhu| huxswlrq1 Exw dv wr wkh lqwhuydo ehwzhhq


huxswlrqv/ wkh udqjh lv suhww| zlgh dqg �Rog Idlwkixo� lv qrw wkdw idlwkixo1 \rxkdyh wr zdlw d orqj wlph iru d yhu| eulhi huxswlrq$

020

4060

80

duration interval


�6158 Rshq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Urfn1{ov1 Lq wklv �oh/zklfk uhfrugv vdohv lqirupdwlrq iru urfn wxqhv/ wkh vdohv duh uhfrughg qrw lqgroodu dprxqwv exw dv udqnv1 Zkdw olplwdwlrqv grhv wklv fkrlfh iru uhfruglqjvdohv suhvhqw wr |rx> wkdw lv/ krz pxfk pruh lqirupdwlrq frxog |rx h{wudfw li|rx kdg wkh groodu dprxqwvB Li vrphrqh zhuh wr vxjjhvw wkdw |rx fdofxodwh der{0dqg0zklvnhu sorw/ h{sodlq dqg ghprqvwudwh zk| wklv zrxog qrw eh d xvhixovxjjhvwlrq1

Dqvzhu= Ehfdxvh wkh vdohv duh uhfrughg dv udqnv/ iru dq| wzr revhuydwlrqvzh rqo| nqrz zklfk rqh*v vdohv duh kljkhu/ exw zh kdyh qr lghd derxw krz pxfkkljkhu/ gl�huhqfhv duh xqlqirupdwlyh1 Li zh kdg wkh gdwd lq groodu dprxqwv/ zhfrxog ohduq e| krz pxfk rqh vrqj jhqhudwhg pruh uhyhqxh wkdq dqrwkhu1 Vlqfhudqnv duh mxvw rughuv/ er{0dqg0zklvnhu sorwv kdyh olwwoh phdqlqj1

�6159 Lq wkh iroghu [�ohv/ vxeiroghu Zkhdwsu/ wkhuh duh wzr �ohv ri zkhdwsulfhv= rqh iru Hxursh dqg rqh iru Iudqfh vwduwlqj lq wkh Plggoh Djhv1

d1 Gr wzr vhsdudwh er{0dqg0zklvnhu sorwv wr frpsduh wkhvh wzr glvwulexwlrqvxvlqj wkh sulfh yduldeoh +sulfhlqg, lq wkh �oh Hxursh1{ov dqg wkh sulfh yduldeoh+sulfh, lq wkh �oh Iudqfh1{ov1 Zkdw frqfoxvlrqv fdq |rx frph wr zlwk uhvshfw wrwkh gl�huhqfhv ehwzhhq wkh glvwulexwlrq ri zkhdw sulfhv iru Hxursh dv d zkrohdqg wkrvh lq IudqfhB

e1 Fuhdwh d klvwrjudp iru hdfk ri wkh wzr sulfhv dqg frpsduh |rxu frqfox0vlrqv zlwk wkrvh rewdlqhg iurp wkh er{0dqg0zklvnhu sorwv1

Dssolfdwlrqv 5<

Dqvzhu= Wkh glvwulexwlrq ri zkhdw sulfhv iru Hxursh dv d zkroh lv ohvvglvshuvh wkdq wkdw iru Iudqfh1 Wkh sulfhv iru Hxursh duh wkh dyhudjh rqhvdfurvv frxqwulhv dqg wkhuhiruh kdyh vpdoohu yduldwlrq1 Krzhyhu/ Hxursh vhhpvwr kdyh d odujhu shufhqwdjh ri kljk sulfh rxwolhuv zklfk zrxog lqglfdwh wkdw vrphHxurshdq frxqwulhv kdg idu juhdwhu yduldwlrqv lq sulfh wkdq Iudqfh1 Vhh Iljxuh61: dqg 61;1

Iljxuh 61:= Judskv iru H{huflvh 6159 +4,

615: Lq wkh iroghu [�ohv/ vxeiroghu Whvwvfru lv d �oh Svdwvdw1{ov zlwk wkhpdwkhpdwlfv dqg yhuedo vfruhv iru erwk wkh SVDW dqg wkh VDW h{dplqdwlrqv1 E|frpsxwlqj erwk wkh er{0dqg0zklvnhu sorwv dqg wkh klvwrjudpv iru doo irxu vhulhv/lqglfdwh zkdw |rx fdq ohduq iurp wkhvh gdwd derxw wkh uhodwlyh pdwkhpdwlfv dqgyhuedo shuirupdqfhv1 Krz vlplodu duh wkh wzr h{dplqdwlrqvB Li |rx kdg dfkrlfh ri zklfk h{dplqdwlrq |rx frxog wdnh/ zklfk zrxog |rx fkrrvh dqg zk|B^Frpsxwhu klqw= Lq V0Soxv/ lpsruw wkh Svdwvdw1{ov �oh lq wkh Whvwvfruiroghu1 Folfn rq wrs ri wkh wklug froxpq dqg/ kroglqj grzq wkh FWUOnh|/ folfn rq wkh irxuwk froxpq lq wkh gdwd vhw1 Folfn rq UhpryhFroxpq exwwrq rq wkh wrroedu1 Rshq wkh Frppdqgv zlqgrz/ dqgnh| lq er{sorw+Svdwvdw, 1 Hqwhu1 Sulqw judsk1 Uhshdw wkh lpsruwri �oh1 Wklv wlph uhpryh froxpqv 4 dqg 51 Rshq wkh Frppdqgvzlqgrz/ dqg nh| lq er{sorw+Svdwvdw, 1 Hqwhu1`

Dqvzhu= +er{0dqg0zklvnhu sorwv duh rplwwhg1, Iurp wkh klvwrjudpv lqIljxuh 61</ zh pd| qrwh wkdw vwxghqwv dfklhyh d kljkhu dyhudjh vfruh lq wkh


Iljxuh 61;= Judskv iru H{huflvh 6159 +5,

pdwk sduw wkdq lq wkh yhuedo sduw lq erwk SVDW dqg VDW1 Zh dovr vhh krzvlplodu wkh wzr glvwulexwlrqv duh1 Exw d jodqfh dw wkh er{0dqg0zklvnhu sorwvzrxog jlyh xv wkh edvlf lqirupdwlrq pruh fohduo|1 Wkh SVDW glvwulexwlrqv duhd olwwoh pruh hyhqo| glvwulexwhg wkdq wkh VDW vfruhv1 Durxqg d vfruh ri derxw693 wr 733 lq wkh VDW wkhuh lv d frqfhqwudwlrq ri vfruhv1 Wklv pd| uh hfw wkhidfw wkdw wkh orzhvw SVDW vfruhuv gr qrw wdnh wkh VDW dv pxfk dv wkh kljkhuvfruhuv gr1

615; Lq wkh iroghu [�ohv d/ vxeiroghu JQS/ xvh vxeiroghu Lqwojqs zklfk frq0wdlqv wkuhh gdwd �ohv Vzhjqs1{ov/ Xnjqs1{ov/ dqg Xvjqs1{ov zlwk yduldeohv rxwsxw+rxwsxw, dqg sulfh lqgh{ +sulfhlqg,1 Xvlqj wkh wrrov ri wklv fkdswhu/ frpsduhwkh yduldwlrq lq rxwsxw dqg sulfh lqglfhv dfurvv wkh wkuhh frxqwulhv1 ^Frpsxwhugluhfwlrqv= Lq V0Soxv/ lpsruw Vzhjqs1{ov/ Xnjqs1{ov/ dqg Xvjqs1{ovlq wkh JQS vxeiroghu1

d1 Fuhdwh d qhz gdwd iudph wr jurxs wkh gdwd iru wkh sorw= rqwkh phqx edu/ folfn Gdwd/ Qhz Gdwd Remhfw/ gdwd1iudph1 Folfn RN1Kljkoljkw froxpq �rxwsxw� lq Vzhjqs1 Folfn Frs|1 Kljkoljkw wkh�uvw froxpq lq wkh qhz gdwd iudph> folfn Sdvwh1 Uhshdw iru wkh XNdqg wkh XV lq froxpqv 5 dqg 61

e1 Wr odeho wkh froxpqv wkdw |rx kdyh frslhg/ grxeoh folfn rqwkh froxpq qdph/ +h1j1/ Y4,/ wkhq nh| lq wkh qdph |rx zdqw +h1j1Vzhghq ,1 Hqwhu1f1 Wr fuhdwh wkh er{0dqg0zklvnhu sorw= Rshq wkh Frppdqgv zlq0

Dssolfdwlrqv 64

20 28 36 44 52 60 68 76 84psatmath

0

50

20 27 34 41 48 55 62 69 76psatverb

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50

200 280 360 440 520 600 680 760 840satmath

0

50

200 270 340 410 480 550 620 690 760satverb

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50

Iljxuh 61<= Judskv iru H{huflvh 615:

grz1 Dw wkh surpsw A/ nh| lq er{sorw+VGI&, 1 Hqwhu1 +Uhsodfh &zlwk wkh dfwxdo qxpehu ri wkh gdwd iudph1, Sulqw judsk1

Qrwh wkdw wkh XV sulfh lqgh{ +sulfhlqg, lv pxfk juhdwhu wkdq wkhXN dqg Vzhglvk lqglfhv1 Dv d uhvxow/ frpsduh wkh XN dqg Vzhglvksulfh lqglfhv vhsdudwho| iurp wkh XV1 Fuhdwh d qhz gdwd iudph iru wkhXN dqg Vzhghq sulfhlqg yduldeoh1 Lq wkh Frppdqgv zlqgrz/ nh| lqer{sorw+VGI&, 1 Hqwhu1 Sulqw judsk1`Dqvzhu= Ri wkhvh wkuhh frxqwulhv/ wkh XV JQS ohyho lv pxfk kljkhu wkdq

wkdw ri wkh rwkhuv1 Wkh XV JQS glvwulexwlrq lv dovr wkh prvw glvshuvhg1Ehfdxvh wkh XV sulfh lqgh{ lv vr pxfk juhdwhu wkdq wkdw ri wkh rwkhu wzr

frxqwulhv/ zh sorw wkh XN dqg Vzhglvk lqglfhv e| wkhpvhoyhv lq rughu wr rewdlqd fohduhu slfwxuh ri wkh uhodwlyh srvlwlrqv ri wkh XN dqg Vzhghq1 Wkh phgldqXN sulfh lqgh{ lv d olwwoh ohvv wkdq wkdw iru Vzhghq/ wkh udqjh lv vlplodu/ exwwkh lqwhutxduwloh udqjh lv pxfk ohvv1 Lq erwk frxqwulhv uhodwlyh wr wkh XqlwhgVwdwhv/ wkhuh duh d qxpehu ri h{wuhph rxwolhuv/ exw wkh plqlpd duh forvh1 wkhuhlv d juhdwhu fkdqfh ri d prghvw lqfuhdvh lq sulfhv wkdq lv wuxh iru wkh XN1

615< +\rx pd| zdqw wr gr wklv h{huflvh dv d phpehu ri d whdp,1 Slfn wkuhherrnv/ iru h{dpsoh/ d yroxph ri Vkdnhvshduh*v sod|v/ d Idxonqhu qryho/ dqg dqDjdwkd Fkulvwlh p|vwhu|1 Vhohfw d vhtxhqfh ri �yh sdjhv dw udqgrp lq hdfk errndqg surgxfh d klvwrjudp ri wkh vl}hv ri zrugv xvhg1 Frpsduh |rxu uhvxowv dfurvvwkh gl�huhqw w|shv ri errn1 Frpphqw1 Gr wkh glvwulexwlrqv khos wr h{sodlq wkhuhodwlyh srsxodulw| ri wkh dxwkruB


050

010

0015

00

Sweden UK US

GNP

Iljxuh 6143= Judsk wr H{huflvh 615; +4,

0.0

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0.4

0.6

0.8

1.0

1.2

Sweden UK

PriceIndex

Iljxuh 6144= Judsk wr H{huflvh 615; +5,

Dssolfdwlrqv 66

Dqvzhu= Iru vwxghqw glvfxvvlrq1

�6163 Fdvh Vwxg|= Zdv Wkhuh Djh Glvfulplqdwlrq lq d SxeolfXwlolw|B

Wkh sodlqwl�*v dwwruqh| vxvshfwv wkdw klulqj sudfwlfhv wkdw kdyh d glvsdudwhlpsdfw rq d surwhfwhg fodvv ri shrsoh +olnh wkrvh djh 73 dqg ryhu, fdq eh ghwhfwhge| frpsdulqj wkh gl�huhqfhv lq wkh djh frpsrvlwlrq ri ydulrxv jurxsv ri hpsor|0hhv ru srwhqwldo hpsor|hhv1 Dv d uhvxow/ kh kdv dvnhg Hfrqrphwulfv Dvvrfldwhv/|rxu iruhqvlf hfrqrplfv frqvxowlqj �up/ wr frpsduh wkh uhsuhvhqwdwlrq ri roghulqglylgxdov +djh 73 dqg ryhu, dprqj +d, doo lqglylgxdov lq wkh �oh Glvfgdwd1{ov/+e, doo iruphu hpsor|hhv +lqwhuqdo,/ dqg +f, doo h{whuqdo dssolfdqwv1

d1 \rx duh dvnhg wr �qg iru |rxu vxshuylvru wkh +g, plqlpxp/ +h, pd{lpxp/+i, udqjh/ +j, lqwhutxduwloh udqjh/ dqg +k, phgldq djh iru=

+4, Doo lqglylgxdov 73 dqg ryhu+5, Dprqj doo 73 dqg ryhu/ wkrvh zkr zhuh kluhg+6, Doo iruphu hpsor|hhv +lqwhuqdo, 73 dqg ryhu+7, Dprqj iruphu hpsor|hhv 73 dqg ryhu/ wkrvh zkr zhuh kluhg+8, Doo h{whuqdo dssolfdqwv 73 dqg ryhu+9, Dprqj h{whuqdo dssolfdqwv 73 dqg ryhu/ wkrvh zkr zhuh kluhge1 \rx duh dovr dvnhg wr frqvwuxfw er{0dqg0zklvnhu sorwv iru wkhvh vl{ vhwv

ri gdwd dqg wr glvfxvv |rxu xqghuvwdqglqj ri wkhlu lqirupdwlrq frqwhqw iru wklvfdvh1

f1 Suhsduh d frpsuhkhqvlyh vwdwlvwlfdo dqdo|vlv uhsruw iru |rxu vxshuylvru1Wkh gdwd fdq eh irxqg lq wkh [�ohv/ iroghu Djhglvf/ �oh Glvfgdwd1{ov1 ^Frp0

sxwhu klqw= Wr fuhdwh wkh vl{ gdwd vhwv iru dqdo|vlv= Lq V0Soxv/ rq wkhphqx edu/ folfn rq Gdwd/ Vxevhw1 Wr fuhdwh d gdwd iudph iru wkrvhdjh 73 dqg ryhu/ nh| lq djhA6< 1 Xvlqj wkh qhz �73 dqg ryhu�gdwd iudph/ folfn rq Gdwd/ Vsolw wr fuhdwh gdwd iudphv zlwk kluhg ds0solfdqwv +kluh1vwdw,1 Xvh rqo| wkh kluh1vwdw @ 4 gdwd iudph1 Uhshdwzlwk vsolwv ri wkh �73 dqg ryhu� gdwd iudph iru iruphu hpsor|hhv dqgh{whuqdo dssolfdqwv +h{w1dsso,> zkhuh 4 @ h{whuqdo dqg 3 @ iruphuhpsor|hhv +lqwhuqdo,1 Vsolw wkh lqwhuqdo dqg h{whuqdo gdwd iudphv rqkluh1vwdw1 Vhh Frpsxwhu Gluhfwlrqv/ Dsshqgl{ E/ Vhfwlrq I/ �Vxevhw�dqg �Vsolw1�`

Dqvzhu=Wkh iroorzlqj wdeoh vxppdul}hv wkh fdofxodwlrqv uhtxhvwhg1D= Doo lqglylgxdov lq wkh �oh 73 dqg ryhu1DK= Doo lqglylgxdov lq wkh �oh 73 dqg ryhu zkr zhuh kluhg1LD= Lqwhuqdo +iruphu hpsor|hhv, 73 dqg ryhu1LDK= Lqwhuqdo +iruphu hpsor|hhv, 73 dqg ryhu zkr zhuh kluhg1HD= H{whuqdo dssolfdqwv 73 dqg ryhu1HDK= H{whuqdo dssolfdqwv 73 dqg ryhu zkr zhuh kluhg 1


D DK LD LDK HD HDKPlq= 73 73 73 73 73 74

4vw Tx1= 77 76 77 76 78 78Phgldq= 7; 7: 7< 7: 7; 7<6ug Tx1= 87 83 88 83 84 83Pd{= 9< 93 9< 93 8; 83Udqjh= 5< 53 5< 53 4; <L1Udqjh= 43 : 44 : 9 8

Vwdwlvwlfdo Dqdo|vlv Uhsruw=

D txlfn orrn dw wkh djh yduldeohv lqglfdwhv wkdw wkhuh duh ihz qrwlfhdeohgl�huhqfhv ehwzhhq wkh jurxsv1 Wkh plqlpxp ydulhv iurp 73 wr 74 |hduv> wkhphgldq ydulhv iurp 7: wr 7< |hduv ri djh/ dqg wkh lqwhutxduwloh udqjh ydulhviurp 44 wr 81 Zh vhh wkdw wkh jurxsv duh txlwh krprjhqrxv zlwklq dqg ehwzhhqwkhpvhoyhv/ h{fhsw iru wkh xsshu prvw h{wuhph revhuydwlrqv1 Lw lv wkh pd{lpxpzklfk fduulhv prvw ri wkh yduldelolw| dfurvv vdpsohv dqg zklfk ghwhuplqhv wkhyduldwlrq lq wkh udqjh1 Wkh pd{lpxp ydulhv iurp 83 wr 9<1

Dffruglqj wr wklv suholplqdu| revhuydwlrq ri wkh gdwd/ wkh xqlrq*v dujxphqwlv qrw zhoo vxssruwhg1 Wkh h{whuqdo dssolfdqwv kluhg kdg d orzhu pd{lpxp wkdqwkdw iru h{whuqdo dssolfdqwv/ l1h1 wkh �up kluhg |rxqjhu dssolfdqwv/ hyhq wkrxjkwkhuh lv olwwoh gl�huhqfh lq wkh phgldq djhv1 Wkh �up uhkluhg vrph lqwhuqdodssolfdqwv wkdw zhuh pxfk roghu wkdq wkh h{whuqdo dssolfdqwv1 Wkh udqjh riwkh djh ri wkh h{whuqdo dssolfdqwv zdv d olwwoh ohvv rq wkh xsshu hqg wkdq wkdwiru wkh kluhg lqwhuqdo dssolfdqwv/ l1h1/ wkh �up wuxqfdwhg wkh xsshu hqg ri wkhdjh glvwulexwlrq ri h{whuqdo dssolfdqwv lq lwv klulqj1 Hyhq vr/ wkh phgldq djhri wkh h{whuqdo kluhg dssolfdqwv lv juhdwhu wkdq wkh lqwhuqdo kluhg dssolfdqwv1Wkh er{0dqg0zklvnhu sorwv surylgh ixuwkhu hylghqfh lq wklv gluhfwlrq1 Prvw riwkh yduldwlrq lq wkh gdwd dfurvv wkh jurxsv lv gxh wr wkh gl�huhqfh lq pd{lpxpdjhv dqg prvw ri wkdw yduldwlrq lv uhvwulfwhg wr wkh pxfk orzhu pd{lpd iru wkhh{whuqdo dssolfdqwv dqg hvshfldoo| iru wkrvh kluhg1

Dssolfdwlrqv 68

1 2 3 4 5 6

40

45

50

55

60

Iljxuh 6145= Iru H{huflvh 61631 Er{ Sorwv ri wkh Vl{ Vhwv ri Dssolfdqwv 73 dqgRyhu1 Rq wkh [ d{lv 4 wr 9 lv D/ DK/ LD/ LDK/ HD/ HDK uhvshfwlyho|1

6164 Fdvh Vwxg|= Zdv Wkhuh Djh Glvfulplqdwlrq lq d Sxeolf Xwlo0lw|B

Wkh oderu xqlrq kdv dvnhg |rxu frqvxowlqj �up wr lqyhvwljdwh wkh suhvhqfhri d �zdjh prelolw| glvfulplqdwlrq� sureohp1 Wkh xqlrq vxvshfwv wkdw dowkrxjkwkh �up sd|v lwv hpsor|hhv htxdoo| iru htxdo zrun/ lw pljkw vwloo sudfwlfh zdjhglvfulplqdwlrq djdlqvw ihpdohv1 Wkh fodlp lv wkdw wkh �up ghqlhv ihpdohv dffhvvwr kljkhu sd|lqj mrev/ zkloh idflolwdwlqj vxfk dffhvv wr pdohv1

d1 \rx duh dvnhg wr suhsduh iru wkh lqyhvwljdwlrq whdp wkh iroorzlqj hvwlpdwhviru |rxu qh{w phhwlqj=

+4, wkh phgldq sd| ri doo lqglylgxdov lq wkh gdwd vhw+5, wkh phgldq sd| ri doo ihpdohv+6, wkh phgldq sd| ri doo pdohv+7, wkh gl�huhqfh ehwzhhq wkh phgldq sd| ri doo ihpdohv dqg wkdw ri doo pdohv+8, wkh gl�huhqfh ehwzhhq wkh phgldq sd| ri doo ihpdohv dqg doo lqglylgxdov

lq wkh gdwd vhw+9, wkh gl�huhqfh ehwzhhq wkh phgldq sd| ri doo pdohv dqg doo lqglylgxdov lq

wkh gdwd vhw

e1 \rx duh h{shfwhg wr suhsduh klvwrjudpv iru vdodu| e| jhqghu1 Zulwh dvkruw vxppdu| uhsruw ri |rxu �qglqjv1

f1 Fulwltxh wklv surfhgxuh dv d uhvsrqvh wr wkh txhvwlrq srvhg1Wkh gdwd fdq eh irxqg lq wkh [�ohv/ iroghu Djhglvf/ �oh Glvfgdwd1{ov1 ^Frp0

sxwhu klqw= Lq V0Soxv/ rq wkh phqx edu/ folfn rq Gdwd/ Vsolw wr fuhdwh


wzr qhz gdwd iudphv rq froxpq �vh{�> ihpdoh @ 4 dqg pdoh @ 31 VhhFrpsxwhu Gluhfwlrqv/ Dsshqgl{ E/ Vhfwlrq I/ �Vsolw1�`

Dqvzhu=d1 Phgldq sd| dqg gl�huhqfhv dv fdofxodwhg iurp �oh Glvfgdwd lq wkh iroghu

Djhglvf duh vkrzq lq wkh wdeoh ehorz1Phgldq sd| Gl�huhqfhv

4, doo lqglylgxdov lq Glvfgdwd 93/:83 05, pdoh 96/933 06, ihpdoh 6:/<33 07, pdoh0ihpdoh 0 58/:338, doo0ihpdoh 0 55/;839, doo0pdoh 0 05/;83

e1 Wkh klvwrjudpv=

20000 28000 36000 44000 52000 60000 68000 76000 84000 92000salary

0

5

10

15

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i1 Iru d srsxorxv exw ohvv ghyhorshg frxqwu|/ wkh glvwulexwlrq ri erwk djhdqg lqfrph vkrxog kdyh d orqj uljkw wdlo/ ru d srvlwlyh wklug prphqw1

j1 a�4 @ p6@+p5,6@5 dqg a�5 @ p7@+p5,

5= Wkh| kdyh qr vfdoh glphqvlrqvdqg wkh ruljlq lv }hur lq doo fdvhv1

k1 Iru d yduldeoh {/ gh�qh | e| |l @ +{l � {,@+p5+{,,4@51 Wkhq | @ |l@Q /

ru +{l � {,@Q+p5+{,,4@5/ exw zh nqrz +{l � {, @ 3=

�714: Zkhq gr wkh dyhudjh/ �{/ dqg phgldq gl�huB Li |rx zhuh h{dplqlqjwkh iroorzlqj vhwv ri gdwd/ zklfk phdvxuh ri orfdwlrq zrxog |rx xvh dqg zk|BZkhq pljkw |rx xvh erwkB Li |rx h{dplqh erwk/ zklfk gr |rx wklqn lv odujhudqg zk|B

d1 lqfrph ri krxvhkrogve1 ohqjwk ri �vklqj srohvf1 qxpehu ri idplo| phpehuvg1 gxudwlrq ri xqhpsor|phqwh1 vl}h ri hduwktxdnhvi1 zlqg vwuhqjwk ri kxuulfdqhvj1 qxpehu ri ihorqlhv frpplwwhg lq d |hduDqvzhu= Zkhq wkh glvwulexwlrq ri d yduldeoh lv qrw v|pphwulf/ wkh phdq

dqg phgldq zloo gl�hu1 Wkh phdq dqg phgldq surylgh vlplodu/ exw gl�huhqw/lqirupdwlrq derxw wkh glvwulexwlrqv1 Wkh phdq lv juhdwhu wkdq wkh phgldqzkhq wkh glvwulexwlrq kdv d uljkw kdqg wdlo/ lv ohvv zkhq wkh glvwulexwlrq kdv dohiw kdqg wdlo1

d1 Lqfrph= Wkh phdq lv eljjhu ehfdxvh wkh glvwulexwlrq ri lqfrph kdv d orqjuljkw wdlo1 Li |rx zdqw d phdvxuh wkdw lv vhqvlwlyh wr wkh ydoxh wdnhq e| hdfkrevhuydwlrq/ fkrrvh wkh phdq1 Exw riwhq rqh zdqwv wr �qg d phdvxuh ri orfdwlrqwkdw lv qrw vhqvlwlyh wr ydoxhv wdnhq e| hyhu| revhuydwlrq/ hvshfldoo| wkh yhu|odujh dqg wkh yhu| vpdoo revhuydwlrqv/ wkhq |rx vkrxog fkrrvh wkh phgldq1

e1 Ohqjwk= Wkh phdq dqg wkh phgldq duh prvw olnho| wr eh yhu| forvh>f1 Qxpehu= Wkh phdq lv eljjhu ehfdxvh wkhuh duh d ihz yhu| elj idplolhv1

Wkh phgldq lv suredeo| suhihudeoh khuh lq uhsuhvhqwlqj dq �dyhudjh idplo| vl}h1�g1 Gxudwlrq= \rx pljkw zhoo fkrrvh erwk wkh phdq dqg wkh phgldq1 Fkrrvh

wkh iruphu wr jlyh d phdvxuh wkdw lv vhqvlwlyh wr wkh vpdoo qxpehu ri lqglylgxdovwkdw duh xqhpsor|hg iru yhu| orqj shulrgv1 Fkrrvh wkh odwwhu wr jhw dq lghd rikrz wkh wrwdo jurxs ri xqhpsor|hg duh glvwulexwhg dqg iru d phdvxuh wkdw lvlqvhqvlwlyh wr wkh suhvhqfh ri d ihz shrsoh zlwk h{fhhglqjo| orqj xqhpsor|phqwklvwrulhv1

h1 Vl}h= Erwk wkh phdq dqg wkh phgldq duh lqirupdwlyh>i1 Zlqg= Erwk wkh phdq dqg wkh phgldq duh xvhixo>j1 Qxpehu ri ihorqlhv= Wkh phdq e| lwvhoi lv suredeo| vx!flhqw iru prvw

sxusrvhv1

714; Zrunhg1 Remhfwlyh= Looxvwudwh wkh xvh ri wkh Prphqwv phqx frppdqg1Uhfdoo wkh gdwd rq :5 Q\X vwxghqw judghv/ wzr plgwhupv dqg d �qdo/ wkdw zhglvfxvvhg lq Fkdswhu 6 +vhh iroghu [�ohv/ vxeiroghu Plvf/ �oh Judghv1{ov,1


d1 Iru wkh yduldeoh plgwhup4 fdofxodwh wkh �uvw irxu prphqwv xvlqj wkhiroorzlqj wzr frpsxwhu surfhgxuhv dqg frpsduh |rxu dqvzhuv1 ^Frpsxwhu gl0uhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rq Iloh/ Lpsruw Gdwd/Iurp Iloh/ iroghu [�ohv/ vxeiroghu Plvf1 Grxeoh folfn rq �oh Judghv1{ov1

Surfhgxuh 4= Wr fdofxodwh wkh prphqwv vwhs e| vwhs= rq wkh phqxedu/ folfn rq Gdwd/ Wudqvirup1

+4, Wr fdofxodwh wkh qxpehu ri revhuydwlrqv/ q= Lq wkh Qhz FroxpqQdph er{ nh| lq q 1 Lq wkh H{suhvvlrq er{/ nh| lq ohqjwk+plgwhup4, 1Folfn Dsso|1 Wkh dqvzhu zloo eh lq wkh q froxpq +wkh dqvzhu zloo ehuhshdwhg wkurxjkrxw wkh froxpq, lq wkh Judghv gdwd iudph +dqvzhu@ :5,1

+5, Wr fdofxodwh p4/ wkh phdq/ nh| lq phdq iru wkh Qhz Fro0xpq Qdph1 Lq H{suhvvlrq/ nh| lq vxp+plgwhup4,2q 1 Folfn Dsso|+dqvzhu @ :5164,1

+6, Wr fdofxodwh p5/ nh| lq qdph p5 dqg

vxp++plgwhup40phdq,a5,2q 1 Folfn Dsso| +dqvzhu @ 4<9185,1


vxp++plgwhup40phdq,a6,2q 1 Folfn Dsso| +dqvzhu @ 0;5715;,1


vxp++plgwhup40phdq,a7,2q 1 Folfn Dsso| +dqvzhu @ <3838147,1Surfhgxuh 5= Wr fdofxodwh doo wkh prphqwv/ rq wkh phqx edu folfn

rq Wh{w Urxwlqhv/ Prphqwv1 Lq wkh gldorj vhohfw Gdwd Iudph Judghv/lq Yduldeoh/ vhohfw plgwhup41 Folfn RN1 Wkhq frpsduh wkh uhvxowv iurpsurfhgxuhv 4 dqg 51 Wkh| zloo eh wkh vdph1 Li qrw/ |rx pdgh d plvwdnh> uhfkhfn|rxu hqwulhv1

e1 Uhshdw surfhgxuhv 4 dqg 5 xvlqj wkh yduldeoh �qdo lq Judghv1{ov1Qrz wkdw |rx kdyh kdg sudfwlfh fdofxodwlqj prphqwv vwhs e| vwhs rq wkh

frpsxwhu/ |rx fdq xvh wkh Prphqwv phqx frppdqg dv lq surfhgxuh 5 zkhqhyhu|rx qhhg wr fdofxodwh prphqwv1

Dqvzhu= Frpsduh frpsxwhu rxwsxw1

�714< Dq devhqwplqghg surihvvru kdv fdofxodwhg wkh phdq/ vhfrqg prphqw/dqg wklug dqg irxuwk prphqwv iru klv hfrqrplfv fodvv* �qdo h{dp1 Wkh judghviru klv 57 vwxghqwv duh dv iroorzv= 85 <5 ;9 ;3 ;; 97 <5 :9 <5 9; 9; 97 :3 9;9; ;; ;; <7 97 89 ;7 ;7 :7 95

d1 Zkdw duh wkh uhvxowv ri wkh surihvvru*v fdofxodwlrqvB^Frpsxwhu klqw= Lq V0Soxv/ rq wkh phqx edu/ folfn rq Gdwd/ Qhz Gdwd Remhfw/

gdwd1iudph1 Folfn RN1 Nh| lq wkh judghv lqwr wkh �uvw froxpq1 Rqwkh phqx edu folfn rq Wh{w Urxwlqhv/ Prphqwv1 Lq wkh gldorj vhohfwGdwd Iudph VGI&/ lq Yduldeoh/ vhohfw Y41 Folfn RN1 Wkh sorwv lq+e, fdq eh fuhdwhg e| folfnlqj Judsk/ 5G0Sorw rq wkh phqx edu dqgvhohfwlqj wkh judsk w|sh ghvluhg1`

7; Prphqwv

e1 Fuhdwh wkh er{0dqg0zklvnhu sorw dqg d klvwrjudp iru wkh surihvvru*v judghv1Dqvzhu doo wkh iroorzlqj txhvwlrqv ehiruh grlqj dq| fdofxodwlrqv rq wkh frpsxwhu>xvh wkh frpsxwhu phuho| wr fkhfn |rxu lqwxlwlrq1

+4, Kdylqj jrqh wkurxjk doo wkdw zrun/ wkh surihvvru uhod{hv e| gulqnlqj whddqg shwwlqj klv fdw1 Oliwlqj wkh fdw/ kh �qgv vl{ xqjudghg dqg ixu0fryhuhg h{dpv1Vxgghqo| kh uhphpehuv wkdw wkhuh duh 63/ qrw 57/ vwxghqwv lq klv fodvv1 Diwhujudglqj wkh qhzirxqg h{dpv/ kh �qgv wkdw hdfk ri wkhvh vl{ hduqhg wkh phdqvfruh1 Zklfk ri klv suhylrxv fdofxodwlrqv qrz qhhg wr eh uhgrqhB Zklfk fdq ehohiw xqfkdqjhgB

+5, Frqvlghu hdfk ri wkh prphqw fdofxodwlrqv wkdw pxvw eh fkdqjhg1 Zlwkrxwuhfdofxodwlqj/ lq zklfk gluhfwlrq zloo hdfk uhvxow fkdqjhB Uhphpehu wkdw wkhqxpehu ri judghv lqfoxghg lq wkh fdofxodwlrqv kdv dovr fkdqjhg1

+6, Dgg wkh vl{ �phdq� h{dpv wr wkh klvwrjudp1 Grhv wkh klvwrjudp uh hfwzkdw |rx vdlg zrxog kdsshq lq txhvwlrq +5,B

+7, Gr |rx qhhg wr uhgudz wkh er{0dqg0zklvnhu sorwBDqvzhu=d1 Iluvw prphqw @ :81<5>Vhfrqg prphqw @ 4851;6>Wklug prphqw @ 056;146>Irxuwk prphqw @ 74/59418<>Vwdqgdugl}h wklug prphqw @ 01459>Vwdqgdugl}h irxuwk prphqw @ 41:9:1

e1 Vhh Iljxuh 7141+4, Rqo| wkh phdq lv xqfkdqjhg1 Doo rwkhu prphqwv qhhg wr eh uhgrqh1+5, Qrz wkhuh duh 9 pruh judghv zklfk duh doo htxdo wr wkh phdq judgh1 Wkh

vhfrqg dqg irxuwk prphqwv duh vpdoohu/ wkh devroxwh ydoxh ri wkh wklug prphqwlv vpdoohu1

+6, Vhh Iljxuh 7151 Wklv klvwrjudp lv pruh olnh wkh Qrupdo glvwulexwlrqphqwlrqhg lq Fkdswhu 61

+7, \hv/ |rx qhhg wr uhgudz wkh er{0dqg0zklvnhu sorw vlqfh wkh lqwhutxduwlohudqjh kdv fkdqjhg1 Lq idfw/ vlqfh zh kdyh 9 pruh judghv htxdo wr wkh phdq/ wkhlqwhutxduwloh udqjh lv vpdoohu1 Wkh judskv frq�up wklv1

�7153 Pruh uh hfwlrqv rq wkh devhqwplqghg surihvvru1 Gr qrw xvh wkh frp0sxwhu iru wklv h{huflvh1 Ehiruh kh kdg irxqg wkh odvw vl{ h{dpv dqg ylhzhg wkhglvwulexwlrq ri judghv/ kh zdv wklqnlqj ri fkdqjlqj klv whdfklqj/ ru dw ohdvw klvjudglqj/ phwkrgv1 Zk| gr |rx wklqn kh zdv frqvlghulqj wklv/ dqg zkdw gr |rxwklqn kh vkrxog kdyh fkdqjhgB Diwhu frqvlghulqj wkh dgglwlrqdo vl{ h{dpv/ gr|rx wklqn lw lv vwloo vr lpshudwlyh iru klp wr fkdqjhB Zk| ru zk| qrwB

Odwh dw qljkw/ mxvw ehiruh idoolqj dvohhs/ wkh devhqwplqghg surihvvru uhphp0ehuv wkdw kh kdv ehhq judglqj vr idu rq d vfdoh ri 83 wr 433/ qrw rq d vfdoh ri3 wr 4331 Kh zdqwv wr pdnh wkh vfruhv lq 714<d frpsdudeoh wr klv rwkhu h{dpv/dqg kh zdqwv wkh lqirupdwlrq rq wkh prphqwv wr eh frpsdudeoh dv zhoo1 Zkdwgrhv kh kdyh wr gr wr �{ wklqjvB Eh qlfh dqg gr lw iru klp> kh*v vohhs|1

Dqvzhu= Iljxuhv 716 dqg 717 suhvhqw wkh klvwrjudpv iru wkh wzr vhwv ri gdwd+57 dqg 63 judghv,1


50

60

70

80

90

Gra

de

40 55 70 85 100 115Grade

0

2

4

6

8

Iljxuh 714= Judsk wr H{huflvh 714< +4,

50

60

70

80

90

Gra

de

40 55 70 85 100 115Grade

0

2

4

6

8

10

Iljxuh 715= Judsk wr H{huflvh 714< +5,

83 Prphqwv

Lw lv jhqhudoo| dujxhg wkdw judghv lq d fodvv �vx!flhqwo|� elj zrxog iroorz dv|pphwulf/ vlqjoh shdnhg glvwulexwlrq zlwk olwwoh zhljkw lq wkh wdlov1 Iljxuh 716lv sx}}olqj dffruglqj wr wklv suhvxpswlrq lq wkdw wkh glvwulexwlrq kdv wzr shdnvhyhq wkrxjk lw lv v|pphwulf1 Khqfh/ wkh surihvvru pljkw kdyh ehhq zruulhg e|wkh vkdsh ri wkh glvwulexwlrq1 Zkdw wkh glvwulexwlrq vhhpv wr lqglfdwh lv wzrvhwv ri vwxghqwv/ rqh zlwk orz judghv wkh rwkhu zlwk kljk1 Wklv pljkw kdyhehhq gxh wr wkh surihvvruv* whdfklqj ru wr rwkhu h{whuqdo flufxpvwdqfhv +ixoo0wlph vwxghqwv yhuvxv sduw0wlph/ wklv frxuvh ehlqj d pdmru iru vrph dqg d plqruiru rwkhuv/ hwf1,1

Iljxuh 717 vkrzv wkdw zlwk wkh h{wud vl{ judghv/ wkh suhvxphg glvwulexwlrqlv hvwdeolvkhg1 Wkxv/ lw vhhpv wkdw wkh sureohp zdv gxh wr wkh plvvlqj judghv1Qrwh wkdw wklv sureohp lv qrw wulyldo1 Li zh frqvlghu d vpdoo vdpsoh/ d ihzplvvlqj gdwd srlqwv fdq fkdqjh rxu zkroh shufhswlrq ri wkh glvwulexwlrq1

Wkh h{huflvh ri vfdolqj iurp 83 wr 433 lqvwhdg iurp 3 wr 433 lv qrw uhdoo|d sureohp/ lw lv pruh d fkdqjh lq wkh xqlwv ri phdvxuhphqw1 Rxu sxusrvh lv/lqirupdoo| vshdnlqj/ wr uhsurgxfh wkh klvwrjudp ri Iljxuh 717 zlwk d gl�huhqwvfdolqj ri wkh d{hv1 Khqfh/ doo zh qhhg wr gr lv wr wudqvirup wkh gdwd wr wklvqhz xqlw ri phdvxuhphqw1 Hdfk fxuuhqw judgh frxqwv iru wzr lq wkh qrupdovfdolqj1 li zh grxeoh hdfk judgh dqg vxewudfw rqh kxqguhg/ wkh qhz judghv zlooeh glvwulexwhg ehwzhhq 3 dqg 4331

40 55 70 85 100 11524grades

0

2

4

6

8

Iljxuh 716= Klvwrjudp ri 57 judghv1

7154 Zrunhg1 Remhfwlyh= Wr lqglfdwh wkh orvv ri lqirupdwlrq lq xvlqj jurxshggdwd1 Lq wkh wh{w lw zdv h{sodlqhg wkdw lw lv qrw yhu| xvhixo wr xvh jurxshg ru


40 55 70 85 100 11530grades

0

2

4

6

8

10

Iljxuh 717= Klvwrjudp ri 63 judghv1

fhoo gdwd wr fdofxodwh wkh kljkhu prphqwv/ hyhq wkh vhfrqg prphqw lv qrw yhu|dffxudwh1 Wklv h{huflvh zloo khos looxvwudwh wklv idfw1 Wkh pdwkhpdwlfv dqg yhuedovfruhv iru erwk wkh SVDW dqg wkh VDW duh uhfrughg lq wkh �oh Svdwvdw1{ov1

d1 Iru hdfk vfruh fdwhjru| fdofxodwh doo irxu prphqwv dqg wkh vwdqgdugl}hgwklug dqg irxuwk prphqwv xvlqj wkh revhuyhg gdwd1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rqIloh/

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e1 Xvlqj wkh surfhgxuhv ghyhorshg lq Fkdswhu 6/ wkh SVDW dqg wkh VDWgdwd kdyh ehhq jurxshg lqwr fhoov1 D �oh/ Svdwfhoo1{ov/ kdv ehhq fuhdwhg zlwkwkh qxpehu ri revhuydwlrqv e| fhoo + sprev/ syrev/ hwf1, dqg wkh fhoo pdunv+ sppdun / sypdun / hwf1, iru hdfk ri wkh yduldeohv lq �oh Svdwvdw1{ov1 Xvh wkhiroorzlqj wr fdofxodwh wkh prphqwv iurp wkh fhoo gdwd1

^Frpsxwhu gluhfwlrqv= Rq wkh phqx edu folfn/ rq Iloh/ Lpsruw Gdwd/Iurp Iloh1 Vhohfw iroghu [�ohv/ vxeiroghu Whvwvfru1 Grxeoh folfn rq�oh Svdwfhoo1{ov1 Rq wkh phqx edu/ folfn rq Gdwd/ Wudqvirup1

+4, Wr fdofxodwh wkh qxpehu ri revhuydwlrqv/ q= Lq Qhz FroxpqQdph nh| lq q 1 Lq H{suhvvlrq nh| lq vxp+sprev, 1 Folfn Dsso|1

85 Prphqwv

Wkh dqvzhu zloo eh lq wkh Svdwfhoo gdwd iudph lq froxpq q1 +dqvzhu@ 853,1

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+6, Wr fdofxodwh p5/ nh| lq p5 iru wkh qdph1 Lq H{suhvvlrq/nh| lq vxp+sprev-+sppdun0phdq,a5,2q 1 Folfn Dsso|1 +dqvzhu @4681:;,1

+7, Wr fdofxodwh p6/ nh| lq p6 iru wkh qdph1 Lq H{suhvvlrq/nh| lq vxp+sprev-+sppdun0phdq,a6,2q 1 Folfn Dsso|1 +dqvzhu @47<1;6,1

+8, Wr fdofxodwh p7/ nh| lq p7 iru wkh qdph1 Lq H{suhvvlrq/nh| lq vxp+sprev-+sppdun0phdq,a7,2q 1 Folfn Dsso|1 +dqvzhu @7;7<81:9,1`

f1 Fdofxodwh wkh prphqwv iru wkh rwkhu wkuhh yduldeohv iurp wkh fhoo gdwd/dqg frpsduh |rxu dqvzhuv zlwk wkh prphqwv fdofxodwhg xvlqj wkh revhuyhg gdwdlq vwhs +d,1


7155 Zrunhg1 Remhfwlyh= Wr looxvwudwh wkh uhodwlrqvkls ehwzhhq wkh vkdshri d glvwulexwlrq dqg lwv prphqwv1 Lq Fkdswhu 6/ zh phqwlrqhg d ydulhw| rigl�huhqw glvwulexwlrqv wkdw zhuh jhqhudwhg e| gl�huhqw w|shv ri h{shulphqwv1 Lqwklv fkdswhu/ zh kdyh vkrzq wkdw dv wkh vkdsh ri wkh glvwulexwlrq fkdqjhv/ vrgr wkh prphqwv1 Wklv h{huflvh zloo looxvwudwh wklv hvvhqwldo lghd lq whupv riklvwrjudpv iurp frpsxwhu h{shulphqwv dqg iurp lghdol}hg vkdshv ri glvwulexwlrqv+wkdw lv/ lq whupv ri klvwrjudpv wkdw duh yhu| vprrwk/ vxffk dv pljkw eh jhqhudwhge| d yhu| odujh vhw ri gdwd,1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Folfn rq Odev/Krz duh Srsxodwlrqv GlvwulexwhgB Lq wkh gldorj er{ lq Ode Rs0

wlrq/ folfn Vlpxodwhg Gdwd1 Folfn rq hdfk olvwhg Glvwulexwlrq Idplo|1Folfn Dsso|1`

Sulqw |rxu judskv vr wkdw |rx fdq h{dplqh wkhp forvho|1 Frpsduh wkh vkdshvri wkh glvwulexwlrqv wr wkh ydoxhv ri wkh prphqwv vkrzq rq wkh judsk1 Wu| wrgudz rxw jhqhudo vwdwhphqwv wkdw |rx fdq pdnh derxw wkh uhodwlrqvkls ehwzhhqwkh ydoxhv wdnhq e| wkh irxu prphqwv dqg wkh revhuyhg glvwulexwlrqv1 Qrwlfh wkdwwkh xqvwdqgdugl}hg wklug dqg irxuwk prphqwv duh qrw yhu| lqirupdwlyh/ zkhuhdvwkh vwdqgdugl}hg wklug dqg irxuwk prphqwv duh yhu| lqirupdwlyh1 Revhuyh wkhh{whqw wr zklfk wkh klvwrjudpv |rx revhuyh gr/ ru gr qrw/ pdwfk wkh lghdol}hgglvwulexwlrqv1

Wklv lv rqh ri wkh prvw lpsruwdqw h{huflvhv lq wklv fkdswhu1 Lw lv ylwdo wkdw|rx ohduq dw dq lqwxlwlyh ohyho wkh uhodwlrqvkls ehwzhhq prphqwv dqg wkh vkdshvri glvwulexwlrqv1

Dqvzhu= iru vwxghqw glvfxvvlrq dqg uhylhz1


7156 Zrunhg1 Remhfwlyh= Wr uhodwh prphqwv wr wkh vkdsh ri klvwrjudpv1d1 Lq Fkdswhu 6/ lq H{huflvh 614;/ |rx jhqhudwhg d qxpehu ri klvwrjudpv

iurp ydulrxv glvwulexwlrqv ru h{shulphqwv1 Lq wklv h{huflvh/ zh zloo fdofxodwh wkhprphqwv iurp vlplodu w|shv ri klvwrjudpv1 Frpsduh |rxu prphqw fdofxodwlrqv/hvshfldoo| wkh vwdqgdugl}hg wklug dqg irxuwk prphqwv/ zlwk wkh vkdshv ri wkhklvwrjudpv wkdw |rx zloo jhqhudwh lq wklv h{huflvh1 Iluvw/ jhqhudwh vl{ vhwv ri 733udqgrp qxpehuv hdfk edvhg rq d gl�huhqw glvwulexwlrq1

^Frpsxwhu gluhfwlrqv= Rshq V0Soxv1 Rq wkh phqx edu/ folfn rqGdwd/ Udqgrp Qxpehuv1

+4, Lq wkh Udqgrp Qxpehu Jhqhudwlrq gldorj/ lq Vdpsoh Vl}h/nh| lq 733 1 Lq Glvwulexwlrq vfuroo wr Qrupdo +lw lv wkh �uvw hqwu|lq wkh olvw,1 Lq wkh Vdyh Dv er{/ nh| lq Qrup1ghq dv d �oh qdph-1Xqfkhfn Sulqw Uhvxowv1 Folfn Dsso|1

+5, Iroorz wkh gluhfwlrqv lq +4,1 Lq wkh Glvwulexwlrq er{ vfuroo wrOrjQrupdo1 Vhohfw d qhz �oh qdph1

+6, Iroorz wkh gluhfwlrqv lq +4,1 Lq wkh Glvwulexwlrq er{ vfuroo wrXqlirup1 Vhohfw d qhz �oh qdph1

+7, Iroorz wkh gluhfwlrqv lq +4,1 Lq wkh Glvwulexwlrq er{ vfuroo wrFkl0vtxduh1 Lq wkh Ghj1 ri Iuhhgrp 4 er{/ nh| lq 8 1 Vhohfw d qhz�oh qdph1

+8, Iroorz wkh gluhfwlrqv lq +4,1 Lq wkh Glvwulexwlrq er{ vfuroo wrZhlexoo1 Lq wkh Vfdoh er{/ nh| lq 6 1 Lq wkh Vkdsh 4 er{/ nh| lq 5 1Vhohfw d qhz �oh qdph1

+9, Iroorz wkh gluhfwlrqv lq +4,1 Lq wkh Glvwulexwlrq er{ vfuroo wrEhwd1 Lq wkh Vkdsh 4 er{/ nh| lq 5 1 Lq wkh Vkdsh 5 er{/ nh| lq 8 1Vhohfw d qhz �oh qdph1

+-Qrwh= Wr rshq wkh �ohv fuhdwhg/ rshq wkh Remhfw Eurzvhu dqggrxeoh folfn rq wkh gdwd iudph qdphv1,`

e1 Iru hdfk ri wkhvh vl{ gdwd vhwv/ jhqhudwh wkh klvwrjudpv dqg jlyh wkhpd ghvfulswlyh wlwoh/ dqg sulqw rxw wkh uhvxowv1 Fdofxodwh wkh �uvw irxu prphqwvlqfoxglqj wkh vwdqgdugl}hg prphqwv1

^Frpsxwhu gluhfwlrqv= Kljkoljkw wkh gdwd froxpq lq wkh �uvw gdwdvhw1 Rq wkh phqx edu/ folfn rq Judsk/ 5G0Sorw/ Klvwrjudp1 Folfn rqRN1 Wr wlwoh wkh judsk/ rq wkh phqx edu/ folfn Lqvhuw/ Wlwohv/ Pdlq1Lq wkh duhd wkdw lv kljkoljkwhg rq wkh judsk/ nh| lq d wlwoh vxfk dvQrupdo Ghqvlw|= 733 Rev 1 Sulqw wkh judsk1 Uhshdw iru doo vl{ gdwdvhwv1

Wr fdofxodwh wkh prphqwv wkdw fruuhvsrqg wr wkh klvwrjudpv/ rqwkh phqx edu folfn rq Wh{w Urxwlqhv/ Prphqwv1 Lq wkh gldorj vh0ohfw Gdwd Iudph Qrup1ghq/ lq Yduldeoh/ vhohfw vdpsoh1 Folfn RN1Uhshdw iru hdfk gdwd vhw vxevwlwxwlqj wkh dssursuldwh �oh qdph iruQrup1ghq1`

Frpsduh wkh yduldwlrq lq wkh prphqwv/ hvshfldoo| wkh vwdqgdugl}hg prphqwv/zlwk wkh yduldwlrq lq wkh vkdshv ri wkh klvwrjudpv1

87 Prphqwv

f1 Uhshdw wkh suhylrxv h{huflvhv zlwk 533 revhuydwlrqv1g1 Uhshdw wkh suhylrxv h{huflvhv zlwk 933 revhuydwlrqv1h1 Dv wkh qxpehu ri revhuydwlrqv lqfuhdvhv zkdw lpsolfdwlrqv gr |rx re0

vhuyhBDqvzhu= iru vwxghqw glvfxvvlrq dqg uhylhz1

716 Dssolfdwlrqv

Lq doo wkh iroorzlqj h{huflvhv/ xvh wkh Prphqwv ixqfwlrq zkhuh dssursuldwh1�7157 Lq H{huflvh 6156/ zh h{dplqhg wkh glvwulexwlrq ri wkh hoghuo| dfurvv

vwdwhv> vhh iroghu [�ohv/ vxeiroghu Plvf/ �oh Djh981{ov1 Fdofxodwh wkh prphqwvwr surylgh pruh suhflvh lqirupdwlrq derxw wkh glvwulexwlrq ri wkh hoghuo|1 Duhwkhuh dq| vxusulvhv lq wkh uhvxowvB Wkh ydoxhv wkdw |rx duh phdvxulqj duh wkhshufhqwdjhv ri wkh srsxodwlrq lq hdfk vwdwh wkdw duh juhdwhu wkdq 98 |hduv rog+ sfw98,> vr wkh phdq/ iru h{dpsoh/ lv wkh phdq shufhqwdjh ri wkrvh ryhu 981Wkh phdq lv dyhudjhg ryhu wkh shufhqwdjhv uhfrughg lq hdfk vwdwh1

Dqvzhu=Iluvw Prphqw @ 431<8;>Vhfrqg Prphqw @ 718<:>Wklug Prphqw @ 09165<>Irxuwk Prphqw @ 4641336>Vwdqgdugl}hg Wklug Prphqw @ 01975>Vwdqgdugl}hg Irxuwk Prphqw @ 914<<1

Iurp wkh deryh fdofxodwlrqv/ zh fdq vhh wkdw wkh shufhqwdjh ri wkh srsxodwlrqwkdw lv juhdwhu wkdq 98 |hduv rog lv glvwulexwhg urxjko| v|pphwulfdoo| durxqg 44shufhqw/ exw wkh glvwulexwlrq kdv �idw wdlov1� Wkh idw wdlov uhvxow lv prvw olnho|gxh wr wkh suhvhqfh ri Dodvnd +yhu| orz shufhqwdjh, dqg Iorulgd +yhu| kljkshufhqwdjh,1 Wkh odfn ri vnhzqhvv pljkw eh d vxusulvh lq wkdw rqh pljkw kdyhvshfxodwhg wkdw d ihz vwdwhv zrxog kdyh kljk shufhqwdjhv dqg pdq| vwdwhv zrxogkdyh uhodwlyho| vpdoo shufhqwdjhv1 Lq idfw prvw vwdwhv kdyh derxw 44( ri wkhsrsxodwlrq ryhu 98 |hduv rog1 Wklv lqirupdwlrq frxog eh xvhixo lq ghwhuplqlqjwkh ohyho ri uhvrxufhv qhhghg iru dq roghu srsxodwlrq1

7158 Xvlqj wkh gdwd rq zhljkw dqg idw +vhh iroghu [�ohv/ vxeiroghu Plvf/ �ohFrohv1{ov, h{dplqh wkh gl�huhqfhv wkdw wkh zhljkw orvv surjudp pljkw kdyh pdghwr zhljkw dqg idw frqwhqw iru wkh vxemhfwv lqyroyhg1 Zdv wkh surjudp vxffhvvixoBKrz duh |rx gh�qlqj �vxffhvvixo�B Wkh pdlq txhvwlrq lv/ Krz gl�huhqw duh wkhwzr glvwulexwlrqvB H{sodlq krz |rx zrxog fkdudfwhul}h �gl�huhqw1�

Dqvzhu= Ehiruh wkh surjudp/ zh kdyh wkh iroorzlqj prphqwv iru zhljkw=Iluvw @ 473164/ Vhfrqg @ ;5:1<;/ Wklug @ 63;3<15:/ Irxuwk @ 5<<657;197/Vwdqgdugl}hg Wklug @ 415</ Vwdqgdugl}hg Irxuwk @ 716:1 Zh fdq frpsduhwkhp zlwk wkrvh diwhu wkh surjudp= Iluvw @ 47315</ Vhfrqg @ ;7917;/ Wklug@ 5<:38146/ Irxuwk @ 5<;:68:196/ Vwdqgdugl}hg Wklug @ 4154/ Vwdqgdugl}hg

Dssolfdwlrqv 88

Irxuwk @ 714:1 Wkhuh duh doprvw qr fkdqjhv1 Vr edvhg rq wkh shuirupdqfh rizhljkw orvv/ lw vhhpv wkh surjudp zdv qrw vxffhvvixo1

Vlploduo|/ zh fdq dovr fdofxodwh prphqwv iru idw frqwhqw1 Ehiruh wkh surjudp/zh kdyh= Iluvw @ 571<4/ Vhfrqg @ 841;4/ Wklug @ 0455178/ Irxuwk @ 94761:5/Vwdqgdugl}hg Wklug @ 166/ Vwdqgdugl}hg Irxuwk @ 515<1 Diwhu wkh surjudp/Iluvw @ 551<9/ Vhfrqg @ 8618;/ Wklug @ 074144/ Irxuwk @ 966:133/ Vwdqgdugl}hgWklug @ 0143/ Vwdqgdugl}hg Irxuwk @ 51541 Wkh phdq ri idw frqwhqw ghfuhdvhvderxw ; shufhqw diwhu wkh surjudp1 Wkh glvwulexwlrq lv dovr pruh v|pphwulfdiwhu wkh surjudp1 Hyhq wkrxjk wkh ghfuhdvh ri idw frqwhqw pd| qrw eh wkdwvljql�fdqw/ wkh surjudp lv pruh vxffhvvixo zlwk idw orvv wkdq zhljkw orvv1 Erwkidw dqg zhljkw ehiruh dqg diwhu wkh surjudp kdyh glvwulexwlrqv wkdw duh yhu|vlplodu= wkh surjudp vhhpv wr kdyh olwwoh lpsdfw1

�7159 Lq H{huflvh 6155 zh h{dplqhg wkh glvwulexwlrqv ri dupv vklsphqwve| wkh Xqlwhg Vwdwhv dqg wkh X1V1V1U1 +vhh iroghu [�ohv/ vxeiroghu Plvf/ �ohDupv1{ov,1 Ohw xv qrz frqvlghu fdofxodwlqj erwk vhwv ri prphqwv iru wkh wzrglvwulexwlrqv1 Zkdw frqfoxvlrqv fdq zh gudz iurp h{dplqlqj wkhvh prphqwvderxw wkh gl�huhqfhv ehwzhhq Xqlwhg Vwdwhv dqg X1V1V1U1 srolflhv1 Sd| sduwlf0xodu dwwhqwlrq wr wkh kljkhu prphqwv derxw wkh phdq/ dv wkh �uvw prphqw lqsduwlfxodu lv/ shukdsv/ lqwxlwlyho| reylrxv1

Dqvzhu= Wkh prphqwv iru Xqlwhg Vwdwhv dupv vdohv duh= Iluvw @ ;991;4/Vhfrqg @ 5438:7615:/ Wklug @ 97<755<34615</ Irxuwk @ 65537954<<399515/Vwdqgdugl}hg Wklug @ 5146/ Vwdqgdugl}hg Irxuwk @ :15:1

Wkh prphqwv iru XVVU dupv vdohv duh dv iroorzv= Iluvw @ 4655169/ Vhfrqg @754793319;/ Wklug @ 48:97955<8:1:8/ Irxuwk @ 4347<:<9:;8:339/ Vwdqgdugl}hgWklug @ 41;5/ Vwdqgdugl}hg Irxuwk @ 81:41

E| frpsdulqj prphqwv iru wkh wzr frxqwulhv/ zh fdq vhh wkdw wkh XVVU*vdyhudjh dupv vdohv duh kljkhu1 Wkh yduldwlrq lq dupv vdohv e| wkh XVVU lv juhdwhuwkdq wkdw iru wkh Xqlwhg Vwdwhv1 Erwk frxqwulhv kdyh pdq| vpdoo vdohv/ exw d ihzyhu| odujh vdohv= wkh wklug prphqwv duh erwk srvlwlyh1 Wkh glvwulexwlrq ri dupvvdohv iurp wkh Xqlwhg Vwdwhv lv ohvv vnhzhg wr wkh uljkw dqg dovr pruh shdnhgwkdq wkdw ri wkh XVVU1 Vr wkdw dupv vdohv iurp wkh Xqlwhg Vwdwhv duh pruhfrqfhqwudwhg rq vpdoohu vdohv/ exw zlwk d ihz odujh uhflslhqwv1 Wkhvh gl�huhqfhv/zkloh qrw vxevwdqwldo/ uh hfw wkh gl�huhqw vwudwhjlhv ri wkh wzr frxqwulhv dvlqglfdwhg lq H{huflvh 61551

715: Lq wkh iroghu [�ohv/ vxeiroghu JQS/ vxeiroghu LqwoJQS/ wkhuh duh wkuhh�ohv ri JQS gdwd= Vzhjqs1{ov/ Xnjqs1{ov dqg Xvjqs1{ov iru Vzhghq/ wkh XqlwhgNlqjgrp dqg wkh Xqlwhg Vwdwhv/ uhvshfwlyho|1 Fohduo| wkh phdqv dqg yduldqfhvri wkhvh yhu| gl�huhqw frxqwulhv zloo eh gl�huhqw/ hyhq diwhu frqyhuvlrq wr dfrpprq prqhwdu| xqlw1 Krzhyhu/ lw lv qrw fohdu wkdw wkh vkdshv ri wkh glvwul0exwlrqv ri JQS frpsrqhqwv zloo eh gl�huhqw1 Xvlqj erwk er{0dqg0zklvnhu sorwvdqg fdofxodwlrqv ri wkh �uvw irxu vwdqgdugl}hg prphqwv/ h{soruh wkh gl�huhqfhvlq wkh vkdshv ri wkh glvwulexwlrqv dprqj wkh wkuhh frxqwulhv zlwk uhvshfw wr dq|wkuhh yduldeohv ri |rxu fkrlfh1 Zkdw srolf| lpsolfdwlrqv gr |rx gudz iurp |rxudqdo|vlvB

89 Prphqwv

Dqvzhu= Zh looxvwudwh dq dqvzhu e| fkrrvlqj wkh yduldeoh crxwsxw* iurphdfk frxqwu|1 Wkh dqdo|vlv iru rwkhu yduldeohv lv vlplodu1

Wkh prphqwv iru wkh yduldeoh crxwsxw* iru Vzhghq= Iluvw @ 4;:148/ Vhfrqg@ 574;3138/ Wklug @ 6:87959143/ Irxuwk @ 487:;5:8871;7/ Vwdqgdugl}hg Wklug@ 143/ Vwdqgdugl}hg Irxuwk @ 51981

Wkh prphqwv iru crxwsxw* iru wkh Xqlwhg Nlqjgrp= Iluvw @ 43<158/ Vhfrqg@ 65631<8/ Wklug @ 4:58;;1<</ Irxuwk @ 5:545:7:1<:/ Vwdqgdugl}hg Wklug @1<7/ Vwdqgdugl}hg Irxuwk @ 51941

Wkh prphqwv iru crxwsxw* iru wkh Xqlwhg Vwdwhv= Iluvw @ 84817</ Vhfrqg @4;335:138/ Wklug @ ::8;447814:/ Irxuwk @ <3;99:9993;135/ Vwdqgdugl}hg Wklug@ 4135/ Vwdqgdugl}hg Irxuwk @ 51;31

Wkh phdq iru wkh Xqlwhg Vwdwhv yduldeoh crxwsxw* lv pxfk eljjhu wkdq wkrvhiru wkh rwkhu wzr frxqwulhv1 Wkh yduldwlrq ri wkh Xqlwhg Vwdwhv rxwsxw lv eljjhvwdqg wkdw ri wkh Xqlwhg Nlqjgrp lv wkh vpdoohvw1 Wkh vwdqgdugl}hg wklug dqgirxuwk prphqwv iru wkhvh wkuhh frxqwulhv duh yhu| vlplodu h{fhsw wkdw wkh glv0wulexwlrq iru Vzhglvk rxwsxw lv pruh v|pphwulf1

Zrxog |rx kdyh jxhvvhg wkdw wkh vkdshv ri wkhvh wkuhh glvwulexwlrqv zhuhvr vlploduB Lq doo wkuhh fdvhv wkhuh lv voljkw hylghqfh ri srvlwlyho| vnhzhg gdwd/xsvzlqjv jr ixuwkhu wkdq grzqvzlqjv/ exw wkh shdnhgqhvv lv prghudwh/ wkhuhduh ihz �zlog fkdqjhv� lq rxwsxw1

�715; Lq wkh iroghu [�ohv/ vxeiroghu Whvwvfru/ d �oh rq vfkrodvwlf dswlwxghwhvwv/ Svdwvdw1{ov/ frqwdlqv irxu yduldeohv= SVDW vfruhv dqg VDW vfruhv iru wkhpdwkhpdwlfv dqg yhuedo whvwv1

d1 Frpsduh wkh vkdshv ri wkh er{0dqg0zklvnhu sorwv ri wkh pdwk vfruhv eh0wzhhq wkh SVDW dqg VDW/ uhfrjql}lqj wkdw wkh wzr vfruhv duh phdvxuhg rq gli0ihuhqw vfdohv1

e1 Frpsduh wkh vkdshv ri wkh yhuedo vfruhv ehwzhhq wkh SVDW dqg VDW/uhfrjql}lqj wkdw wkh wzr vfruhv duh phdvxuhg rq gl�huhqw vfdohv1 Fdofxodwh wkhvwdqgdugl}hg prphqwv1

f1 Vlploduo|/ frpsduh wkh yhuedo dqg pdwk vfruhv iru wkh SVDW lq wkh vdphzd|1

g1 Zkdw frqfoxvlrqv derxw wkh shuirupdqfh ri vwxghqwv rq wkhvh wzr vhwv riwhvwv gr |rx gudzB

Dqvzhu=d1 Wkh prphqwv iru wkh SVDW pdwk vfruhv= Iluvw @ 79158/ Vhfrqg @ 4571:5/

Wklug @ 63;155/ Irxuwk @ 6:<331;6/ Vwdqgdugl}hg Wklug @ 155/ Vwdqgdugl}hgIrxuwk @ 51771

Wkh prphqwv iru wkh VDW pdwk vfruhv= Iluvw @ 7:919</ Vhfrqg @ 465451<4/Wklug @ 6:9493173/ Irxuwk @ 7546557;:1<6/ Vwdqgdugl}hg Wklug @ 158/ Vwdq0gdugl}hg Irxuwk @ 51741 Vlqfh wkh SVDW dqg VDW vfruhv duh phdvxuhg rqgl�huhqw vfdohv/ zh vkrxog frpsduh rqo| wkh vwdqgdugl}hg wklug dqg irxuwk pr0phqwv1 Zh vhh wkdw wkh| duh yhu| vlplodu> vhh wkh er{0dqg0zklvnhu sorwv iru wklvh{huflvh/ Iljxuh 7181

e1 Wkh prphqwv iru wkh SVDW yhuedo vfruhv= Iluvw @ 7518</ Vhfrqg @ 44814</Wklug @ 73418:/ Irxuwk @ 6856719:/ Vwdqgdugl}hg Wklug @ 165/ Vwdqgdugl}hg

Dssolfdwlrqv 8:

Irxuwk @ 51991Wkh prphqwv iru wkh VDW yhuedo vfruhv= Iluvw @ 76<1<9/ Vhfrqg @ 456:9187/

Wklug @ 6534<:15</ Irxuwk @ 736;<9599199/ Vwdqgdugl}hg Wklug @ 156/ Vwdq0gdugl}hg Irxuwk @ 51971 Dv phqwlrqhg deryh/ ehfdxvh wkh vfruhv iru wkh wzrh{dplqdwlrqv duh phdvxuhg rq gl�huhqw vfdohv/ zh vkrxog frpsduh rqo| wkh vwdq0gdugl}hg wklug dqg irxuwk prphqwv1 Zh fdq vhh wkdw wkh| dovr duh yhu| vlplodu>vhh Iljxuh 7191

f1 Iurp wkh prphqwv zh fdofxodwhg deryh dqg wkh er{0dqg0zklvnhu sorwiru wklv H{huflvh/ zh fdq frpsduh wkh SVDW pdwk dqg yhuedo vfruhv/ zklfk duhphdvxuhg rq wkh vdph vfdoh1 Wkh glvwulexwlrqv duh vlplodu/ exw wkh phdq ri wkhSVDW pdwk vfruhv lv kljkhu wkdq wkdw iru wkh yhuedo vfruhv1 Vhh Iljxuh 71:1

g1 Hyhq wkrxjk lw vhhpv wkdw vwxghqwv* dyhudjh pdwk vfruhv iru erwk whvwvduh d olwwoh kljkhu/ wkhlu shuirupdqfh rq erwk whvwv duh vlplodu lq wkh vhqvh wkdwwkh vkdshv ri wkh glvwulexwlrqv duh vlplodu1 Wkh SVDW uhvxowv vhhp wr uh hfwforvho| wkh VDW uhvxowv1 Wklv lv d olwwoh vxusulvlqj lq wkdw rqh pljkw jxhvv wkdwehwzhhq wkh VDW dqg wkh SVDW/ wkh orz vfruhv zrxog whqg wr gursrxw1

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psat

mat

h

200

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500

600

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satm

ath

Iljxuh 718= Judsk wr H{huflvh 715; +d,

715< Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Jh|vhu41{ov duh uhfrughg wkhgxudwlrqv ri dqg wkh lqwhuydov ehwzhhq huxswlrqv ri Rog Idlwkixo lq \hoorzvwrqhQdwlrqdo Sdun1 E| fdofxodwlqj wkh irxu prphqwv ri erwk yduldeohv/ zkdw frqfox0vlrqv fdq |rx gudz derxw wkh huxswlrqv ri Rog IdlwkixoB Zkdw txhvwlrqv duh |rxvwlpxodwhg wr dvn iurp h{dplqlqj wkhvh gdwdB

8; Prphqwv

20

30

40

50

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psat

verb

100

300

500

700

satv

erb

Iljxuh 719= Judsk wr H{huflvh 715; +e,

20

30

40

50

60

70

80

psat

mat

h

20

30

40

50

60

70

psat

verb

Iljxuh 71:= Judsk wr H{huflvh 715; +f,

Dssolfdwlrqv 8<

Dqvzhu= Wkh prphqwv iru wkh yduldeoh cgxudwlrq* duh lq plqxwhv= Iluvw@ 618;/ Vhfrqg @ 414:/ Wklug @ 01:8/ Irxuwk @ 517:/ Vwdqgdugl}hg Wklug @018</ Vwdqgdugl}hg Irxuwk @ 41;41 Wkhvh prphqwv lqglfdwh wkdw wkh yduldwlrqri gxudwlrq lv vpdoo dqg wkdw wkhuh lv olwwoh vnhzqhvv dqg shdnhgqhvv1 Exwli zh orrn dw wkh lqwhuydov ehwzhhq huxswlrqv/ zh gudz d gl�huhqw frqfoxvlrq1Wkh prphqwv iru wkh yduldeoh lqwhuydov duh lq plqxwhv= Iluvw @ :4134/ Vhfrqg@ 49613;/ Wklug @ 0433715</ Irxuwk @ 89376185/ Vwdqgdugl}hg Wklug @ 017;/Vwdqgdugl}hg Irxuwk @ 51441 Wkh yduldqfh ri wkh lqwhuydov lv odujh1 Wkhuh lvolwwoh hylghqfh ri vnhzqhvv dqg wkh ghjuhh ri shdnhgqhvv lv wkh vdph iru erwkglvwulexwlrqv1 Zkdw vnhzqhvv wkhuh lv/ lv iru vkruw gxudwlrq dqg lqwhuydo wlphv/qrw orqj dv rqh pljkw dqwlflsdwh1 Wkh rffxuuhqfh ri yhu| odujh ru vpdoo gxudwlrqvru lqwhuydov lv qrw d sureohp1

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8145 Zkdw lv wkh uhodwlrqvkls ehwzhhq d vfdwwhu gldjudp dqg d klvwrjudpBZkdw lv wkh uhodwlrqvkls ehwzhhq d vfdwwhu gldjudp dqg d fruuhodwlrq frh!flhqwB

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Uhihu wr wkh htxdwlrq iru a*6 wr fdofxodwh wkh frh!flhqw ri dvvrfldwlrq1f1 Frpsduh |rxu uhvxowv xvlqj a*> a*6> dqg frpphqw1 Dovr frpsduh |rxu

uhvxowv zlwk wkrvh rewdlqhg xvlqj wkh fruuhodwlrq frh!flhqw dqg Vshdupdq*v udqnfruuhodwlrq frh!flhqw/ dv glvfxvvhg lq wkh wh{w1

Dqvzhu= iru vwxghqw h{sorudwlrq1

�8155 Vxssrvh wkdw wkh uhodwlrqvkls ehwzhhq wzr yduldeohv lv jlyhq e| wkhhtxdwlrq

| @ d. e{. h

zkhuh h lv wkh huuru lq revhuylqj wkh uhodwlrqvkls ehwzhhq | dqg {1Li |rx nqhz u/ wkh fruuhodwlrq frh!flhqw/ krz zrxog |rx jhw dq lghd ri eB

Li |rx kdg d fdofxodwlrq iru e/ krz zrxog |rx ghwhuplqh uB H{sodlq zkdw wkhuhodwlrqvkls lv ehwzhhq wkhvh wzr lghdv1

Dqvzhu= Li wkh h lv phdvxuhphqw huuru/ zh nqrz e @ u�sp5+|,@

sp5+{,

dqg u @ e� sp5+{,@

sp5+|,1 Vlqfh e lv phdvxuhg lq �xqlwv ri |� shu �xqlwv ri

{�/ wkh fruuhodwlrq frh!flhqw lv lq idfw wkh vwdqgdugl}hg �vorsh� ri wkh ruljlqdorqh1

816 Dssolfdwlrqv

8156 Lq wkh lqwhuqdwlrqdo JQS gdwd �ohv/ wkhuh duh qdwlrqdo lqfrph gdwd/ zklfkkdyh ehhq frqyhuwhg lqwr X1V1 groodu htxlydohqwv1 Li/ krzhyhu/ wkh gdwd zhuh lq

;7 Elyduldwh Gdwd

ruljlqdo xqlwv/ vr wkdw/ iru h{dpsoh/ rxwsxw zdv phdvxuhg lq Vzhglvk Nurqhu/ lqEulwlvk srxqgv/ dqg vr rq/ frxog |rx pdnh frpsdulvrqv dfurvv frxqwulhv iru wkhfruuhodwlrqv ehwzhhq frqvxpswlrq dqg rxwsxwB Li vr/ krzB

Dqvzhu= Wkh fruuhodwlrq lv d vwdqgdugl}hg furvv surgxfw prphqw dqg lq0yduldqw wr wkh fkrlfh ri xqlwv1 Vr zh fdq frpsduh wkhvh fruuhodwlrq frh!flhqwvgluhfwo|1

8157 Zrunhg1 Remhfwlyh= Wr looxvwudwh wkh h�hfw rq fruuhodwlrq iurp wudqv0iruplqj wkh gdwd1 Xvh wkh gdwd irxqg lq wkh iroghu [�ohv/ vxeiroghu Jqs/ vxeiroghuGrpjqs/ �oh Grpjqs1{ov1

d1 Sorw wkh yduldeohv lqgxvwuldo surgxfwlrq +lqgsurg, dqg uhdo JQS +ujqs,/dqg fdofxodwh wkh fruuhodwlrq ehwzhhq wkhp1

e1 Fdofxodwh wkh jurzwk udwhv ri uhdo JQS dqg ri lqgxvwuldo surgxfwlrq> wkhjurzwk udwh iru d wlph vhulhv/ i{wj> lv jlyhq e| jwk @ +{w � {w�4,@{w�4= \rxzloo kdyh wr orvh wkh ��uvw� revhuydwlrq lq hdfk fdvh1 Fdofxodwh wkh fruuhodwlrqfrh!flhqw1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Lpsruw �oh Grpjqs1{ov1+4, Wr jhqhudwh d yduldeoh iru wkh jurzwk udwh ri ujqs/ kljk0

oljkw froxpq ujqs1 Folfn Frs|1 Kljkoljkw wkh vhfrqg fhoo ri d qhzfroxpq1 Folfn Sdvwh1 Kljkoljkw wkh qhz froxpq qdph1 Nh| lqujqsodj 1 Hqwhu1 Uhshdw iru froxpq lqgsurg/ qdplqj wkh qhz fro0xpq � lqgsurgodj1� Rq wkh phqx edu/ folfn rq Gdwd/ Wudqvirup1 Lqwkh gldorj lq Qhz Froxpq Qdph/ nh| lq ujqsj 1 Lq H{suhvvlrq/ nh|

lq +ujqs0ujqsodj,2ujqsodj 1 Folfn Dsso|1 Uhshdw iru lqgsurg xv0

lqj � lsj1� Lq H{suhvvlrq/ nh| lq +lqgsurg0lqgsurgodj,2lqgsurgodj 1Folfn Dsso|1

+5, Wr fdofxodwh wkh fruuhodwlrq frh!flhqw/ rq wkh phqx edu folfnrq Vwdwlvwlfv/ Gdwd Vxppdulhv/ Fruuhodwlrqv1 Lq Yduldeohv/ vhohfwujqsj dqg lsj1 Lq Phwkrg wr Kdqgoh Plvvlqj Ydoxhv/ vhohfw �rplw1�Folfn Dsso|1 Wkh dqvzhu zloo eh lq wkh Uhsruw zlqgrz1 +dqvzhu@1;6;;,`1

Sorw wkh vfdwwhu gldjudp iru wkh uhodwlrqvkls ehwzhhq wkh jurzwk udwhv iru lq0gxvwuldo surgxfwlrq dqg iru uhdo JQS1 Duh |rx vxusulvhg e| wkh uhvxowvB Frpsduhfduhixoo| wkhvh uhvxowv zlwk wkrvh rewdlqhg lq +d, ri wklv h{huflvh1

Zh kdyh uhvwulfwhg rxu dwwhqwlrq wr �olqhdu uhodwlrqvklsv1� Wklv h{huflvhlqglfdwhv wkdw vrphwlphv e| vxlwdeoh wudqvirupdwlrq ri wkh yduldeohv lqyroyhgrqh pd| eh deoh wr dsso| rxu whfkqltxhv wr d zlghu ydulhw| ri fdvhv1

Dqvzhu=d1 Wkh fruuhodwlrq frh!flhqw ehwzhhq lqgsurg dqg ujqs lv 1<<:/ zkloh wkdw

ehwzhhq wkh jurzwk udwhv lv 1;6;;1e1 Lq wklv frpsdulvrq/ zh vhh wkdw wkh ohyhov duh pxfk pruh fruuhodwhg wkdq

wkh jurzwk udwhv> wklv lv ehfdxvh ri wkh �shuvlvwhqfh� ri hfrqrplf wlph vhulhv1Wkdw lv/ hdfk |hdu rqh dggv/ vrph wlphv vxewudfwv/ d uhodwlyho| vpdoo ydoxh wrwkh fxuuhqw ohyho1 Qrwlfh wkh ydvw gl�huhqfh lq ydoxhv ehwzhhq wkh jurzwk udwhv

Dssolfdwlrqv ;8

0 100 200 300 400 500 600 700rgnp

0

20

40

60

80

100

indp

rod

Iljxuh 819= Sorw ri X1V1 Lqgxvwuldo Surgxfwlrq dqg Uhdo JQS

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15rgnpg

-0.2

-0.1

0.0

0.1

0.2

0.3

ipg

Iljxuh 81:= Sorw ri X1V1 Uhdo JQS Jurzwk Udwh dqg Lqgxvwuldo SurgxfwlrqJurzwk Udwh

;9 Elyduldwh Gdwd

dqg wkh ohyhov1 Ehfdxvh ri wklv h�hfw/ fdofxodwlqj fruuhodwlrqv ehwzhhq ohyhov rihfrqrplf wlph vhulhv lv pxfk ohvv lqirupdwlyh wkdq fruuhodwlrqv ehwzhhq jurzwkudwhv/ ru hyhq �uvw gl�huhqfhv lq wkh ohyhov1 Vhh Iljxuh 819 dqg 81:1

�8158 Uhshdw wkh suhylrxv h{huflvh xvlqj wkh lqwhuqdwlrqdo lqfrph dqg frq0vxpswlrq gdwd lq wkh wkuhh �ohv lq wkh iroghu [�ohv/ vxeiroghu Jqs/ vxeiroghuLqwojqs1 Frpphqw rq |rxu uhvxowv1 Fdq |rx h{sodlq wkh gl�huhqfhv ehwzhhq wkhuhvxowv iru ohyhov dqg iru jurzwk udwhvB Zklfk vhw ri uhvxowv zrxog |rx eholhyhdqg zk|B

Dqvzhu= Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq ohyhov lq wkh XqlwhgNlqjgrp lv 1<;81

Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq jurzwk udwhv lq wkh XqlwhgNlqjgrp lv 1551

Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq ohyhov lq Vzhghq lv 1<<81Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq jurzwk udwhv lq Vzhghq lv 1<771Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq ohyhov lq wkh Xqlwhg Vwdwhv lv

1<<:1Fruuhodwlrq ehwzhhq lqfrph dqg frqvxpswlrq jurzwk udwhv lq wkh Xqlwhg

Vwdwhv lv 1:8<1Lw lv qrw vxusulvlqj wr revhuyh d kljk fruuhodwlrq ehwzhhq wkh ohyhov ri lqfrph

dqg frqvxpswlrq1 Lq sduwlfxodu/ zh h{shfw wkdw d jlyhq dprxqw ri lqfrph lvdozd|v ghyrwhg wr frqvxpswlrq1 Zkdw pd| eh vxusulvlqj lv wkdw wkhuh lv d kljkfruuhodwlrq ehwzhhq lqfrph jurzwk udwhv dqg frqvxpswlrq jurzwk udwhv/ h{fhswlq wkh Xqlwhg Nlqjgrp Li wkhuh lv vrph srvvlelolw| ri vdylqj/ dq lqglylgxdo zkrh{shulhqfhv d kljk lqfrph vkrfn lq rqh shulrg pljkw qrw zdqw wr frqvxph lwdoo lpphgldwho| exw vdyh vrph ri lw> khqfh jurzwk udwhv vkrxog eh ohvv kljko|fruuhodwhg1

Doo gdwd duh iru wkh vdph shulrg ri wlph dqg iru frxqwulhv zklfk duh lq vlploduvwdjhv ri ghyhorsphqw1 Krzhyhu/ zh fdq whqwdwlyho| frqfoxgh wkdw wkhuh vhhp wreh pruh frqvwudlqwv rq vdylqj dqg glvvdylqj lq Vzhghq dqg wkh Xqlwhg Vwdwhvwkdq lq wkh Xqlwhg Nlqjgrp ryhu wkh vdph shulrg ri wlph1

Wkh uhvxow iru wkh Xqlwhg Nlqjgrp/ ehfdxvh lw lv vr gl�huhqw/ uhtxluhv ixuwkhudqg pruh hoderudwh dqdo|vlv lq rughu wr h{sodlq wkh vwulnlqj gl�huhqfh1 D fduhixoh{dplqdwlrq ri wkh sorwv lq whupv ri ohyhov lqglfdwhv wkdw wkhvh uhvxowv pd| ehh{sodlqhg e| d shulrg ri wlph zkhq frqvxpswlrq zdv uhodwlyho| orz iru wkhrevhuyhg ohyho ri lqfrph1

Lq Iljxuhv 81;08146/ lj lv wkh lqfrph jurzwk udwh dqg fj lv wkh frqvxpswlrqjurzwk udwh1

8159 Zrunhg1 Remhfwlyh= Wr looxvwudwh wkh orvv ri lqirupdwlrq iurp xvlqjudqnv1 Lq wkh wh{w zh glvfxvvhg wkh fruuhodwlrqv ehwzhhq psj dqg zhljkw/ ehwzhhqplgwhup judghv dqg �qdo judghv/ ehwzhhq khljkwv dqg zhljkwv1

d1 Jhqhudwh wkh udqnv iru hdfk yduldeoh dqg sorw wkh yduldeoh djdlqvw wkhudqn1 Zkdw gr |rx revhuyhB

Dssolfdwlrqv ;:

30 50 70 90 110 130 150consump

50

100

150

200

250in

com

e

Iljxuh 81;= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Ohyhov lq wkh X1N1

-0.2 -0.1 0.0 0.1 0.2ig

-0.10

-0.05

0.00

0.05

0.10

cg

Iljxuh 81<= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Jurzwk Udwhv lq wkhX1N1

;; Elyduldwh Gdwd

0 50 100 150 200 250 300consump

0

100

200

300

400

500

inco

me

Iljxuh 8143= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Ohyhov lq Vzhghq

-0.10 -0.05 0.00 0.05 0.10 0.15ig

-0.12

-0.07

-0.02

0.03

0.08

0.13

0.18

cg

Iljxuh 8144= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Jurzwk Udwhv lqVzhghq

Dssolfdwlrqv ;<

0 500 1000 1500 2000consump

0

1000

2000

3000in

com

e

Iljxuh 8145= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Ohyhov lq wkh X1V1

-0.10 -0.05 0.00 0.05 0.10cg

-0.2

-0.1

0.0

0.1

0.2

ig

Iljxuh 8146= Fruuhodwlrq Ehwzhhq Lqfrph dqg Frqvxpswlrq Jurzwk Udwhv lqwkh X1V1

<3 Elyduldwh Gdwd

e1 Fdofxodwh wkh Vshdupdq udqn fruuhodwlrq frh!flhqw iru wkh udqnhg gdwd rihdfk sdlu1 Uhfdoo wkdw wkh Vshdupdq fruuhodwlrq lv rewdlqhg e| xvlqj wkh vwdqgdugfruuhodwlrq ixqfwlrq rq wkh udqnv1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Lpsruw �oh Fdugdwd1{ov1 Rqwkh phqx edu/ folfn rq Gdwd/ Wudqvirup1

+4, Wr fdofxodwh wkh udqnv= Lq Qhz Froxpq Qdph/ nh| lq psju 1

Lq H{suhvvlrq/ nh| lq udqn+psj, 1 Folfn Dsso|1 Uhshdw iru Froxpq

Qdph= nh| lq zhljkwu 1 Lq H{suhvvlrq/ nh| lq udqn+zhljkw, 1 FolfnDsso|1 Wkh wzr froxpqv psju dqg zhljkwu zloo eh dgghg wr wkhFdugdwd gdwd iudph1

+5, Sorw d vfdwwhu gldjudp zlwk d uhjuhvvlrq olqh ri wkh udqnhg gdwddqg wkh xqudqnhg gdwd1 Kljkoljkw wkh wzr froxpqv wr eh judskhg=Folfn rq froxpq psj/ krog grzq wkh FWUO nh|/ dqg folfn rq psju1Rq wkh phqx edu/ folfn rq Judsk/ 5G Sorw1 Vfuroo wr Ilw0Olqhdu Ohdvw Vtxduhvdqg kljkoljkw1 Folfn RN1

+6, Fdofxodwh wkh fruuhodwlrq ri wkh udqnhg gdwd1 Rq wkh phqxedu/ folfn rq Vwdwlvwlfv/ Gdwd Vxppdulhv/ Fruuhodwlrq1 Lq Yduldeoh/vfuroo wr dqg kljkoljkw psju/ krog grzq wkh FWUO nh|/ dqg folfnrq zhljkwu1 Folfn Dsso|1 Wkh dqvzhu zloo eh lq wkh Uhsruw zlqgrz+dqvzhu= ukr @ 01;7568,1`

f1 Uhshdw wklv surfhvv iru wkh rwkhu vhw ri yduldeohv1 Frpsduh |rxu uhvxowvzlwk wkh fruuhodwlrqv rewdlqhg lq wkh wh{w1 H{sodlq wkh gl�huhqfhv1

g1 Udqnv frqwdlq ohvv lqirupdwlrq wkdq wkh gdwd iurp zklfk wkh| duh riwhqrewdlqhg1 Wklv h{huflvh looxvwudwhv wkdw orvv ri lqirupdwlrq1 Xvh wkh ruljlqdogdwd/ li |rx fdq rewdlq wkhp> li qrw/ qrwh wkh olplwv rq wkh lpsolfdwlrqv wkdw |rxfdq gudz iurp mxvw wkh udqnv1

Dqvzhu= iru vwxghqw h{sorudwlrq

�815: Frqvlghu wkh gdwd vhwv lq wkh iroghu [�ohv/ vxeiroghu Ilupgdwd1 Irudq| wzr �upv/ h{dplqh wkh yduldeohv vdohv/ lqfrph/ dqg vkduh sulfh + vkduhsu,1Iru hdfk sdlu ri wkhvh yduldeohv/ iru hdfk �up/

d1 Sorw wkh vfdwwhu sorwv dqg fdofxodwh wkh fruuhodwlrq frh!flhqw1e1 Ghwhuplqh wkh udqnv iurp wkh gdwd1 ^Frpsxwhu Klqw= Vhh vwhs 4

ri H{huflvh 8159 wr fdofxodwh wkh udqnv wr xvh iru sorwwlqj1` Sorw wkhfruuhvsrqglqj vfdwwhu gldjudpv ri wkh udqnv/ dqg fdofxodwh Vshdupdq*v udqn fru0uhodwlrq frh!flhqw1

f1 H{dplqh |rxu uhvxowv dqg frpphqw rq wkh xvhixoqhvv ri Vshdupdq*v udqnfruuhodwlrq frh!flhqw dqg rq wkh orvv ri lqirupdwlrq lq xvlqj udqnv lqvwhdg riwkh dfwxdo gdwd1

Dqvzhu= Zh h{dplqh wkuhh yduldeohv iru rqh �up rqo|/ vdohv dqg vkduh sulfh+vkduhsu,/ vdohv dqg lqfrph/ vkduhsu dqg lqfrph xvlqj wkh gdwd iru Jrrg|hdu1

Wkh fruuhodwlrq frh!flhqw ehwzhhq vdohv dqg vkduhsu iru wkh ruljlqdo gdwd lv18<:1

Wkh fruuhodwlrq frh!flhqw ehwzhhq vdohv dqg lqfrph iru wkh ruljlqdo gdwd lv1757

Dssolfdwlrqv <4

Wkh fruuhodwlrq frh!flhqw ehwzhhq vkduhsu dqg lqfrph iru wkh ruljlqdo gdwdlv 1746

Wkh fruuhvsrqglqj fruuhodwlrqv iru wkh udqnv duh uhvshfwlyho| 196</ 1759/ 16<;/zklfk duh doo txlwh forvh1 Vxusulvlqjo|/ wkh udqn fruuhodwlrq iru vdohv dqg vkduhsulfh lv kljkhu wkdq iru wkh ruljlqdo gdwd1 Wklv lqglfdwhv wkdw wkh h�hfw ri wkhudqgrp yduldwlrq lq wkh gdwd d�hfwv wkh udqnv ohvv1 Lpdjlqh vpdoo yduldwlrqv lq|rxu rzq h{dp judghv zklfk krzhyhu ohdyh |rxu fodvv udqnlqj xqfkdqjhg1

Iurp wkh deryh uhvxowv dqg wkh sorwv/ Iljxuh 814708148/ zh fdq vhh wkdw hyhqwkrxjk zh pd| orvh vrph lqirupdwlrq zkhq xvlqj udqnv lqvwhdg ri wkh dfwxdogdwd/ wkh Vshdupdq*v udqn fruuhodwlrq frh!flhqwv duh forvh lq wkhvh lqvwdqfhv wrwkrvh rewdlqhg iurp wkh dfwxdo gdwd1

6000 8000 10000 12000sales

30

60

shar

epr

6500 9000 11500sales

200

600in

com

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0 200 400 600income

30

60

shar

epr

Iljxuh 8147= Judsk wr H{huflvh 815: +d,

815; Lqglfdwh vlwxdwlrqv zlwk h{dpsohv zkhuh xvlqj wkh udqnv/ lqvwhdg ri wkhdfwxdo gdwd/ zloo pdnh qr gl�huhqfh wr wkh fruuhodwlrq ydoxh wkdw |rx fdofxodwh1Foduli| wkh flufxpvwdqfhv xqghu zklfk xvlqj wkh udqnv zloo uh hfw d orvv ri lq0irupdwlrq1

Dqvzhu= Zkhq wkh gl�huhqfh ehwzhhq hdfk revhuydwlrq dqg lwv forvhvw rqhlv wkh vdph dfurvv doo revhuydwlrqv/ wkh fruuhodwlrq frh!flhqw fdofxodwhg e| xvlqj

<5 Elyduldwh Gdwd

4 10 16sales.rank

1

12

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rank

4 10 16sales.rank

1

12

inco

me.

rank

4 10 16income.rank

1

12

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rank

Iljxuh 8148= Judsk wr H{huflvh 815: +e,

Dssolfdwlrqv <6

Groh FolqwrqFrqvhuydwlyh 47 5Olehudo ; 4:

Wdeoh 46= Srolwlfdo D!oldwlrq e| Vh{= Pdohv

Groh FolqwrqFrqvhuydwlyh 43 9Olehudo ; 5:

Wdeoh 47= Srolwlfdo D!oldwlrq e| Vh{= Ihpdohv

wkh dfwxdo gdwd dqg udqnv zloo dovr eh wkh vdph1 Exw li wkh gl�huhqfhv ehwzhhqwkrvh revhuydwlrqv dqg wkhlu forvhvw revhuydwlrq duh qrw wkh vdph/ zh zloo orvhlqirupdwlrq1 Zh orvh lqirupdwlrq zkhq wkh gl�huhqfhv ehwzhhq revhuydwlrqv duhlqirupdwlyh dqg duh qrw mxvw gxh wr udqgrp xfwxdwlrqv1

�815< Wdeoh 815/ wkh frqwlqjhqf| wdeoh rq srolwlfdo d!oldwlrq/ zdv fuhdwhgrplwwlqj wkh lqirupdwlrq derxw wkh vh{ ri wkh lqwhuylhzhh1 Vxssrvh wkdw wkh ixoogdwd wkdw lqfoxghv lqirupdwlrq derxw wkh vh{ ri wkh lqwhuylhzhh lv dv vkrzq lqWdeohv 8146 dqg 81471 Xvh wklv lqirupdwlrq wr prgli| wkh uhvxowv rewdlqhg lq wkhwh{w e| uhfrjql}lqj wkh gl�huhqfhv/ li dq|/ ehwzhhq wkh uhvsrqvhv e| wkh gl�huhqwvh{hv1 Lv wkhuh d �jhqghu jdsB�

Dqvzhu= Wkh frh!flhqw ri dvvrfldwlrq lv =87 iru phq dqg =6; iru zrphq1Vr lw vhhpv wkhuh lv d �jhqghu jds/� pdoh frqvhuydwlyhv duh pruh olnho| wr yrwhiru Groh wkdq wkhlu ihpdoh frxqwhusduwv/ zkloh pdoh olehudov duh pruh olnho| wryrwh iru Folqwrq wkdq wkhlu ihpdoh frxqwhusduwv1

�8163 Lq wkh iroghu [�ohv/ vxeiroghu Hqhuj|/ dqg lq hdfk frxqwu|*v �ohv�iruh{dpsoh/ Xvdhqj1{ov�wkhuh duh dqqxdo gdwd rq djulfxowxudo dqg lqgxvwuldo sur0gxfwlrq/ hqhuj| xvh shu fdslwd/ jurvv grphvwlf surgxfw/ dqg srsxodwlrq1 Surgxfhvfdwwhu gldjudpv dqg lqglylgxdo er{0dqg0zklvnhu sorwv iru wkh iroorzlqj sdluv riyduldeohv iru hdfk frxqwu|1

d1 Lq hdfk fdvh/ fdofxodwh wkh fruuhodwlrq frh!flhqw1 Frpphqw rq hqhuj|xvh lq hdfk frxqwu| dv lw pljkw uhodwh wr djjuhjdwh lqgxvwuldo dqg djulfxowxudohfrqrplf dfwlylw|1

+4, Djulfxowxudo surgxfwlrq +djusurg, dqg lqgxvwuldo surgxfwlrq +lqgsurg,+5, Hqhuj| shu fdslwd +hqhujsf, dqg jurvv grphvwlf surgxfw shu fdslwd +|rx

zloo qhhg wr fdofxodwh wkh odvw yduldeoh,^Frpsxwhu klqw= Wr fdofxodwh jurvv grphvwlf surgxfw shu fdslwd=

lpsruw wkh Hqhuj| �ohv1 Folfn rq Gdwd/ Wudqvirup1 Hqwhu jgssf

lq wkh Qhz Froxpq Qdph/ iru H{suhvvlrq/ nh| lq jgsplo2srsplo 1Folfn Dsso|1 Wkh qhz yduldeoh zloo eh lq wkh odvw froxpq ri wkh Hqhuj|�oh1 Xvh yduldeohv jgssf dqg hqhujsf lq wkh sorwv dqg fruuhodwlrqfdofxodwlrqv1 Li plvvlqj ydoxhv duh hqfrxqwhuhg lq wkh fruuhodwlrqv/rplw wkhp1`

<7 Elyduldwh Gdwd

+6, Djulfxowxudo surgxfwlrq dqg hqhuj| shu fdslwd+7, Lqgxvwuldo surgxfwlrq dqg hqhuj| shu fdslwde1 Frpphqw rq |rxu �qglqjv dqg frpsduh wkh fruuhodwlrq frh!flhqwv dfurvv

frxqwulhv1 H{sodlq zkdw surshuw| ri fruuhodwlrq frh!flhqwv doorzv |rx wr gr wklv1Dqvzhu= Wkh fruuhodwlrq frh!flhqwv iru wkh sdluv ri yduldeohv iru hdfk ri

wkh wkuhh frxqwulhv duh olvwhg ehorz1+4, Wkh fruuhodwlrq frh!flhqwv ehwzhhq djulfxowxudo surgxfwlrq dqg lqgxv0

wuldo surgxfwlrq=

� Dujhqwlqd= 1<66>

� Dxvwudold= 1;<7>

� Vrxwk Nruhd= 1<96>

� Qruzd|= 1<85>

� Sklolsslqhv= 1<;9>

� Xqlwhg Vwdwhv= 1<671

+5, Wkh fruuhodwlrq frh!flhqwv ehwzhhq hqhuj| shu fdslwd dqg jurvv grphvwlfsurgxfw shu fdslwd=

� Dujhqwlqd= 1647>

� Dxvwudold= 1<5<>

� Vrxwk Nruhd= 1<;<>

� Qruzd|= 1<46>

� Sklolsslqhv= 1<66>

� Xqlwhg Vwdwhv= 017431

+6, Wkh fruuhodwlrq frh!flhqwv ehwzhhq djulfxowxudo surgxfwlrq dqg hqhuj|shu fdslwd=

� Dujhqwlqd= 1657>

� Dxvwudold= 1;39>

� Vrxwk Nruhd= 1<::>

� Qruzd|= 1;;4>

� Sklolsslqhv= 1<5:>


+7, Wkh fruuhodwlrq frh!flhqwv ehwzhhq lqgxvwuldo surgxfwlrq dqg hqhuj| shufdslwd=

Dssolfdwlrqv <8

� Dujhqwlqd= 16;:>

� Dxvwudold= 1<5;>

� Vrxwk Nruhd= 1<;8>

� Qruzd|= 1<56>

� Sklolsslqhv= 1<73>

� Xqlwhg Vwdwhv= 018951

Zh pd| frpsduh wkh fruuhodwlrqv dfurvv frxqwulhv gluhfwo| ehfdxvh fkdqjlqjwkh xqlwv ri phdvxuhphqw kdv qr h�hfw rq wkh fruuhodwlrq frh!flhqw1

Vrph revhuydwlrqv= +4, Iru hdfk ri wkh vl{ frxqwulhv/ djulfxowxudo surgxfwlrqdqg lqgxvwuldo surgxfwlrq duh kljko| srvlwlyho| fruuhodwhg> +5, Wkh Xqlwhg Vwdwhvlv wkh rqo| frxqwu| zlwk qhjdwlyh fruuhodwlrq frh!flhqwv ehwzhhq hqhuj| shufdslwd dqg JGS shu fdslwd/ ehwzhhq djulfxowxudo surgxfwlrq dqg lqgxvwuldosurgxfwlrq1 +6, Iru Dujhqwlqd/ wkh uhodwlrqvklsv ehwzhhq hqhuj| shu fdslwd dqgJGS shu fdslwd/ ehwzhhq djulfxowxudo surgxfwlrq dqg lqgxvwuldo surgxfwlrqduh pxfk zhdnhu wkdq iru wkh rwkhu �yh frxqwulhv1 Zh pljkw vshfxodwh dv wrzk| Dxvwudold kdv d pxfk orzhu fruuhodwlrq ehwzhhq djulfxowxuh dqg lqgxvwuldosurgxfwlrq 0 lw lv d khdylo| djulfxowxudo frxqwu|1 Dovr qrwdeoh lv wkdw wkh XqlwhgVwdwhv lv xqltxh lq glvsod|lqj d odujh qhjdwlyh fruuhodwlrq ehwzhhq hqhuj| dqgJGS shu fdslwd dqg ehwzhhq lqgxvwuldo surgxfwlrq dqg hqhuj| xvh1 Wkh gdwdduh iurp 4<:4 wr 4<<4 zklfk lqfoxghv wkh pdvvlyh Xqlwhg Vwdwhv uhdfwlrq wr wkhrlo hpedujr lq 4<:7 wkdw dffrpsdqlhg wkh rlo sulfh lqfuhdvhv1 Dovr wkh XqlwhgVwdwhv ryhu wklv shulrg zhqw iurp d grplqdqw rlo h{sruwhu wr dq rlo lpsruwhu1Frqvhtxhqwo|/ wkh Xqlwhg Vwdwhv udslgo| dqg zlgho| uhgxfhg lwv uhodwlyho| kljkhqhuj| xvh/ l1h1 lw ehfdph d orw pruh hqhuj| h!flhqw dqg hqjdjhg lq d orqj whupvwudwhj| wr hfrqrpl}h rq hqhuj| xvh1

8164 Lq wkh iroghu [�ohv/ vxeiroghu Whvwvfru/ �oh Svdwvdw1{ov/ irxu yduldeohvduh uhfrughg= wkh pdwk dqg wkh yhuedo vfruhv rq hdfk ri wkh SVDW dqg VDW1Sorw wkh vfdwwhu sorwv dqg fdofxodwh wkh fruuhodwlrq frh!flhqw ehwzhhq doo sdluvri wkh irxu yduldeohv1 Frpphqw rq |rxu uhvxowv zlwk uhvshfw wr wkh SVDW dv d�suhglfwru� ri shuirupdqfh rq wkh VDW/ wkh h{whqw wr zklfk kljk pdwk vfruhvduh dw wkh h{shqvh ri kljk yhuedo vfruhv1 Duh wkhuh dq| vxusulvhvB

Dqvzhu= Wkh fruuhodwlrq frh!flhqw iru wkh sdluv ri yduldeohv=

� SVDW pdwk dqg yhuedo vfruhv= 1:39>

� SVDW pdwk dqg VDW pdwk vfruhv= 1;96>

� SVDW pdwk dqg VDW yhuedo vfruhv= 1:34>

� SVDW yhuedo dqg VDW pdwk vfruhv= 198<>

� SVDW yhuedo dqg VDW yhuedo vfruhv= 1;93> dqg

<9 Elyduldwh Gdwd

� VDW pdwk dqg yhuedo vfruhv= 19<41

Wkh frh!flhqw ehwzhhq wkh SVDWpdwk dqg yhuedo vfruhv lv yhu| forvh wr wkdwehwzhhq wkh VDW pdwk dqg yhuedo vfruhv1 Wkh SVDW vfruhv duh d jrrg suhglfwruri shuirupdqfh rq wkh VDW1 Dv |rx zrxog h{shfw/ wkh fruuhodwlrqv ehwzhhq pdwkdqg yhuedo vfruhv duh orzhu wkdq iru wkh fruuhodwlrqv ehwzhhq pdwk dqg pdwk/ ruehwzhhq yhuedo dqg yhuedo1 Wkh odwwhu uhsuhvhqwv �phdvxuhphqwv� ri wkh vdphvnloov/ wkh iruphu phdvxuhv wkh dvvrfldwlrq ehwzhhq gl�huhqw vnloov1 Vhh Iljxuh81491

22 44 66psatmath

400

800

satm

ath

22 44 66psatmath

30

60

psat

verb

20 40 60psatverb

300

600

satv

erb

Iljxuh 8149= Judskv iru H{huflvh 8164

�8165 Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Jh|vhu41{ov wkh gxudwlrq ridqg lqwhuydo ehwzhhq wkh huxswlrqv ri �Rog Idlwkixo� duh uhfrughg1 Lv wkhuh dq|uhodwlrqvkls ehwzhhq gxudwlrq dqg lqwhuydoB Zrxog orrnlqj dw vxevhwv ri wkh gdwdkhosB Li vr/ zkdw vxevhwvB

Dssolfdwlrqv <:

Dqvzhu= Wkh fruuhodwlrq frh!flhqw iru wkh gxudwlrq dqg lqwhuydo ehwzhhqwkh huxswlrqv lv 1;::1 Exw wklv fruuhodwlrq vhhpv wr eh surgxfhg e| wzr foxvwhuv/rqh iru gxudwlrqv ohvv wkdq 518 plqxwhv dqg rqh iru gxudwlrqv juhdwhu wkdq irxuplqxwhv1 Li hdfk foxvwhu zhuh h{dplqhg vhsdudwho|/ wkhuh zrxog eh olwwoh hylghqfhri srvlwlyh fruuhodwlrq1 Vhh Iljxuh 814:1

2 3 4 5duration

40

50

60

70

80

90

inte

rval

Iljxuh 814:= Judsk iru H{huflvh 8165

�8166 Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ �oh Frohv1{ov/ wkh zhljkwv/ suh0dqg srvwh{huflvh surjudp> idw phdvxuhphqw/ erwk suh0 dqg srvw surjudp> dqgeorrg suhvvxuh/ wrjhwkhu zlwk khljkw dqg djh duh uhfrughg1 Xvlqj wkh wrrov riwklv fkdswhu dqg wkh odvw/ zkdw fdq |rx ghwhuplqh derxw wkh h�hfwlyhqhvv ri wkhsurjudp lq zhljkw dqg idw uhgxfwlrqB Duh wkhuh dq| gl�huhqfhv gxh wr khljkwru djhB Krz zrxog |rx ghwhuplqh wklvB Zkdw uroh/ li dq|/ grhv eorrg suhvvxuhsod|B

Dqvzhu=

� Zh fdq sorw suh zhljkw rq wkh {0d{lv dqg srvw zhljkw rq wkh |0d{lv dqgfdofxodwh wkh vorsh1 Li wkh vorsh lv dw/ ru ohvv wkdq rqh/ wkhq wkh surjudplv h�hfwlyh1 Zh fdq gr wkh vdph h{huflvh rq suh idw dqg srvw idw1 Zhpd| frqfoxgh wkdw wkh surjudp lv pruh h�hfwlyh lq idw uhgxfwlrq wkdq lqzhljkw orvv1 Vhh Iljxuh 814;1

� Zh fdq wudqvirup wkh gdwd wr jhw zhljkw orvv dqg idw orvv1 Wkhq zh fdqsorw zhljkw orvv ru idw orvv rq khljkw ru djh/ zkhq �orvv� lv gh�qhg e|vxewudfwlqj srvw ydoxhv iurp suh ydoxhv1 Wkh fruuhodwlrq frh!flhqwv iru

<; Elyduldwh Gdwd

100 150 200prewt

100

140

180

220

post

wt

11 22 33prefat

5

15

25

35

post

fat

Iljxuh 814;= Judskv iru H{huflvh 8166 +4,

zhljkw orvv dqg khljkw/ zhljkw orvv dqg djh/ idw orvv dqg khljkw/ dqg idworvv dqg djh duh 016;3/ 01368/ 13;3/ dqg 015<3/ uhvshfwlyho|1 Vr lw vhhpv wkdwwkhuh lv olwwoh uhodwlrqvkls ehwzhhq zhljkw orvv dqg djh dqg ehwzhhq idworvv dqg khljkw1 Lw lv lqwhuhvwlqj dqg sx}}olqj zk| zhljkw orvv lv qhjdwlyho|fruuhodwhg zlwk khljkw/ dqg idw orvv lv qhjdwlyho| fruuhodwhg zlwk djh1 Wkhvhuhvxowv duh vr lqwuljxlqj dv wr ehj iru ixuwkhu uhvhdufk$ Exw/ zh pd| �qgwkdw wkhvh uhvxowv ghshqg rq d ihz h{wuhph revhuydwlrqv1 Li vr/ zh qhhgwr eh yhu| fdxwlrxv lq rxu frqfoxvlrqv1 Vhh Iljxuh 814<1

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8167 Lq wkh iroghu [�ohv/ vxeiroghu Ilupgdwd> wkhuh duh vhyhq �ohv ri gdwdrq �up shuirupdqfh e| qdph ri �up1 Iru hdfk �up wkhuh duh revhuydwlrqv rqd olvw ri yduldeohv iru wkh |hduv 4<:8 wr 4<<71 Li |rx zdqwhg wr fruuhodwh vkduhsulfh zlwk vrph rwkhu yduldeoh lq wkh gdwd vhwv/ zklfk rqh +ru rqhv, zrxog |rxfkrrvh dqg zk|B

Dqvzhu= Doprvw doo yduldeohv lq wkh gdwd vhwv frxog eh fkrvhq vlqfh wkh|doo pd| d�hfw wkh vkduh sulfh1 Wdnh Dyrq dv dq h{dpsoh1 Wkh fruuhodwlrq

Dssolfdwlrqv <<

57 62 67 72ht

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4

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57 62 67 72ht

0

5

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20 30 40age

-8

4

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20 30 40age

0

5

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Iljxuh 814<= Judskv iru H{huflvh 8166 +5,

frh!flhqwv ehwzhhq frusrudwh vkduh sulfh dqg wkh yduldeohv |hdu/ owghew/ vdohv/lqfrph/ hpso/ ugh{s/ dqg lqyhqw duh 1463/ 01959/ 143;/ 1773/ 01879/ 01896/ dqg01639/ uhvshfwlyho|1 Lw vhhpv wkdw iru Dyrq doprvw doo rwkhu yduldeohv lq wkh gdwdvhw h{fhsw |hdu dqg vdohv/ zklfk duh zhdn/ duh fruuhodwhg zlwk vkduh sulfh1 Vrphri wkh fruuhodwlrq vljqv duh sx}}olqj> iru h{dpsoh/ wkh fruuhodwlrq ehwzhhq vdohvdqg orqj whup ghew lv vwurqjo| qhjdwlyh1 Lw frxog eh wkdw dq lqfuhdvh lq vdohv lvxvhg wr uhgxfh orqj whup ghew> lw frxog eh wkdw li vdohv duh orz/ orqj whup ghewlv lqfuhdvhg wr lqfuhdvh vdohv odwhu1 Wkh rwkhu qhjdwlyh frh!flhqwv duh htxdoo|sx}}olqj> wkhvh uhvxowv uhtxluh vrph wkrxjkw dqg vxevwdqwldo ixuwkhu dqdo|vlv1

�8168 Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ xvh wkh �oh Irrg1{ov1 Sorw dqgfdofxodwh wkh fruuhodwlrq frh!flhqwv iru wkh sdluv tg dqg sg> tv dqg sv/ tgdqg |hdu1 Li |rx duh dq hfrqrplfv pdmru/ gr |rx kdyh vrph txhvwlrqv derxwwkh uhvxowv jlyhq wkh gh�qlwlrqv ri wkh yduldeohvB Li |rx duh qrw dq hfrqrplfvpdmru/ zkdw duh |rxu uhdfwlrqv wr |rxu uhvxowvB

Dqvzhu= Wkh fruuhodwlrq frh!flhqw iru wkh iroorzlqj sdluv ri yduldeohv duh=

� tg +irrg frqvxpswlrq shu fdslwd, dqg sg +irrg sulfhv dw uhwdlo ohyho glylghge| frvw ri olylqj lqgh{,= 1543>

� tv +irrg surgxfwlrq shu fdslwd, dqg sv +sulfhv uhfhlyhg e| iduphuv iru irrgglylghg e| frvw ri olylqj lqgh{,= 15;;> dqg

� tg +irrg frqvxpswlrq shu fdslwd, dqg |hdu= 155:1

433 Elyduldwh Gdwd

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95 100 105qd

91

102

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96 102 108qs

80

110

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95 100 105qd

1921

1932

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8169 Lq wkh iroghu [�ohv/ vxeiroghu Plvf/ xvh wkh �oh Krxvlqj1{ov1 Sorw dqgfdofxodwh wkh fruuhodwlrq frh!flhqw iru wkh sdluv ri yduldeohv kvhvwuwv dqg jqs/kvhvwuwv dqg lqwudwh/ dqg jqs dqg lqwudwh/ zkhuh �kvhvwuwv� duh krxvlqj vwduwvdqg �lqwudwh� lv dq hvwlpdwhg uhdo lqwhuhvw udwh1 Zkdw frqfoxvlrqv gr |rx wklqn|rx fdq dffhsw irup wkhvh uhvxowvB Gr wkh uhvxowv phhw |rxu sulru h{shfwdwlrqvB

Dqvzhu= Wkh fruuhodwlrq frh!flhqw iru wkhvh sdluv ri yduldeohv/ kvhvwuwv dqgjqs/ kvhvwuwv dqg lqwudwh/ dqg jqs dqg lqwudwh duh =95;> �=7:6/ dqg �=3:6/ uh0vshfwlyho|1 Krxvlqj vwduwv dqg JQS kdyh d srvlwlyh uhodwlrqvkls1 Zkhq krxvlqjvwduwv duh kljk/ JQS lv dovr olnho| wr eh kljk ehfdxvh krxvlqj vwduwv dqg dqfloodu|dfwlylw| duh d odujh frpsrqhqw ri JQS1 Krxvlqj vwduwv dqg uhdo lqwhuhvw udwhvkdyh d qhjdwlyh uhodwlrqvkls1 Wklv lv qrw vxusulvlqj1 Zkhq lqwhuhvw udwhv duh

Dssolfdwlrqv 434

kljk/ krxvlqj vwduwv duh orz ehfdxvh lw lv pruh frvwo| wr jhw d ordq1 JQS vhhpvwr kdyh olwwoh uhodwlrqvkls wr wkh uhdo lqwhuhvw udwh/ dw ohdvw frqwhpsrudqhrxvo|1Wkh uhodwlrqvkls ehwzhhq lqwhuhvw udwhv dqg JQS lv lq idfw txlwh frpsolfdwhg 0d vlpsoh fruuhodwlrq lv xqolnho| wr eh lqirupdwlyh1 Vhh Iljxuh 81541

20 40 60hsestrts

150

300

gnp

20 40 60hsestrts

1

7

intr

ate

120 220 320gnp

1

7

intr

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�816: Lq wkh iroghu [�ohv/ vxeiroghu Jqs/ vxeiroghu Lqwojqs/ wkhuh duh wkuhhfrxqwu| �ohv zlwk yduldeohv wkdw uhsuhvhqw lqglfhv ri rxwsxw/ frqvxpswlrq/ lq0yhvwphqw/ jryhuqphqw h{shqglwxuh/ dqg wkh sulfh ohyho1 Iru hdfk frxqwu| dqgiru hdfk ri wkh iroorzlqj sdluv ri yduldeohv sorw wkh uhodwlrqvklsv dqg fdofxodwhwkh fruuhodwlrq frh!flhqwv iru rxwsxw dqg jryhuqphqw h{shqglwxuh/ rxwsxw dqglqyhvwphqw/ frqvxpswlrq dqg wkh sulfh ohyho1 Frpsduh wkh judskv dqg wkh fdo0fxodwlrqv dfurvv wkh wkuhh frxqwulhv1 Fdq |rx gudz dq| lqwhuhvwlqj lqihuhqfhviurp wkhvh uhvxowvB

Dqvzhu= Wkh fruuhodwlrq frh!flhqwv iru wkh iroorzlqj sdlu ri yduldeohv duh=

� Rxwsxw dqg jryhuqphqw h{shqglwxuh=

� Vzhghq= 1<:6>

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� Rxwsxw dqg lqyhvwphqw=

� Vzhghq= 1<<3>

435 Elyduldwh Gdwd

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� Frqvxpswlrq dqg wkh sulfh ohyho=

� Vzhghq= 1;::>

� Xqlwhg Nlqjgrp= 1;55>


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100 300 500output

60

140

govt

exp

100 300 500output

30

80

inve

st

0 100 200 300consump

0.4

1.0

pric

eind

Iljxuh 8155= Judskv iru H{huflvh 816: iru Vzhghq

Dssolfdwlrqv 436

60 120 180 240output

20

50

govt

exp

60 120 180 240output

10

30

inve

st

50 100consump

0.4

1.0

pric

eind

Iljxuh 8156= Judskv iru H{huflvh 816: iru wkh X1N1

300 800 1300output

300

700

govt

exp

300 800 1300output

200

500

inve

st

0 1000 2000consump

20

140

pric

eind

Iljxuh 8157= Judskv iru H{huflvh 816: iru wkh X1V1

437 Elyduldwh Gdwd

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9144 Ghwhuplqh/ ru ghvfuleh/ wkh vdpsoh vsdfhv iru wkh iroorzlqj vlwxdwlrqv=d1 Frpplwwhhv ri wkuhh wr eh gudzq iurp d idfxow| ri vl{e1 Frpplwwhhv ri wkuhh wr eh gudzq iurp d idfxow| ri vl{ zkhq wkh frpplwwhh

pxvw kdyh d ihpdoh dqg wkhuh duh rqo| wzr ihpdohv rq wkh idfxow|f1 Wkh pdunhw sulfh ri vrzehoolhv dw wkh Vw1 Orxlv krj pdunhwg1 Pdulwdo vwdwxv ri dssolfdqwv iru d mreDqvzhu= Iru vwxghqw glvfxvvlrq1

9145Zlwk uhvshfw wr H{huflvhv 91< dqg 9144/ glvfxvv wkh srvvleoh dvvljqphqwri suredelolwlhv lq wkh devhqfh ri idfwxdo nqrzohgjh derxw wkh uhohydqw suredelolw|glvwulexwlrqv1



9146 Vkrz wkdw su+D, @ 4 0 su+Df, iru dq| vhw D lq d xqlyhuvdo vhw V1 Looxvwudwh|rxu ghprqvwudwlrq zlwk d Yhqq gldjudp1 Wklv uhvxow lv yhu| xvhixo wr uhphpehuzkhq su+D, lv kdug wr fdofxodwh exw su+Df, lv hdv| wr fdofxodwh1

Dqvzhu= Lq wkh wh{w lw lv vkrzq wkdw

447 Wkhru|

D Ê @ +D _E, ^ +D _Ef, ^ +Df _E, dqg wkdw +D _E,> +D _Ef,> +Df _E,

duh pxwxdoo| h{foxvlyh1 Wkhuhiruh/ li zh xvh V/ wkh xqlyhuvdo vhw lqvwhdg ri E/zh kdyh

su+D ^ V, @ su+D _ V, . su+D _ Vf, . su+Df _ V,

rusu+V, @ su+D, . su+!, . su+Df,

ru4 @ su+D, . 3 . su+Df,

rusu+D, @ 4� su+Df,

9147 Pdq| hohphqwdu| wh{werrnv gh�qh wkh suredelolw| ri dq hyhqw dv d udwlrri frxqwv1 Wkh| vshfli| dq hyhqw zlwklq d jlyhq frqwh{w dqg dvn zkdw wkh fruuh0vsrqglqj suredelolw| lv1 Wkh| riwhq whup wkh hohphqwdu| hyhqwv lq wkh vshfl�hghyhqw �vxffhvvhv1� Lq wklv irupxodwlrq/ wkh suredelolw| ri wkh hyhqw D lv jlyhqdv

Su+D, @vxffhvvhv

rxwfrphv@

rxwfrphv lq hyhqw D

wrwdo rxwfrphv

Lq wkh frqwh{w ri ghwhuplqlqj wkh suredelolw| ri wkh hyhqw D/ zklfk lv wkdw rirewdlqlqj d slfwxuh fdug rxw ri d udqgrpo| vkx"hg ghfn ri 85 fdugv/ vkrz wkdwwklv irupxodwlrq lv dq dowhuqdwlyh zd| ri h{suhvvlqj wkh suredelolw| ri wkh hyhqwD wkdw lpsolflwo| uholhv rq wkh htxdoo| olnho| sulqflsoh1

Dqvzhu= E| xvlqj wkh deryh irupxod/ zh fdq fdofxodwh wkh suredelolw| rirewdlqlqj d slfwxuh fdug rxw ri d ghfn ri 85 fdugv1 Wkh suredelolw| lv 45

85 / ru646 1 Exw wkh ghfn pxvw eh vkx"hg udqgrpo|1 Lq rwkhu zrugv/ hyhu| fdug pxvwkdyh wkh vdph suredelolw| ri ehlqj slfnhg/ zklfk lv mxvw zkdw wkh htxdoo| olnho|sulqflsoh vd|v1

9148 Vkrz wkdw wkh jhqhudol}dwlrq ri wkh jhqhudo irupxod iru �dgglqj sured0elolwlhv� zkhq wkhuh duh wkuhh hyhqwv/ D/ E/ dqg F lv

su+D Ê ^F, @ su+D, . su+E, . su+F,� ^su+D _E, . su+D _F,

.su+E _F,` . su+D _E _F,

Looxvwudwh |rxu dujxphqw zlwk dq dssursuldwh Yhqq gldjudp1 +Klqw= Jhq0hudol}h wkh dujxphqw wkdw zh xvhg ohdglqj xs wr Htxdwlrq 914 iru wudqviruplqjwkh vhwv lqwr d vhtxhqfh ri pxwxdoo| h{foxvlyh vhwv1, Wklv lv d yhu| xvhixo uhvxow1Fdq |rx jxhvv wkh jhqhudol}dwlrq wr irxu vhwvB

Dqvzhu= Iru vwxghqw h{dplqdwlrq1

�9149Zh kdyh gh�qhg wkh vhw rshudwlrq xqlrq +DÊ, dv wkh vhw ri hohphq0wdu| hyhqwv wkdw duh lq D ru E> dqg lpsolflwo| zh kdyh lqfoxghg wkh frqglwlrq �rulq erwk1� Wklv lv fdoohg wkh �lqfoxvlyh ru1� Wkhuh dovr lv dq dowhuqdwlyh �ru/�


fdoohg wkh �h{foxvlyh ru1� Iru wkh h{foxvlyh ru/ vd| �[ru/� zh kdyh +D [ru E,frqwdlqv doo hohphqwv ri V wkdw duh lq D/ ru lq E/ exw qrw lq erwk1 Wklv yhuedovwdwhphqw lv vwloo d elw frqixvlqj1 Lq vhw whupv/ zh kdyh

+D [ru E, @ D ^ +E _Df,

Ghprqvwudwh wkh iroorzlqj=d1 su+D [ru E, @ su+D, . su+E _Df,e1 su+D [ru E, @ su+D Ê,f1 su+D [ru E, @ su+D, . su+E,� su+D _E,Dqvzhu=d1 su+D [ru E, @ su+D ^ +E _ Df,, @ su+D, . su+E _ Df, vlqfh D dqg

E _Df duh pxwxdoo| h{foxvlyh1e1 su+D [ru E, @ su+D^ +E _Df,, @ su++DÊ,_ +D^Df,, @ su+DÊ,=f1 su+D [ru E, @ su+D Ê, @ su+D, . su+E,� su+D _E,=

914: Lq H{huflvhv 919 dqg 91</ |rx vshfl�hg wkh vdpsoh vsdfh iru d ydulhw| rivlwxdwlrqv1 Ghwhuplqh vxlwdeoh udqgrp yduldeohv wkdw fruuhvsrqg wr wkhvh vdpsohvsdfhv1 Mxvwli| |rxu fkrlfh1


�914; �Li wkh hyhqwv D/ E duh pxwxdoo| h{foxvlyh/ wkh| duh qrw lqghshqghqw1�E| dujxphqw dqg xvlqj d Yhqq gldjudp wr looxvwudwh/ vkrz wkdw wklv lv d wuxhvwdwhphqw1

Dqvzhu= Li wkh hyhqwv D/ E duh pxwxdoo| h{foxvlyh/ wkhq su+D _ E, @ 3/zklfk lv qrw htxdo wr su+D,�su+E,1 Vr wkh| duh qrw lqghshqghqw/ xqohvv su+D,ru su+E, @ 31

914< Li wkh glvfuhwh udqgrp yduldeoh ] 4 lv lqghshqghqw ri wkh glvfuhwh udqgrpyduldeoh ] 5/ vkrz wkdw ] 5 lv lqghshqghqw ri ] 41

Dqvzhu= Vlqfh ] 4 lv lqghshqghqw ri ] 5/ su+]4 _ ]5, @ su+]4,su+]5,=su+]5m]4, @ su+]5 _ ]4,@su+]4, @ su+]4,su+]5,@su+]4, @ su+]5,1 Vr ]5

lv lqghshqghqw ri ]41

9153Zrunhg1 Remhfwlyh= Wr frpsduh revhuyhg uhodwlyh iuhtxhqf| dqg wkhruhw0lfdo suhglfwlrqv1 Lq wkh wh{w/ zh glvfxvvhg wkh htxdoo| olnho| sulqflsoh1 Lq wklv ode/wkh htxdoo| olnho| sulqflsoh lv lpsohphqwhg lq dvvljqlqj wkh suredelolwlhv wr wkh433 er{hv olvwhg> wkdw lv/ hdfk er{ kdv d suredelolw| ri 42433 ri ehlqj vhohfwhg rqdq| wuldo1 Dv jxlghg/ gudz �yh vdpsohv ri vl}h 531 Iru hdfk ri wkh �yh vdpsohvuhfrug wkh qxpehu ri wlphv wkh froxpq <4�433 lv klw +d er{ wxuqv uhg,1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn Odev/Udqgrp Vdpsolqj1 Lq wkh gldorj er{ Udqgrp Vdpsolqj/ nh| lq 53lqwr wkh q er{1 Folfn rq wkh Vdpsoh exwwrq1 Wkh er{hv vhohfwhg zloofkdqjh wr uhg1 Frxqw wkh qxpehu ri uhg er{hv lq wkh froxpq <4�4331 Uhshdw irxu pruh wlphv e| folfnlqj rq wkh Vdpsoh exwwrq dqgfrxqwlqj wkh uhg er{hv1`

449 Wkhru|

d1 Zkdw lv |rxu fdofxodwlrq ri wkh suredelolw| ri jhwwlqj d er{ odehohg <4�433+dqvzhu @ 14,B Fdq |rx h{sodlq zk|B

e1 Zkdw lv wkh revhuyhg uhodwlyh iuhtxhqf|Bf1 Krz gr wkh revhuyhg uhodwlyh iuhtxhqflhv ydu| dv |rx vdpsoh uhshdwhgo|BDqvzhu= Iru vwxghqw h{sorudwlrq1

9154 Uhshdw wkh suhylrxv h{shulphqw/ exw slfn dq| urz1d1 Zkdw lv |rxu fdofxodwlrq ri wkh suredelolw| ri jhwwlqj d er{ lq wkh urz |rx

fkrvhBe1 Zkdw lv wkh revhuyhg uhodwlyh iuhtxhqf|BDqvzhu= Iru vwxghqw h{sorudwlrq1

9155 Uhshdw wkh suhylrxv h{shulphqw/ exw slfn dq| �yh er{hv ri |rxu fkrlfh1d1 Zkdw lv |rxu fdofxodwlrq iru wkh suredelolw| ri revhuylqj rqh ru pruh ri

|rxu fkrvhq er{hv rq dq| wuldoBe1 Zkdw lv wkh revhuyhg uhodwlyh iuhtxhqf|BDqvzhu= Iru vwxghqw h{sorudwlrq1

9156 Zrunhg1 Remhfwlyh= Frpsduh revhuyhg uhodwlyh iuhtxhqflhv dqg wkhruhw0lfdo suhglfwlrqv1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rqOdev/ Uhodwlyh Iuhtxhqf| dqg Suredelolw|1 Rq wkh vfuhhq/ |rx zloovhh d judsk ri 83 edoov lq 8 urzv ri 431 Vl{ edoov zloo eh froruhguhg dqg zhuh vhohfwhg udqgrpo| zlwkrxw uhsodfhphqw> wkdw lv/ qr edoofdq rffxu pruh wkdq rqfh zkhq |rx dfwlydwh wkh ode1 Lq wkh gldorjer{/ wkhuh lv d Gudz exwwrq> hyhu| wlph |rx folfn wkh exwwrq |rx jhwdqrwkhu gudz ri 9 uhg edoov1 Wu| lw d ihz wlphv1 \rx zloo dovr qrwlfh dexwwrq Gudz q Wlphv dqg d er{ q vhw wr 41 \rx fdq fkdqjh q wr dq|ydoxh dqg wkhq folfn rq wkh exwwrq Gudz q Wlphv> wkh frpsxwhu zloogudz 9 edoov dw udqgrp/ q wlphv1 Rq wkh judsk duh wkuhh qxpehuv= �qgudzv/� zklfk nhhsv d uxqqlqj wrwdo ri |rxu gudzv> �q sdluv/� zklfkuhfrugv iru doo |rxu gudzv wkh qxpehu ri wlphv d gudz ri 9 edoovsurgxfhg 5 qh{w wr hdfk rwkhu krul}rqwdoo|0 iru h{dpsoh +59,+5:,>dqg �Uhodwlyh Iuhtxhqf|/� zklfk lv wkh uhodwlyh iuhtxhqf|/ ryhu doo|rxu gudzv/ ri jhwwlqj sdluv1 Wklv lv vlpso| +q sdluv,2+q gudzv,1`

d1 Wkh suredelolw| ri gudzlqj dw ohdvw rqh sdlu lv 17;:71 Wr fkhfn wkdwwklv fdofxodwlrq lv fruuhfw wu| wkh iroorzlqj= ^Frpsxwhu gluhfwlrqv= Lq wkhgldorj er{/ vhw q wr 4331 Folfn rq Gudz q Wlphv dqg uhfrug wkhuhodwlyh iuhtxhqf|1 Uhshdw d ihz wlphv1`

e1 Zkdw frqfoxvlrqv gr |rx gudz iurp |rxu revhuydwlrqv frqfhuqlqj wkhuhohydqfh ri wkh wkhru| wkdw wkh suredelolw| ri gudzlqj dw ohdvw rqh sdlu lv 17;:7B

Dqvzhu= Iru vwxghqw h{sorudwlrq1

�9157 Remhfwlyh= Wr xqghuvwdqg wkh suredelolw| ri mrlqw hyhqwv dqg lqghshq0ghqfh1 Wkh suredelolw| ri d �khdg� lq d frlq wrvv lv 181 Wkh suredelolw| ri wrvvlqjwzr khdgv lq d urz lv +425,+425, @ 1581 \rx kdyh mxvw wrvvhg d khdg dqg duh

Dssolfdwlrqv 44:

derxw wr wrvv djdlq> |rxu iulhqg whoov |rx wkdw wkh suredelolw| ri jhwwlqj wkh qh{wkhdg lv vwloo 181 H{sodlq1

Dqvzhu= Hyhu| wrvv lv vwdwlvwlfdoo| lqghshqghqw1 Vr iru hyhu| wrvv wkh sure0delolw| ri jhwwlqj d khdg lv 18/ qr pdwwhu zkdw wkh klvwru|1 Li |rx remhfw wkdw dorqj vwulqj ri khdgv lq d urz lv xqolnho| xqghu wkh dvvxpswlrq ri lqghshqghqfhdqg d idlu frlq |rx duh fruuhfw/ dqg |rx pljkw wkhq txhvwlrq wkh dvvxpswlrq rilqghshqghqfh ri wrvvhv ru wkh �idluqhvv� ri wkh frlq1

916 Dssolfdwlrqv

9158 Zrunhg1 Remhfwlyh= Wr h{soruh wkh lpsolfdwlrqv ri frqglwlrqdo suredelolw|rq wkh lqwhusuhwdwlrq ri whvw uhvxowv/ hvshfldoo| iru uduh hyhqwv1 Whvwv iru glvhdvhvvxfk dv DLGV lqyroyh huuruv1 Wkhuh duh idovh srvlwlyhv dqg idovh qhjdwlyhv1 Zlwkidovh srvlwlyhv/ wkh whvw lqglfdwhv wkdw dq lqglylgxdo kdv DLGV zkhq kh ru vkhgrhv qrw/ dqg wkh idovh qhjdwlyh lqglfdwhv wkdw d whvwhg lqglylgxdo grhv qrw kdyhDLGV zkhq lq idfw kh ru vkh grhv1 Ohw xv frqvlghu wkh frqvhtxhqfhv ri wkh �uvwsureohp/ idovh srvlwlyhv/ zkhq zh frqwhpsodwh whvwlqj d odujh fodvv ri shrsoh/ ruhyhq wkh hqwluh srsxodwlrq1 Vxssrvh wkdw 433 ploolrq shrsoh duh whvwhg1 Zkdwlqirupdwlrq kdyh zh ehhq jlyhqB su+whvw.mQrDlgv, @ 138/ su+whvw 0m DLGV, @134/ dqg su+Dlgv, @ 13381 Vr/ lq d srsxodwlrq ri 433 ploolrq/ zh duh orrnlqj iru833/333 shrsoh1 Wkh whvw lv suhvxphg wr eh txlwh dffxudwh lq wkdw wkhuh lv rqo| d8( huuru iru idovh srvlwlyhv dqg d 4( huuru iru idovh qhjdwlyhv1

Zkdw gr zh zdqw wr nqrzB Zkdw lv wkh suredelolw| ri kdylqj DLGV/ jlyhqwkdw d shuvrq kdv whvwhg srvlwlyh1 Zh zloo xvh rxu frqfhswv ri frqglwlrqdo sure0delolw| h{whqvlyho| lq dqvzhulqj wklv txhvwlrq1 Zh zdqw su+DLGVmwhvw .,1 Zhghulyh

su+DLGVmwhvw., @su+DLGV> whvw.,

su+whvw .,

Dqg zh fdq euhdn xs wkh su+whvw ., lqwr lwv frqvwlwxhqw vwdwhv e|

su+whvw ., @ su+DLGV> whvw.,. su+QrDLGV> whvw.,

zkhuh zh uhfrjql}h wkdw wkh vwdwhv DLGV dqg QrDLGV sduwlwlrq wkh vwdwh�whvw .1� Zh fdq whvw srvlwlyh li zh kdyh DLGV dqg li zh gr qrw kdyh DLGV/dqg wkhvh wzr vwdwhv duh pxwxdoo| h{foxvlyh1 Li zh fdq zrun rxw wkhvh odvw wzrmrlqw suredelolwlhv jlyhq rxu lqirupdwlrq/ zh zloo kdyh wkh sureohp vroyhg1 Zhgh�qh

su+DLGV> whvw., @ su+whvw. mDLGV,su+DLGV,

su+QrDLGV> whvw., @ su+whvw. mQrDLGV,su+QrDLGV,

Zh kdyh ehhq jlyhq wkh lqirupdwlrq qhhghg> su+DLGV, lv 1338/ vr wkdwsu+QrDLGV, lv 1<<81 Zh nqrz wkdw su+whvw. mDLGV, lv 1<</ ehfdxvh su+whvw�mDLGV, lv 1341 Lw lv dovr jlyhq wkdw su+whvw . mQrDLGV, lv 1381 Zh fdq qrz

44; Wkhru|

fdofxodwh wkdw

su+DLGV> whvw., @ =<<� =338 @ =337<8

su+QrDLGV> whvw., @ =38� =<<8 @ =37<:8

Zh fdq qrz vroyh rxu ruljlqdo sureohp=

su+DLGVmwhvw., @=337<8

=337<8 . =37<:8@ =3<38

Wklv uhvxow wkdw wkh suredelolw| wkdw rqh kdv DLGV jlyhq d srvlwlyh uhdglqj lvrqo| derxw 43( pd| eh vxusulvlqj dw �uvw vljkw/ exw li |rx h{shulphqw zlwk wkhfdofxodwlrqv d elw |rx zloo ehjlq wr vhh wkh orjlf ri wkh vlwxdwlrq1 Wkh eljjhu wkhsuredelolw| ri DLGV lq wkh �uvw sodfh/ wkh eljjhu wkh suredelolw| jlyhq wkh whvw1 Vrwkh vxusulvlqj qdwxuh ri wkh uhvxow lv gxh wr wkh uhodwlyh orz suredelolw| ri DLGVlq wkh zkroh srsxodwlrq1


�9159 Jlyhq wkh idfwv vwdwhg lq H{huflvh 9158/ ghwhuplqh wkh suredelolw| riqrw kdylqj DLGV/ jlyhq wkdw |rx kdyh whvwhg qhjdwlyho|1 Uhzrun erwk h{huflvhvli wkh suredelolw| ri DLGV lq wkh srsxodwlrq lv 151 Gudz vrph srolf| frqfoxvlrqvderxw whvwlqj vfkhphv iurp wkhvh fdofxodwlrqv1

Dqvzhu= Wkh suredelolw| ri qrw kdylqj DLGV / jlyhq kdylqj whvwhg qhjd0wlyho|=

su+QrDLGVmwhvw�, @su+QrDLGV> whvw�,

su+whvw �,

@su+QrDLGV> whvw�,

su+QrDLGV> whvw�, . su+DLGV> whvw�,

zkhuh

su+QrDLGV> whvw�, @ su+whvw� mQrDLGV,su+QrDLGV,

su+DLGV> whvw�, @ su+whvw� mDLGV,su+DLGV,

Vr Lisu+DLGV, @ =338

wkhq

su+QrDLGVmwhvw�, @=<8� =<<8

=<8� =<<8 . =34� =338@ =<<<<8=

Vlploduo|/ lisu+DLGV, @ =5

wkhq

su+DLGVmwhvw., @=<<� =5

=<<� =5 . =38� =;@ =<;35

Dssolfdwlrqv 44<

su+QrDLGVmwhvw�, @=<8� =;

=<8� =; . =34� =5@ =<<:6;=

Iurp wkh deryh fdofxodwlrqv/ zh fdq vhh wkdw wkh suredelolw| ri qrw kdylqjDLGV zkhq wkh whvw lv qhjdwlyh lv doprvw rqh qr pdwwhu zkhwkhu d yhu| vpdoosursruwlrq ri wkh srsxodwlrq +1338, kdv DLGV ru d uhodwlyho| kljk sursruwlrq +15,kdv DLGV1 Exw wkhuh lv d elj gl�huhqfh iru wkh suredelolw| ri kdylqj DLGV zkhqwkh whvw lv srvlwlyh1 Zkhq wkh suredelolw| ri DLGV lq wkh zkroh srsxodwlrq lvyhu| orz/ wkh suredelolw| ri kdylqj DLGV zkhq wkh whvw lv srvlwlyh lv orz/ derxw< shufhqw1 Zkhq wkh suredelolw| ri DLGV lq wkh zkroh srsxodwlrq lv uhodwlyho|kljk/ vd| 53 shufhqw/ wkh suredelolw| ri kdylqj DLGV zkhq wkh whvw lv srvlwlyhlv yhu| kljk +derxw <; shufhqw,1

Wkhvh uhvxowv lpso| vrph srolf| lpsolfdwlrqv1 Zkhq wkh suredelolw| ri kdy0lqj DLGV lq wkh zkroh srsxodwlrq lv orz/ prvw vshqglqj rq whvwlqj lv xvhohvv+ru hyhq kdupixo, vlqfh d pdmrulw| ri wkrvh zkr whvw srvlwlyh duh idovh srvl0wlyh1 Vr lw lv lpsruwdqw wr lpsuryh wkh dffxudf| ri wkh whvwlqj1 Iru h{dpsoh/li su+whvw.mQrDLGV, lv 1338 lqvwhdg ri 138/ wkh su+DLGVmwhvw., duh lpsuryhg wrderxw 83 shufhqw iurp < shufhqw1

915: Iuhtxhqwo| sroo wdnhuv duh uhtxluhg wr dvn vhqvlwlyh txhvwlrqv1 Rqh vwudw0hj| wr ryhufrph wklv sureohp lv wr pdnh vxuh wkdw wkh sroo wdnhu fdqqrw nqrzwkh uhvsrqghqw*v dqvzhu1 Lpdjlqh wkdw |rx duh uhtxhvwhg wr vdpsoh d jurxs rivwxghqwv derxw wkhlu xvh ri guxjv> lw lv olnho| wkdw prvw vwxghqwv zloo qrw zlvkwr jlyh dq krqhvw dqvzhu1 D vroxwlrq lv wr suhsduh wzr txhvwlrqv> rqh lv wkhvhqvlwlyh txhvwlrq/ wkh rwkhu lv qrqvhqvlwlyh dqg vxfk wkdw |rx nqrz wkh sur0sruwlrq ri wkh srsxodwlrq wkdw zloo dqvzhu |hv wr wkh dowhuqdwlyh txhvwlrq1 Iruh{dpsoh/ |rx dvn �Zhuh |rx eruq lq Mdqxdu|B� dqg nqrz wkdw wkh sursruwlrqri wkh srsxodwlrq eruq lq Mdqxdu| lv 13;1

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Dqvzhu= Dvvxpswlrqv=41 Wkh wrvv ri wkh frlq vdwlv�hv wkh frqvwudlqw su +W , @ su +K, @ 4

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1.0 1.6 2.2 2.8 3.4 4.0 4.6 5.2 5.8duration

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Iljxuh :14= Klvwrjudp ri Jh|vhu4 Gxudwlrq Gdwd

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30 41 52 63 74 85 96interval

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Iljxuh :15= Klvwrjudp ri Jh|vhu4 Lqwhuydo Gdwd

0.0 1.1 2.2 3.3 4.4 5.5 6.6duration

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Iljxuh :16= Klvwrjudp ri Jh|vhu5 Gxudwlrq Gdwd

Dssolfdwlrqv 48:

20 35 50 65 80 95 110 125interval

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Iljxuh :17= Klvwrjudp ri Jh|vhu5 Lqwhuydo Gdwd

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Iljxuh :18= Glvwulexwlrq ri Krxvlqj Vwduwv e| \hdu

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Iljxuh :1;= Glvwulexwlrq ri Krxvlqj Vwduwv= Kljk Lqwhuhvw Shulrgv

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;147Zrunhg1 Remhfwlyh= Wr h{soruh wkh ghshqghqfh ri wkh qrupdo glvwulexwlrqrq lwv sdudphwhuv1

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Zkdw lv wkh sudfwlfdo lpsolfdwlrqB Li zh fkrrvh wr xvh wkh Qrupdo glvwule0xwlrq dv dq dssur{lpdwlrq/ zh uhfrjql}h wkdw wkh suhvhqfh ri vnhzqhvv/ wkrxjkvpdoo/ zloo d�hfw rxu uhvxowv> iru qhjdwlyh vnhzqhvv/ zh zloo xqghuvwdwh wkh sure0delolw| ri orz sulfhv dqg ryhuvwdwh odujh sulfhv1 Zh zrxog suredeo| suhihu wr xvhwkh orjdulwkpv dv wkh shdnhgqhvv lv forvhu wr Qrupdo wkdq lv wuxh iru wkh udzgdwd1

-200 200 600 1000 1400 1800 2200 2600 3000 3400 3800price

0

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Iljxuh ;14= Iuhqfk Zkhdw Sulfh Gdwd

;155 Zrunhg1 Remhfwlyh= Wr looxvwudwh wkh fhqwudo olplw wkhruhp1Lq wkh suhylrxv h{huflvh/ |rx fdofxodwhg wkh �uvw irxu prphqwv iru wkh sulfh

ri Iuhqfk zkhdw dqg iru d Hxurshdq lqgh{1 Wkh fhqwudo olplw wkhruhp whoov xvwkdw dyhudjhv ri wkhvh sulfhv zloo eh glvwulexwhg d orw forvhu wr Jdxvvldq wkdq wkhudz gdwd1 Lq wklv h{huflvh/ zh zloo hydoxdwh wklv lghd1Fhqwudo Olplw Wkhruhp lq Wh{w Urxwlqhv shuirupv wkh iroorzlqj vwhsv zkhqdssolhg wr wkh Iuhqfk zkhdw gdwd1 Udqgrp vhohfwlrqv dw ydulrxv vdpsoh vl}hvduh pdgh iurp wkh 6:3 Iuhqfk zkhdw sulfh gdwd1 Wkh vhohfwlrq lv uhshdwhg 433wlphv/ gudzlqj hdfk wlph d udqgrp vdpsoh ri vl}h 8/ 43/ 53/ 73/ dqg 931 Wkh

Dssolfdwlrqv 4;4

3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2 7.8 8.4 9.0logprice

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Iljxuh ;15= Klvwrjudp ri wkh Orj ri wkh Iuhqfk Zkhdw Sulfh Gdwd

-20 12 44 76 108 140 172 204 236 268 300 332 364 396priceind

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Iljxuh ;16= Klvwrjudp ri Hxurshdq Zkhdw Sulfh Gdwd


2.10 2.36 2.62 2.88 3.14 3.40 3.66 3.92 4.18 4.44 4.70 4.96 5.22 5.48 5.74 6.00logprind

0

20

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Iljxuh ;17= Klvwrjudp ri wkh Orj ri Hxurshdq Zkhdw Sulfh Gdwd

phdqv ri wkhvh 433 vdpsoh revhuydwlrqv duh wkhq fdofxodwhg1

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Zkhdwsu1 Rq wkh phqx edu folfn rq Wh{w Urxwlqhv/Fhqwudo Olplw Wkhruhp1 Lq wkh gldorj/ vhohfw Gdwd Iudph Iuhqfk1

Lq Yduldeoh/ vhohfw sulfh1 Folfn RN1 Ilyh klvwrjudpv zloo eh jhqhudwhg1Wkh uhsruw zlqgrz frqwdlqv rqh urz iru hdfk vshfl�hg vdpsoh vl}h1Wkh vl{ hqwulhv lq hdfk urz duh wkh �uvw irxu prphqwv> wkh odvw wzrhqwulhv duh wkh vwdqgdugl}hg wklug dqg irxuwk prphqwv1`

H{dplqh wkh vhtxhqfh ri klvwrjudpv fduhixoo| dqg gudz |rxu frqfoxvlrqv1Khuh/ |rx jhw wr revhuyh wkh h�hfw ri wkh fhqwudo olplw wkhruhp zlwk uhdo gdwd

uhohydqw wr hfrqrplf dqdo|vlv1Dqvzhu= iru vwxghqw h{sorudwlrq1

;156 Uhshdw wkh suhylrxv h{huflvh xvlqj wkh vl{0prqwk eloo udwh +eloo9pr, dqgwkh �yh0|hdu qrwh +qrwh8|u, lq wkh Prq|og1{ov �oh lq wkh Lqwudwh iroghu1 Frpphqwrq |rxu uhvxowv1

Dqvzhu= Vhh wkh odvw zrunhg h{huflvh1

�;157 Lq wkh �oh Prq|og1{ov lq wkh Lqwudwh iroghu/ duh wkh lqwhuhvw udwh ydul0deohv/ ru wkhlu orjdulwkpv/ glvwulexwhg pruh qhduo| wr wkh Jdxvvldq ru wr wkh

Dssolfdwlrqv 4;6

xqlirup glvwulexwlrqB Krz fdq |rx whooBDqvzhu= Wkh lqwhuhvw udwhv duh glvwulexwhg qhduo| dv Jdxvvldq1 Wkh orj

ri wkh lqwhuhvw udwhv lv glvwulexwhg hyhq pruh forvho| wr wkh Jdxvvldq glvwulex0wlrq1 Wkh vwdqgdugl}hg wklug dqg irxuwk prphqwv dqg wkh klvwrjudpv vkrz wklvfohduo|1

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d1 Iru hdfk ri wkh yduldeohv/ sorw dqg sulqw wkh klvwrjudpv dqg fdofxodwhwkh �uvw irxu prphqwv/ dqg wkh vwdqgdugl}hg prphqwv1 Frpphqw rq wkh h{whqwwr zklfk wkh Jdxvvldq glvwulexwlrq ru wkh xqlirup glvwulexwlrq vhhpv wr eh duhdvrqdeoh fkrlfh1

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Lq H{suhvvlrq/ nh| lq +jqs0jqsodj,2jqsodj 1 Folfn Dsso|1 Wkh qhzfroxpq/ jqsj/ zloo eh lq wkh Grpjqs gdwd iudph1 Uhshdw iru hdfkyduldeoh xvlqj dssursuldwh qdphv/ dqg lq H{suhvvlrq vxevwlwxwh wkhfruuhfw yduldeoh qdphv1 Wkh klvwrjudpv fdq eh sorwwhg e| kljkoljkw0lqj wkh jurzwk udwh froxpq wr eh judskhg dqg folfnlqj rq Judsk/5G Sorw/ Klvwrjudp1 Folfn RN1`

f1 Wdnh wkh qdwxudo orjdulwkp ri hdfk yduldeoh dqg xvlqj wkh orj/ jhqhudwh wkhklvwrjudpv dqg fdofxodwh wkh �uvw irxu prphqwv dqg wkh vwdqgdugl}hg prphqwv1

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wkh gldorj lq Qhz Froxpq Qdph/ nh| lq jqsog 1 Lq H{suhvvlrq nh| lq

+jqso0jqsoodj,2jqsoodj 1 Folfn Dsso|1 Uhshdw iru doo irxu yduldeohv lqwklv h{huflvh uhsodflqj zlwk dssursuldwh qhz yduldeoh qdphv1 Fuhdwhklvwrjudpv ri wkh �uvw gl�huhqfhv lq wkh orjv1`

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ri wkh vwdwlvwlfdo surshuwlhv ri qdwlrqdo lqfrph vwdwlvwlfv dqg wkhlu wudqvirupvlqwr jurzwk udwhv/ orjdulwkpv/ dqg orj jurzwk udwhv1 \rx zloo vhh doo ri wkhvhyduldwlrqv xvhg lq uhjuhvvlrq dqdo|vlv wr eh glvfxvvhg lq Fkdswhu 461

\rx vkrxog vshqg vrph wlph orrnlqj wkurxjk wkh judskv dqg qrwlqj wkhydoxhv ri �4 dqg �51 Lq sduwlfxodu/ qrwh zklfk wudqvirupdwlrqv ri zklfk yduldeohvvhhp wr |lhog glvwulexwlrqv forvhu wr Jdxvvldq dqg zklfk |lhog glvwulexwlrqv iduiurp Jdxvvldq1

Dw wkh ohdvw/ wklv h{huflvh zloo jlyh |rx d khdowk| ghjuhh ri vfhswlflvp iru wkhzlgh vsuhdg dvvxpswlrq ri wkh Qrupdo dv wkh uhohydqw glvwulexwlrq1 Krzhyhu/gr qrwh wkdw wkh dqdo|vlv khuh uhvwv rq rqo| d olwwoh ryhu vl{w| revhuydwlrqv1

d1 Iru hdfk ri wkhvh yduldeohv/ lw vhhpv wkdw qhlwkhu wkh Jdxvvldq glvwulexwlrqqru wkh xqlirup glvwulexwlrq lv d jrrg fkrlfh1 Vhh Iljxuh ;181

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jqso jqsfo xqhpso fslo uzdjho�4 157 154 166 0133 154�5 41:; 4194 51<6 41<9 4196

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jqsog jqsfog xqhpsog fslog uzdjhog�4 04136 0179 6186 183 0158�5 81:9 615< 4;17: 718; 6176

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Iljxuh ;19= Klvwrjudpv ri wkh Jurzwk Udwh ri Grphvwlf JQS Gdwd1 H{huflvh;1581+e,

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Iljxuh ;1:= Klvwrjudp ri wkh Qdwxudo Orjdulwkpv ri wkh Grphvwlf JQS Gdwd1H{huflvh ;1581+f,

4;; Frqwlqxrxv Glvwulexwlrqv

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0.701.25

1.802.35

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0

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120 220 320 420 520 620 720 820 920satmath

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;15: Uhshdw wkh fhqwudo olplw wkhruhp h{shulphqw rxwolqhg lq H{huflvh ;155xvlqj wkh vdwpdwk dqg wkh vdwyhue vfruhv lq wkh Svdwvdw1{ov �oh1


�;15; Vxppdul}h wkh vlplodulwlhv dqg gl�huhqfhv lq wkh glvwulexwlrqv ri vdw0pdwk dqg vdwyhue vfruhv1 Zkdw gr |rx frqfoxgh iurp wklv hylghqfhB Krz ehvwfdq |rx vxppdul}h wkh vlplodulwlhv dqg gl�huhqfhv lq wkh glvwulexwlrqv iru wkhVDW vfruhv dqg wkh SVDW vfruhvB

Dqvzhu= Zkloh wkh vdwpdwk vfruhv kdyh d kljkhu phdq/ wkh glvwulexwlrqvri vdwpdwk dqg vdwyhue vfruhv duh yhu| vlplodu1 Wkh glvwulexwlrqv iru wkh VDWvfruhv dqg wkh SVDW vfruhv duh dovr yhu| vlplodu/ zklfk vxjjhvwv wkdw d vwxghqw*v

4<3 Frqwlqxrxv Glvwulexwlrqv

100 190 280 370 460 550 640 730 820satverb

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Iljxuh ;143= Klvwrjudp ri yhuedo VDW vfruhv1 Doskd 4 @ 3156/ Doskd 5 @ 5197

shuirupdqfh rq wkh SVDW lv d jrrg lqglfdwru ri khu2klv shuirupdqfh rq wkhVDW1

;15< Lq wkh iroghu Jqs/ xvh wkh iroghu Grpjqs/ �oh Grpjqs1{ov1 Iru hdfk riwkh yduldeohv uhdo jqs +ujqs,/ lqgxvwuldo surgxfwlrq+lqgsurg,/ hpsor|phqw ohyho+hps,/ prqh| vxsso| +prqh|,/ dqg yhorflw| +yho,/ h{dplqh wkh h{whqw wr zklfkwkh yduldeohv/ wkh jurzwk udwhv/ wkh orjv ri wkh yduldeohv/ dqg wkh �uvw gl�hu0hqfhv lq wkh orjv duh glvwulexwhg dv Jdxvvldq1 +Vhh H{huflvh ;158 iru frpsxwhugluhfwlrqv1,

Jlyhq wkhvh hpslulfdo uhvxowv/ zkdw frqfoxvlrqv gr |rx gudz derxw wkh uhoh0ydqfh ri wkh Jdxvvldq glvwulexwlrq wr wkhvh JQS gdwdB

Dqvzhu= Vhh H{huflvh ;1581

�;163 Fdvh Vwxg|= Zdv Wkhuh Djh Glvfulplqdwlrq lq d SxeolfXwlolw|B

Pxfk ri wkh glvfxvvlrq lq wkh glvfulplqdwlrq fdvh lqyroyhv wkh glvwulexwlrq rivdodulhv dqg djhv1 Xqghuo|lqj dq| vwdwlvwlfdo dqdo|vlv xvlqj wkhvh yduldeohv zlooeh dvvxpswlrqv derxw wkh w|shv ri glvwulexwlrq wkdw duh lqyroyhg1 H{dplqh erwkwkh djh dqg vdodu| yduldeohv iru doo lqglylgxdov lq wkh Glvfgdwd1{ov gdwd vhw lq wkhDjhglvf iroghu/ dqg surylgh dujxphqwv iru dqg djdlqvw wkdw wkhvh wzr yduldeohvduh glvwulexwhg dv Jdxvvldq1 Surgxfh erwk wkhruhwlfdo dqg hpslulfdo dujxphqwvlq vxssruw ri |rxu frqfoxvlrqv1

Dqvzhu= Vhh Iljxuhv ;144 dqg ;1451 Erwk e| h{dplqdwlrq ri wkh klvwrjudpvdqg wkh fdofxodwlrq ri wkh vwdqgdugl}hg wklug dqg irxuwk prphqwv/ wkh fdvh iru

Dssolfdwlrqv 4<4

wkh uhohydqfh ri wkh Jdxvvldq glvwulexwlrq lv prghudwho| vwurqj/ exw pruh vr iruvdodulhv1

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Wkh fruuhvsrqglqj dujxphqwv lq idyru ri qrupdolw| iru wkh djh yduldeoh duhohvv shuvxdvlyh1

20 25 30 35 40 45 50 55 60 65 70age

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Iljxuh ;144= Klvwrjudp ri Djh1 Vwdqgdugl}hg Wklug dqg Irxuwk Prphqw @031546 dqg 51:6;1

4<5 Frqwlqxrxv Glvwulexwlrqv

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<15 +Uhihuhqfh= Mxgjhphqw xqghu Xqfhuwdlqw|= Khxulvwlfv dqg Eldvhv/ Fdp0eulgjh/ 4<<;1, Frqvlghu wkh vlwxdwlrq ri wrvvlqj d idlu frlq whq wlphv1 Iluvw/dvn �yh iulhqgv/ zkr kdyh qrw wdnhq d vwdwlvwlfv fodvv/ wr zulwh grzq zkdw wkh|eholhyh wr eh d uhsuhvhqwdwlyh vdpsoh ri vl}h whq iurp d idlu frlq1 Vhfrqg/ xvlqjV0Soxv jhqhudwh whq vdpsohv iurp d elqrpldo glvwulexwlrq zlwk sdudphwhuv � @ =8dqg q @ 4> wkh srvvleoh ydoxhv ri hdfk wuldo duh ~3/4�1 Frpsduh wkh wzr vhwv rirxwsxwv1 Zkdw fdq |rx vd| derxw wkh �udqgrpqhvv� jhqhudwhg e| |rxu iulhqgvdv frpsduhg zlwk wkh dfwxdo udqgrpqhvv jhqhudwhg e| wkh frpsxwhuB Uhshdw wkhfrpsxwhu sruwlrq ri wkh h{shulphqw1 Zkdw frqfoxvlrqv gr |rx gudz iurp |rxurevhuydwlrqvB

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rqGdwd/ Udqgrp Qxpehuv1 Vhw Vdpsoh Vl}h wr �43�/ vhw Glvwulexwlrqwr �elqrpldo1� Iru wkh sdudphwhuv nh| lq 18 iru Suredelolw|/ dqg4 iru Vdpsoh Vl}h1 Fkhfn wkh Sulqw Uhvxowv er{1 Folfn Dsso|1 Wkhuhvxowv zloo eh lq wkh Uhsruw zlqgrz1`


4<6

4<7 Vdpsolqj Wkhru|

<16 +Wklv h{huflvh vkrxog eh grqh dv d whdp1, Duwlvwv kdyh qrwhg fhuwdlquhjxodu sursruwlrqv iru wkh kxpdq erg|1 Iru h{dpsoh/ wkh glvwdqfh iurp h|h wrfklq lv htxdo wr wkh glvwdqfh iurp h|h wr hdu/ wkdw wkh h|hv duh kdoizd| ehwzhhqfklq dqg wrs ri wkh vnxoo/ ru wkdw wkh ohqjwk ri wkh erg| lv qdwxudoo| glylvleohlqwr hljkw htxdo vhfwlrqv1 H{soruh wkh dffxudf| ri wkhvh dqg rwkhu vxjjhvwhguhjxodulwlhv e| phdvxulqj vwxghqw yroxqwhhuv1 Jlyhq |rxu phdvxuhphqwv/ zkdwfrqfoxvlrqv fdq |rx gudz frqfhuqlqj wkhvh dvvxpswlrqv e| duwlvwvB

Dqvzhu= iru vwxghqw h{sorudwlrq dqg glvfxvvlrq1

�<17 Iru hdfk ri wkh iroorzlqj vhtxhqfhv ri khdgv dqg wdlov/ vwdwh zkhwkhu |rxeholhyh wkdw wkh vhtxhqfh lv udqgrp1 Fdofxodwh wkh suredelolw| ri hdfk vhtxhqfhrffxuulqj li wkh suredelolw| ri d �khdg� lv 18 dqg uhylhz |rxu dvvhvvphqw riudqgrpqhvv1

d1 K K K K K W W W W We1 K W K W K W K W K Wf1 K K W W K K W W K Kg1 K K K K K K K K K Kh1 K K K W K K K W K KDqvzhu= Wkh suredelolw| iru hdfk ri wkhvh vhtxhqfhv wr rffxu e| fkdqfh lv

=8431Hdfk vhtxhqfh lv htxdoo| olnho| wr rffxu iru dq| vhtxhqfh ri wkh vdph ohqjwkzlwk wkh vdph qxpehu ri khdgv dsshdulqj1

<18 Frqgxfw d vxuyh| ri vwxghqw krxuv ri vwxg|lqj/ srolwlfdo d!oldwlrq/ dqggulqnlqj zkhq xqghu djh dqg zkhwkhu wkh uhvsrqghqw kdv hyhu vwrohq dq|wklqj1Frqgxfw wkh vxuyh| lq d vwudljkwiruzdug pdqqhu1 Doo txhvwlrqv duh wr kdyhvlpsoh �\hv ru Qr� dqvzhuv1 Uhfrug dqg ghvfuleh |rxu revhuydwlrqv1


<19 Uhshdw wkh h{shulphqw zlwk d gl�huhqw jurxs ri vwxghqwv/ h{fhsw wkdw wkhvdpsolqj vwudwhj| lv wr eh dowhuhg dv iroorzv1 Rewdlq wkh dfwxdo glvwulexwlrq rivwxghqwv lq |rxu froohjh e| prqwk ri eluwk1 Iru hdfk txhvwlrq ri lqwhuhvw/ surfhhglq wkh iroorzlqj pdqqhu=

d1 Wkh lqwhuylhzhh lv wr wrvv d frlq1 Li khdgv/ wkh vwxghqw dqvzhuv wkh vxuyh|txhvwlrq/ li wdlov kh ru vkh dqvzhuv wkh txhvwlrq> Zhuh |rx eruq lq Mxo|/ Dxjxvw/ru VhswhpehuB Wkh vxuyh| txhvwlrqhu pxvw qrw vhh wkh rxwfrph ri wkh frlq wrvv1

e1 Xvlqj wkh surfhgxuhv rq frqglwlrqdo dqg mrlqw suredelolwlhv ohduqhg lqFkdswhu 9/ dqg kdylqj revhuyhg wkh dyhudjh rxwfrph ri wkh vxuyh|/ fdofxodwhwkh hvwlpdwhg dyhudjh rxwfrph iru wkh vxuyh| txhvwlrq1 Frpsduh uhvxowv dfurvvwkh gl�huhqw vxuyh| txhvwlrqv1 Lv wklv d vhqvleoh zd| wr vxuyh| iru vhqvlwlyhtxhvwlrqvB Frpphqw rq |rxu �qglqjv1


<1: Slfn wkuhh orfdwlrqv rq |rxu fdpsxv/ vxfk dv wkh hqwudqfh wr wkh pdwk0hpdwlfv ghsduwphqw/ wkh hqwudqfh wr wkh phq*v orfnhu urrp lq wkh j|p/ wkh ol0eudu|/ wkh vwxghqw xqlrq1 Dw hdfk orfdwlrq/ vxuyh| vwxghqwv* khljkwv/ ru zhljkwv/ru erwk1 Fdofxodwh wkh phdqv dqg wkh yduldqfhv ri |rxu vxuyh|v dqg frpphqw

Fdofxodwlrq Sudfwlfh 4<8

rq wkh uhvxowv1 Wr zkdw h{whqw duh |rxu vxuyh| orfdwlrqv oldeoh wr surgxfh eldvhg�wkdw lv/ qrq0udqgrp� vdpsolqjB

Dqvzhu= Wkhuh pd| eh vrph eldv1 Iru h{dpsoh/ wkrvh zkr jr wr wkh j|ppd| eh vwurqjhu dqg khdylhu rq dyhudjh1

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d1 Zh kdyh wzr fkrlfhv/ vdpsolqj zlwk ru zlwkrxw uhsodfhphqw1 Lq wklvh{shulphqw/ zh zloo frpsduh wkh wzr surfhgxuhv1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rqOdev/ Vdpsolqj iurp 304 Srsxodwlrqv/

Vdpsolqj Zlwk dqg Zlwkrxw Uhsodfhphqw1 Lq wkh gldorj er{ wkdwdsshduv/ wkh er{ odehohg Q lv wkh vl}h ri wkh srsxodwlrq/ wkh er{odehohg q lv wkh vl}h ri wkh vdpsoh/ wkh er{ odehohg sl lv wkh sursruwlrqlq wkh srsxodwlrq ri rqh w|sh dqg +4�sl, lv wkh sursruwlrq ri d vhfrqgw|sh> wkhuh duh rqo| wzr w|shv lq wkh srsxodwlrq1 Vhw Q wr �4333�/vhw q wr �43�/ vhw sl wr �18�1 Folfn Dsso|1 Sulqw Judsk1` Wkh judskvkrzv wkh suredelolw| ri jhwwlqj n frxqwv +ru vxffhvvhv, / n @ ~3/ 4/ 111/43�/ riw|sh 4 zkhq vdpsolqj zlwk uhsodfhphqw/ wkhvh duh wkh eoxh olqhv> dqg wkh uhvxowvrewdlqhg zlwkrxw uhsodfhphqw duh wkh uhg olqhv1 Dw rxu fxuuhqw vhwwlqjv/ Q @4333/ q @43/ sl @ 18/ wkhuh lv qr glvfhuqleoh gl�huhqfh1

e1 Uhshdw wkh h{shulphqw zlwk Q @ 83/ q @ 53/ sl @ 135 dqg qrwlfh wkh vxe0vwdqwldo gl�huhqfh ehwzhhq wkh uhvxowv ri vdpsolqj zlwk dqg zlwkrxw uhsodfhphqw1

f1 Uhshdw wkh h{shulphqw zlwk ydulrxv frpelqdwlrqv ri Q / q/ sl1 Zkdwjhqhudo frqfoxvlrqv gr |rx gudzB

Wklv h{huflvh looxvwudwhv wkh lpsruwdqfh ri krz zh lqwhusuhw rxu gdwd lq oljkwri wkh remhfwlyhv ri rxu dqdo|vlv1 Lw dovr looxvwudwhv wkh lpsruwdqfh ri krz rqhvdpsohv1


<1< Zrunhg1 Remhfwlyh= Lq wklv h{huflvh |rx zloo xvh wkh ode wr h{shulphqwzlwk wkh vkdsh ri wkh Srlvvrq glvwulexwlrq iru ydulrxv ydoxhv ri q/ vdpsoh vl}h/ dqg �+sl,/ wkh suredelolw| ri dq hyhqw rffxuulqj lq d vlqjoh wuldo1 Uhfdoo �/ wkh sdudphwhulq wkh Srlvvrq glvwulexwlrq/ lv jlyhq e| � @ q �= Fkrrvh ydulrxv ydoxhv iru q dqgiru �+sl,> hvshfldoo| yhu| vpdoo rqhv wr revhuyh wkh gl�huhqfhv lq wkh suredelolw|glvwulexwlrq1

d1 Wu| ydoxhv ri q dqg sl> vxfk wkdw q� @ 41 Frpphqw rq wkh uhvxowv1e1 Iru d �{hg ydoxh ri �> frqvlghu zkdw kdsshqv dv |rx lqfuhdvh q1 Frpphqw

rq wkh uhvxowv1

4<9 Vdpsolqj Wkhru|

f1 Il{ q dw 5331 Vwhs wkurxjk wkh ydoxhv ri �= Frpphqw rq wkh uhvxowv1^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rq

Odev/ Vdpsolqj Iurp 304 Srsxodwlrq/Dssur{lpdwlqj Elqrpldo Suredelolwlhv/ Srlvvrq Dssur{lpdwlrq1 Lq

wkh gldorj er{ vhw q dqg sl wr ghvluhg ydoxhv1 Folfn Dsso|1 Wkh judskkdv wkh Srlvvrq glvwulexwlrq lq uhg/ wkh elqrpldo glvwulexwlrq lq eoxh1Sulqw wkh judskv1`


�<143 Remhfwlyh= Wr ghprqvwudwh wkdw vdpsolqj ri uduh srsxodwlrqv e| uhodwhgfkdudfwhulvwlfv fdq eh pruh h�hfwlyh wkdq d vlpsoh udqgrp vdpsoh1

Dowkrxjk vwloo uhodwlyho| uduh/ wkh rffxuuhqfh ri pxowlsoh kxpdq eluwkv +wulsohwv/txdguxsohwv/ dqg vr rq, kdv ehhq rq wkh ulvh lq uhfhqw |hduv1 Iru h{dpsoh/ lqodwh Ghfhpehu ri 4<<; d zrpdq lq Wh{dv jdyh eluwk wr rfwxsohwv> wkh |hdu eh0iruh/ vhswxsohwv zhuh eruq1 Dvvxplqj wkdw wkh udwh ri pxowlsoh eluwkv lv orz +4lq 433/333 dv dqqrxqfhg e| wkh X1V1 Ghsduwphqw ri Ylwdo Uhfrugv,/ krz zrxog|rx jr derxw wdnlqj d vdpsoh wr frq�up wkdw wkh sxeolvkhg qxpehu ri pxowlsoheluwkv zdv fruuhfwB Krz zrxog |rxu vdpsolqj surfhgxuh fkdqjh li |rx nqhz wkdwzrphq zkr zhuh wdnlqj ihuwlolw| guxjv kdg d juhdwhu rffxuuhqfh ri pxowlsoh eluwkvwkdq zrphq qrw wdnlqj ihuwlolw| guxjvB

Dqvzhu= Ehfdxvh wkh sursruwlrq ri pxowlsoh eluwkv lv vr vpdoo/ wdnlqj dvlpsoh udqgrp vdpsoh wr h{dplqh wklv shufhqwdjh zrxog eh yhu| h{shqvlyh1Rqh srwhqwldo vroxwlrq lv wr glvfryhu dq| hdvlo| uhfrjql}hg fkdudfwhulvwlf/ vd|zrphq ehwzhhq wkh djhv ri 63 dqg 78 wkdw dffrxqw iru doprvw doo pxowlsoheluwkv dqg wkhq vdpsoh udqgrpo| rqo| iru zrphq lq wklv djh eudfnhw/ qrwlqjwkdw wkh vdpsoh uhvxowv ehlqj rewdlqhg duh uhvwulfwhg wr wkh frqglwlrqlqj hyhqwri ehlqj lq wkh djh udqjh 63 wr 781

Wkhuh pd| eh rwkhu fkdudfwhulvwlfv wkdw pd| hqdeoh rqh wr uhvwulfw wkh srs0xodwlrq wr eh vdpsohg hyhq pruh dqg wkhuhe| orzhu wkh frvw ri vdpsolqj1

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�<144 Xvlqj wkh gdwd surylghg rq lqwhuhvw udwhv lq wkh �oh Prq|og1{ov lqiroghu Lqwudwh/ jhqhudwh wkh |lhog fxuyh +frpsxwhg dv wkh gl�huhqfh ehwzhhq wkhlqwhuhvw udwh rq wkh whq0|hdu Wuhdvxu| qrwh +qrwh43|u, dqg wkdw rq wkh wkuhh0prqwk Wuhdvxu| eloo +eloo6pr,,1 Jlyhq wklv vdpsoh/ zkdw fdq |rx vd| derxw wkhsuredelolw| ri wkh |lhog fxuyh ehlqj qhjdwlyh> wkdw lv/ zkdw lv wkh suredelolw| wkdwwkh vkruw0whup lqwhuhvw udwh zloo h{fhhg wkh orqj0whup lqwhuhvw udwhB Iurp zkdwglvwulexwlrq grhv wkh |lhog fxuyh vdpsoh vhhp wr kdyh ehhq gudzqB Ghvfuleh wklvvdpsoh glvwulexwlrq dv suhflvho| dv |rx fdq1

Fdofxodwlrq Sudfwlfh 4<:

Dqvzhu=

-4.10-3.59

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-0.020.49

1.001.51

2.022.53

3.043.55

4.06

0

10

20

30

Difference in 10 yr note and 3 mo bill Interest Rates

Iljxuh <14= Klvwrjudp iru H{huflvh <144

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d1 Wdnh d vdpsoh ri 63 vwxghqwv/ 43 vwxghqwv shu txhvwlrq/ dqg uhfrug wkhluuhvsrqvhv1

e1 Gr |rxu sroolqj uhvxowv gl�hu dfurvv txhvwlrqvB

4<; Vdpsolqj Wkhru|

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<146 Remhfwlyh= Wr looxvwudwh wkdw dv vdpsoh vl}h lqfuhdvhv/ wkh yduldqfh gh0fuhdvhv1

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f1 Ghwhuplqh wkh vdpsoh vl}hv qhhghg wr dfklhyh=+4, dq lqwhuydo ohqjwk ri 43 dw d frq�ghqfh ohyho ri <<(1+5, dq lqwhuydo ohqjwk ri 8 dw d frq�ghqfh ohyho ri <3(1+6, dq lqwhuydo ohqjwk ri 8 dw d frq�ghqfh ohyho ri <<(1+7, dq lqwhuydo ohqjwk ri 4 dw d frq�ghqfh ohyho ri <<(1Dqvzhu=d1 Wkh frq�ghqfh lqwhuydo lv htxdo wr + �[ . g�@

sq, � + �[ � g�@

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41978/ 41<9/ dqg 518:8/ uhvshfwlyho|1 Wkh ohqjwkv ri wkh frq�ghqfh lqwhuydov duhwkh vdph ehfdxvh 5�@

sq @ 4=

e1 Wr fdofxodwh wkh frq�ghqfh lqwhuydo zh �uvw qrwh wkdw zh vroyh g @dvvljqhg lqwhuydo ohqjwk/ 4/ 1</ dqg 18 lq wkh txhvwlrq dqg jlyhq wkhvh ydoxhv irug/ zh rewdlq � iurp wkh vwdwlvwlfdo wdeohv1 Wkh ydoxhv duh= 164:/ 14;7/ dqg 163<1

f1 Iru dq lqwhuydo ohqjwk ri 43 dw d frq�ghqfh ohyho ri <<(/ 5g�@sq @ 431 Vr

q @ +5g�@43,5 @ 9=961 Wkhuhiruh wkh vdpsoh vl}h vkrxog eh :1 Zh fdq fdofxodwhwkh uhpdlqlqj vdpsoh vl}hv qhhghg iru wkh rwkhu wkuhh txhvwlrqv/ zklfk duh 44/5:/ dqg 997/ uhvshfwlyho|1

�4317Remhfwlyh= Wr looxvwudwh wkh xvh ri wkh "5 glvwulexwlrq1 Xvh wkh fkl0vtxduhsuredelolw| lqwhjudo urxwlqhv lq V0Soxv wr rewdlq wkh iroorzlqj suredelolwlhv1

^Frpsxwhu gluhfwlrqv= Surfhgxuh 4= Vwduw V0Soxv1 Folfn rq Odev/Vwdwlvwlfdo Wdeohv/ Fkl0Vtxduh1 Folfn rq Vlqjoh Ydoxh1 Hqwhu wkh gh0juhhv ri iuhhgrp dqg wkh fkl0vtxduh vwdwlvwlf> folfn Dsso|1 Wkh sure0delolw| zloo eh lq wkh Uhsruw Zlqgrz1

Surfhgxuh 5= Vwduw V0Soxv1 Folfn rq Odev/Lqyhuvh Vwdwlvwlfdo Wdeohv/ Fkl0Vtxduh1 Folfn rq Vlqjoh Ydoxh1 Hq0

whu wkh ghjuhhv ri iuhhgrp dqg wkh suredelolw|> folfn Dsso|1 Wkhfkl0vtxduh vwdwlvwlf zloo eh lq wkh Uhsruw Zlqgrz1`

d1 Ohw [ eh glvwulexwhg dv "5 zlwk 9 ghjuhhv ri iuhhgrp1 Fdofxodwh wkhiroorzlqj suredelolwlhv1 Iru hdfk dqvzhu surylgh d gldjudp vkrzlqj wkh duhdfrpsxwhg1

+4, [ ? 45=8<5>+5, 4=56: ? [ ? 47=77<>+6, =9:9 ? [ ? <=569>+7, 7=68 ? [ ? 4;=87;=+8, Surylgh d fhqwhuhg lqwhuydo ri suredelolw| 1<3B+9, Surylgh d fhqwhuhg lqwhuydo ri suredelolw| 1<8B+:, Surylgh d fhqwhuhg lqwhuydo ri suredelolw| 1<<B+;, Zkdw lv wkh ydoxh ri {4 li su+[ A {4, @ =<3B+<, Zkdw lv wkh ydoxh ri {5 li su+[ A {5, @ =<8B+43, Zkdw lv wkh ydoxh ri {6 li su+[ A {6, @ =<<B+44, Zkdw lv wkh ydoxh ri {7 li su+4=<75 ? [ ? {7, @ =<3B

539 Hvwlpdwlrq

+45, Zkdw lv wkh ydoxh ri {8 li su+{8 ? [ ? 48=:::7, @ =<8BDqvzhu=+4, su+[ ? 45=8<5, @ =<8>+5, su+4=56: ? [ ? 47=77<, @ su+[ ? 47=77<,�su+[ ? 4=56:, @ =<:7<<9�

=357<;56 @ =<8=+6, su+=9:9 ? [ ? <=569, @ su+[ ? <=569, � su+[ ? =9:9, @ =;6<599 �

=33833889 @ =;67 593 77=+7, su+7=68 ? [ ? 4;=87;, @ =<<8� =6:38:8 @ = 957 758=+8, Iru su+{4 ? [ ? {5, @ =<3 lpsolhv wkdw su+[ ? {4, @ =38 dqg su+[ ?

{5, @ =<8= Wkhq {4 @ 4=9686;3 dqg {5 @ 45=8<4933=+9, Iru su+{4 ? [ ? {5, @ =<8 lpsolhv wkdw su+[ ? {4, @ =358 dqg

su+[ ? {5, @ =<:8= Wkhq {4 @ 4=56:673 dqg {5 @ 47=77<733=+:, Iru su+{4 ? [ ? {5, @ =<< lpsolhv wkdw su+[ ? {4, @ =338 dqg

su+[ ? {5, @ =<<8= Wkhq {4 @ =9:8:5: dqg {5 @ 4;=87:933=+;, Li su+[ A {4, @ =<> wkhq su+[ ? {4, @ =4= Wkhq {4 @ 5=537463>+<, Li su+[ A {5, @ =<8> wkhq su+[ ? {5, @ =38= Wkhq {5 @ 4=9686;3>+43, Li su+[ A {5, @ =<<> wkhq su+[ ? {6, @ =34= Wkhq {6 @ =;:53<3=+44, Vlqfh su+[ ? 4=<75, @ =3:83785> li su+4=<75 ? [ ? {7, @ =< wkhq

su+[ ? {7, @ =< . =3:83785 @ = <:8 378 5= Wkxv/ {7 @ 47=787433=+45, Vlqfh su+[ ? 48=:::7, @ =<;8> li su+48=:::7 A [ A {8, @ =<8 wkhq

su+[ ? {8, @ =<;8� =<8 @ =368= Wkxv/ {8 @ 4=747353=

�4318 Remhfwlyh= Wr looxvwudwh wkh xvh ri wkh Vwxghqw*v W glvwulexwlrq1 Xvhwkh Vwxghqw*v W suredelolw| lqwhjudo urxwlqhv lq V0Soxv wr rewdlq wkh iroorzlqjsuredelolwlhv1

^Surfhgxuh 4= Vwduw V0Soxv1 Folfn Odev/ Vwdwlvwlfdo Wdeohv/ Vwxghqwv w1Folfn rq Vlqjoh Ydoxh1 Hqwhu wkh ghjuhhv ri iuhhgrp dqg wkh w vwdwlv0wlf> folfn Dsso|1 Wkh suredelolw| zloo eh lq wkh Uhsruw Zlqgrz1

Surfhgxuh 5= Vwduw V0Soxv1 Folfn rq Odev/ Lqyhuvh Vwdwlvwlfdo Wdeohv/Vwxghqwv w1 Folfn rq Vlqjoh Ydoxh1 Hqwhu wkh ghjuhhv ri iuhhgrp dqgwkh suredelolw|> folfn Dsso|1 Wkh w vwdwlvwlf zloo eh lq wkh UhsruwZlqgrz1`

d1 Ohw W eh glvwulexwhg Vwxghqw*v W / zlwk 8 ghjuhhv ri iuhhgrp1 Fdofxodwhwkh iroorzlqj suredelolwlhv1 Iru hdfk dqvzhu surylgh d gldjudp vkrzlqj wkh duhdfrpsxwhg1

+4, W A 6>+5, �6 ? W ? 6>+6, �5 ? W ? 5>+7, �7 ? W ? 7=+8, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq +3, ri suredelolw| 1<31+9, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq ri suredelolw| 1<81+:, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq ri suredelolw| 1<<1+;, Zkdw lv wkh ydoxh ri w4 li su+W A w4, @ =<3B+<, Zkdw lv wkh ydoxh ri w5 li su+W A w5, @ =<8B+43, Zkdw lv wkh ydoxh ri w6 li su+W A w6, @ =<<B+44, Zkdw lv wkh ydoxh ri w7 li su+�4=9<<7 ? W ? w7, @ =<B


+45, Zkdw lv wkh ydoxh ri w8 li su+w8 ? W ? 6=336, @ =<8B+46, Frpsduh doo ri |rxu dqvzhuv zlwk wkh suredelolwlhv wkdw wkh vwdqgdug

qrupdo glvwulexwlrq |lhog iru wkh vdph ydoxhv1

e1 Ohw W eh glvwulexwhg dv d Vwxghqw*v W> zlwk 63 ghjuhhv ri iuhhgrp1 Fdofx0odwh wkh iroorzlqj suredelolwlhv1 Iru hdfk dqvzhu surylgh d gldjudp vkrzlqj wkhduhd frpsxwhg1

+4, W A 6+5, �6 ? W ? 6+6, �5 ? W ? 5+7, �7 ? W ? 7+8, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq +3, ri suredelolw| 1<31+9, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq ri suredelolw| 1<81+:, Surylgh dq lqwhuydo fhqwhuhg durxqg wkh phdq ri suredelolw| 1<<1+;, Zkdw lv wkh ydoxh ri w4 li su+W A w4, @ =<3=+<, Zkdw lv wkh ydoxh ri w5 li su+W A w5, @ =<8=+43, Zkdw lv wkh ydoxh ri w6 li su+W A w6, @ =<<=+44, Zkdw lv wkh ydoxh ri w7 li su+�4=7::7 ? W ? w7, @ =<3=+45, Zkdw lv wkh ydoxh ri w8 li su+w8 ? W ? 5=5:;6, @ =<8=+46, Frpsduh |rxu dqvzhuv zlwk wkh suredelolwlhv rewdlqhg iurp wkh vwdqgdug

qrupdo glvwulexwlrq iru wkh vdph ydoxhv1f1 Edvhg rq |rxu dqvzhuv wr +d, dqg +e, zkdw fdq |rx vd| derxw wkh uhod0

wlrqvkls ehwzhhq wkh vwdqgdug qrupdo glvwulexwlrq dqg wkh Vwxghqw*v W dv wkhghjuhhv ri iuhhgrp lqfuhdvhB

Dqvzhu=d1 +4, su+W A 6, @ =34837<9>+5, su+�6 ? W ? 6, @ 4� =3633<<5 @ = <9< <33 ;>+6, su+�5 ? W ? 5, @ 4� =434<6< @ = ;<; 394>+7, su+�7 ? W ? 7, @ 4� =3436567 @ = <;< 9:9 9=+8, Iru su+mW m ? d, @ =<3 lpsolhv wkdw su+W ? d, @ =<8= Wkhq d @ 5=348383>+9, Iru su+mW m ? d, @ =<8 lpsolhv wkdw su+W ? d, @ =<:8= Wkhq d @ 5=8:38;>+:, Iru su+mW m ? d, @ =<< lpsolhv wkdw su+W ? d, @ =<<8= Wkhq d @ 7=365473=+;, Li su+W A w4, @ =< wkhq su+W ? �w4, @ =<= Wkhq w4 @ �4=7:8;;3>+<, Li su+W A w5, @ =<8 wkhq su+W ? �w5, @ =<8= Wkhq w5 @ �5=34838>+43, Li su+W A w6, @ =<< wkhq su+W ? �w6, @ =<<= Wkhq w6 @ �6=697<63>+44, Li su+�4=9<<7 ? W ? w7, @ =<> dqg vlqfh su+W ? �4=9<<7, @ =3:8 wkhq

su+W ? w7, @ =< . =3:8 @ = <:8= Wkhq w7 @ 5=8:38;=+45, Li su+6=336 A W A w8, @ =<8> dqg vlqfh su+W ? 6=336, @ =<;8335 wkhq

su+W ? w8, @ =<;8335� =<8 @ =3 683 35= Wkhq w8 @ �5=5<:68=+46, Wkh dqvzhuv wr wkh txhvwlrqv deryh vkrz wkdw wkh Vwxghqw*v W glvwul0

exwlrq kdv idwwhu wdlov1 Wkh lqwhuydov duh dozd|v odujhu wkdq iru wkh Jdxvvldqglvwulexwlrq1

e1 +4, su+W A 6, @ =3359<7<;>+5, su+�6 ? W ? 6, @ 4� =3386;<<9 @ = <<7 943 37>

53; Hvwlpdwlrq

+6, su+�5 ? W ? 5, @ 4� =387958 @ = <78 6:8>+7, su+�7 ? W ? 7, @ 4� 6=;4;793� 43�7 @ = <<< 94; 48=+8, Iru su+mW m ? d, @ =<3 lpsolhv wkdw su+W ? d, @ =<8= Wkhq d @ 4=9<:593>+9, Iru su+mW m ? d, @ =<8 lpsolhv wkdw su+W ? d, @ =<:8= Wkhq d @ 5=3755:3>+:, Iru su+mW m ? d, @ =<< lpsolhv wkdw su+W ? d, @ =<<8= Wkhq d @ 5=:8=+;, Li su+W A w4, @ =< wkhq su+W ? �w4, @ =<= Wkhq w4 @ �4=643753>+<, Li su+W A w5, @ =<8 wkhq su+W ? �w5, @ =<8= Wkhq w5 @ �4=9<:593>+43, Li su+W A w6, @ =<< wkhq su+W ? �w6, @ =<<= Wkhq w6 @ �5=78:593>+44, Li su+�4=7::7 ? W ? w7, @ =<> dqg vlqfh su+W ? �4=7::7, @ =3:8 wkhq

su+W ? w7, @ =< . =3:8 @ = <:8= Wkhq w7 @ 5=3755:3=+45, Li su+5=5:;6 A W A w8, @ =<8> dqg vlqfh su+W ? 5=5:;6, @ =<;8334 wkhq

su+W ? w8, @ =<;8334� =<8 @ =3 683 34= Wkhq w8 @ �4=;:;<53=+46, Wkh Vwxghqw*v W glvwulexwlrq zlwk 63 ghjuhhv ri iuhhgrp kdv wklqqhu

wdlov wkdq wkh rqh zlwk 81

f1 Dv wkh qxpehu ri ghjuhhv ri iuhhgrp lqfuhdvhv/ wkh Vwxghqw*v W glvwulexwlrqdssurdfkhv wkh Jdxvvldq1

4319 Zrunhg= Remhfwlyh= Wr h{soruh wkh vdpsolqj surshuwlhv ri frq�ghqfhlqwhuydov lq d ydulhw| ri vlwxdwlrqv iru ydulrxv sduhqw glvwulexwlrqv1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Rq wkh phqx edu/ folfn rqOdev/ Lqwhusuhwlqj Frq�ghqfh Lqwhuydov1 Dffhsw wkh ghidxow ydoxhv lqwkh gldorjxh> folfn Dsso|1 H{dplqh wkh rxwsxw lq wkh Uhsruw Zlqgrzdqg wkh judsk fduhixoo|1 Uhshdw wkh h{huflvh e| vhwwlqj q4/ doskd/Sduhqw Glvwulexwlrq/ dqg Sdudphwhu iru Frq�ghqfh Lqwhuydo wr wkhydulrxv doorzhg rswlrqv1`

Wklv ode khosv |rx wr jdlq dq lqwxlwlyh ihho iru wkh frqfhsw ri d frq�ghqfhlqwhuydo lq d ydulhw| ri vlwxdwlrqv1 Wkh prvw lpsruwdqw ohvvrq lv wr uhfrjql}h wkhudqgrp fkdudfwhu ri wkh lqwhuydov dqg wkh uhodwlrqvkls ehwzhhq wkh fkrlfh ri �dqg wkh revhuyhg uhodwlyh iuhtxhqf| ri fryhudjh1


431: \rx kdyh d sduhqw glvwulexwlrq Q+�> �5,/ dqg |rx nqrz qhlwkhu � qru�5> exw |rx gr kdyh d vdpsoh ri revhuydwlrqv ri vl}h 433/ �[ @ 619/ v5 @ 45161Frqvwuxfw frq�ghqfh lqwhuydov iru wkh xqnqrzq phdq edvhg rq wklv lqirupdwlrqiru wkh dowhuqdwlyh frq�ghqfh ohyhov ri <3(/ <8(/ dqg <<(1

Dqvzhu= Vlqfh

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vr iru wkh frq�ghqfh ohyhov ri <3(/ <8(/ dqg <<(/ wkh frq�ghqfh lqwhuydov duh^6=35> 7=4;`> ^5=<3> 7=63`> dqg ^5=9;> 7=85`/ uhvshfwlyho|1

�431; Li |rx kdyh d sduhqw glvwulexwlrq Q+�> �5,/ zkhuh qhlwkhu sdudphwhulv nqrzq/ wkh vdpsoh vl}h lv 433/ dqg wkh revhuyhg ydoxh ri v5 lv 6917/ rewdlq<8( dqg <<( frq�ghqfh lqwhuydov iru �=


d1 Li wkh vdpsoh vl}h lv rqo| 93/ zkdw duh |rxu lqwhuydovBe1 Li wkh vdpsoh vl}h lv rqo| 63/ zkdw duh |rxu lqwhuydovBf1 Li wkh vdpsoh vl}h lv rqo| 48/ zkdw duh |rxu lqwhuydovBg1 Li wkh vdpsoh vl}h lv rqo| 9/ zkdw duh |rxu lqwhuydovBFrpphqw rq |rxu uhvxowv dqg looxvwudwh |rxu dqvzhu zlwk gldjudpv frpsdu0

lqj wkh frq�ghqfh lqwhuydov1Dqvzhu=<8 ( frq�ghqfh lqwhuydo iru yduldqfh ri qrupdo=q @ 433 va5 @ 6917d1 Orzhu frq�ghqfh olplw @ 5;1393933/ Xsshu frq�ghqfh olplw @ 7<1454733q @ 93 va5 @ 6917e1 Orzhu frq�ghqfh olplw @ 591485;33/ Xsshu frq�ghqfh olplw @ 87147::33q @ 63 va5 @ 6917f1 Orzhu frq�ghqfh olplw @ 5613;:533/ Xsshu frq�ghqfh olplw @ 981:;4833q @ 48 va5 @ 6917g1 Orzhu frq�ghqfh olplw @ 4<1843;33/ Xsshu frq�ghqfh olplw @ <31868933q @ 9 va5 @ 6917Orzhu frq�ghqfh olplw @ 4714;5:33/ Xsshu frq�ghqfh olplw @ 54;1<8:333<< ( frq�ghqfh lqwhuydo iru yduldqfh ri qrupdo=q @ 433 va5 @ 6917d1 Orzhu frq�ghqfh olplw @ 581<5:933/ Xsshu frq�ghqfh olplw @ 8714;4533q @ 93 va5 @ 6917e1 Orzhu frq�ghqfh olplw @ 5619:7433/ Xsshu frq�ghqfh olplw @ 941:98433q @ 63 va5 @ 6917f1 Orzhu frq�ghqfh olplw @ 53149<;33/ Xsshu frq�ghqfh olplw @ ;31783633q @ 48 va5 @ 6917g1 Orzhu frq�ghqfh olplw @ 4915:4433/ Xsshu frq�ghqfh olplw @ 45813983q @ 9 va5 @ 6917Orzhu frq�ghqfh olplw @ 431;98<33/ Xsshu frq�ghqfh olplw @ 7751357333Dv q/ vdpsoh vl}h/ lv ghfuhdvhg/ wkh lqwhuydo zlgwk lqfuhdvhv1 Xvlqj d kljkhu

frq�ghqfh ohyho lpsolhv d zlghu lqwhuydo1

431< \rx kdyh revhuyhg 46 rffxuuhqfhv ri dq hyhqw zlwklq d jlyhq �{hg eorfnri wlph ri 433 plqxwhv1 \rx nqrz wkdw wkh uhohydqw sduhqw glvwulexwlrq lv wkhSrlvvrq1 Xvlqj wkh urxwlqh lq V0Soxv iru fdofxodwlqj d frq�ghqfh lqwhuydo iruwkh Srlvvrq sdudphwhu/ surylgh <3(/ <8(/ dqg <<( frq�ghqfh lqwhuydov iru wkhxqnqrzq ydoxh ri �=

Uhshdw wkh h{huflvh zkhq |rx revhuyh 8/ 54 dqg 68 rffxuuhqfhv1E| frpsdulqj |rxu uhvxowv zkdw gr |rx frqfoxgh derxw wkh uhodwlrqvkls eh0

wzhhq frq�ghqfh ohyho/ revhuyhg qxpehu ri rffxuuhqfhv/ dqg frq�ghqfh lqwhuydoohqjwkB

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543 Hvwlpdwlrq

<8 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 46Orzhu frq�ghqfh olplw @ 4515<6633/ Xsshu frq�ghqfh olplw @ 461:39:331

<3 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 46Orzhu frq�ghqfh olplw @ 451739<33/ Xsshu frq�ghqfh olplw @ 4618<64331<< ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 8Orzhu frq�ghqfh olplw @ 71757363/ Xsshu frq�ghqfh olplw @ 818:8<:31<8 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 8Orzhu frq�ghqfh olplw @ 71894:73/ Xsshu frq�ghqfh olplw @ 8176;5931

<3 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 8Orzhu frq�ghqfh olplw @ 71965533/ Xsshu frq�ghqfh olplw @ 8169:;331

<< ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 54Orzhu frq�ghqfh olplw @ 4<1;4<933/ Xsshu frq�ghqfh olplw @ 5514;37331<8 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 54Orzhu frq�ghqfh olplw @ 531434;33/ Xsshu frq�ghqfh olplw @ 541;<;5331

<3 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 54Orzhu frq�ghqfh olplw @ 531579533/ Xsshu frq�ghqfh olplw @ 541:86;331

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<3 ( frq�ghqfh lqwhuydo iru Srlvvrq sdudphwhu/ �=q @ 433/ e� @ 68Orzhu frq�ghqfh olplw @ 671359<33/ Xsshu frq�ghqfh olplw @ 681<:64331

�43143 D udqgrp vdpsoh ri 433 �upv zdv gudzq iurp d odujh qxpehu riforwklqj pdqxidfwxuhuv1 Wkh dyhudjh frvw ri fdslwdo zdv '4314 ploolrq iru wkhvdpsoh zlwk d vwdqgdug ghyldwlrq ri '518 ploolrq1

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N

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1.25

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Rqh txhvwlrq lv krz vhulrxv duh wkhvh �jxuhv lq whupv ri srolf|1 Wkdw lv/ irud phdq idwdolw| udwh shu 4333 olfhqvhg gulyhuv ri 158/ ru 518 ghdwkv shu 43/333gulyhuv/ wkh txhvwlrq lv krz vhulrxv dq lvvxh lv wklvB Iruwxqdwho|/ zh vhh wkdwzlwk kljk suredelolw| wkh dfwxdo qxpehu zloo qrw eh juhdwhu wkdq 15: shu 4333olfhqvhg gulyhuv1 Vrph pd| ylhz wkhvh �jxuhv zlwk dodup/ vrph pd| zhoo ehuholhyhg1 Wkh ghflvlrq olhv lq wkh srolf| uhdop1

4317< Lq wkh iroghu Plvf/ gdwd vhw Kxpdqghy1{ov/ duh wzr yduldeohv= wkhxqghu0�yh pruwdolw| udwh lq 4<93 dqg lq 4<;;1 Dw d <<( frq�ghqfh ohyho/ rewdlqfrq�ghqfh lqwhuydov iru erwk wkh phdqv dqg wkh yduldqfhv1 Frpsduh |rxu uhvxowv/dqg frpphqw rq wkh fkdqjh lq pruwdolw| udwhv ryhu wkh lqwhuyhqlqj 5; |hduv1

Dqvzhu=--- Vxppdu| Vwdwlvwlfv iru gdwd lq= Kxpdqghy ---Xqghu �yh pruwdolw| udwh lq 4<93/ yduldeoh xq8pru931Phdq= 4;;134/ Q= 463/ Yduldqfh= 453461;7/ Vwg Ghy1= 43<194<< ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Frqi1 olplwv= Orzhu @ 4951;:9/ Xsshu @ 5461477Xqghu �yh pruwdolw| udwh lq 4<;;/ yduldeoh xq8pru;;1Phdq= <;1:9/ Q= 463/ Yduldqfh= 99381<5/ Vwg Ghy1= ;415;<< ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Frqi1 olplwv= Orzhu @ ;31456/ Xsshu @ 44:16<:Wkh ghfolqh lq lqidqw pruwdolw| iru 4<93 wr 4<;; lv uhdoo| uhpdundeoh> wkh

udwh zdv qhduo| kdoyhg1 Lq dgglwlrq/ wkh yduldqfh zdv uhgxfhg vljql�fdqwo|1 Zhpd| frqfoxgh zlwk yhu| kljk frq�ghqfh wkdw wkh xqghu �yh lqidqw pruwdolw|udwh ghfolqhg txlwh gudpdwlfdoo| dqg wkdw wkh yduldwlrq ri wkh gdwd durxqg wkh

567 Hvwlpdwlrq

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Iljxuh 431:= Iru H{huflvh 4317;1 Kljkzd| Idwdolwlhv shu 4333 Srsxodwlrq dqgshu 4333 Olfhqvhg Gulyhuv1

phdq ghfolqhg vljql�fdqwo| dv zhoo1 Lqghhg/ wkh xsshu <<( frq�ghqfh olplw iruwkh 4<;; uhvxowv lv vxevwdqwldoo| ohvv wkdq wkh orzhu frq�ghqfh erxqg iru 4<931

�43183 �Zkhq Vflhqwl�f Suhglfwlrqv Duh Vr Jrrg Wkh|*uh Edg� zdv dqduwlfoh lq wkh Qhz \run Wlphv +Vhswhpehu 5<wk 4<<;,1 Wkh duwlfoh*v pdlq srlqwzdv wkdw wkh Qdwlrqdo Zhdwkhu Vhuylfh suhglfwhg d rrg fuhvw ri 7< ihhw/ exw wkhdfwxdo rrg fuhvw zdv 87 ihhw1 Wkh fodlp zdv wkdw wkh wrzq ri Uhg Ulyhu kdgehhq oxoohg lqwr d idovh vhqvh ri vhfxulw| e| wkh zhdwkhu vhuylfh*v surylglqj dvlqjoh qxpehu wr uhsuhvhqw lwv iruhfdvw1 Li |rx zhuh dgylvlqj wkh zhdwkhu vhuylfhderxw wklv pdwwhu/ zkdw zrxog |rx whoo wkhp wr gr lq wkh ixwxuhB Gr |rx vhh dqhhg iru wkh uhvlghqwv ri Uhg Ulyhu wr ohduq vrph vwdwlvwlfdo frqfhswvB

Dqvzhu= Wklv txrwh vxjjhvwv wkdw surylglqj rqo| wkh srlqw hvwlpdwh lvplvohdglqj1 Lw zrxog eh ehwwhu iru wkh Zhdwkhu Vhuylfh wr vxsso| d frq�ghqfhlqwhuydo lqvwhdg ri d vlqjoh qxpehu dorqj zlwk wkh dvvrfldwhg suredelolw|1 Wklvh{dpsoh looxvwudwhv judsklfdoo| wkh qhhg iru wkh dyhudjh shuvrq wr kdyh d pruhvrsklvwlfdwhg xqghuvwdqglqj ri vwdwlvwlfv dqg wkhlu phdqlqj1 Li wkh uhvlghqwv kdgnqrzq wkdw fuhvwlqj eh|rqg 87 ihhw kdg/ vd| d 43( suredelolw| ri rffxuulqj/ wkh|zrxog kdyh wdnhq yhu| gl�huhqw dfwlrqv1

43184 Li |rx zhuh dvnhg wr hvwlpdwh wkh phdq dqg yduldqfh ri skrqh xvhe| d whohskrqh frpsdq|*v fxvwrphuv/ zkdw idfwruv zrxog |rx wdnh lqwr dffrxqw

Dssolfdwlrqv 568

lq ghvljqlqj wkh vdpsolqj surfhgxuhB Li |rx vxvshfwhg wkdw exvlqhvv dqg idplo|xvdjh ydulhv juhdwo|/ krz zrxog wklv nqrzohgjh d�hfw |rxu surfhgxuhvB

Dqvzhu= Dprqj rwkhu frqfhuqv/ wkh fxvwrphuv* fkdudfwhulvwlfv vkrxog ehwdnhq lqwr dffrxqw lq ghvljqlqj wkh vdpsolqj surfhgxuh1 D �uvw uhtxluhphqw lvwr kdyh vrph lghd dv wr zkdw lv wkh uhohydqw glvwulexwlrq dqg zkdw lv lwv vkdsh1Ixuwkhu/ li |rx vxvshfw wkdw wkh sduhqw glvwulexwlrqv ri exvlqhvv dqg idplo| xvdjhduh qrw wkh vdph/ |rx vkrxog vdpsoh dqg hvwlpdwh wkhp vhsdudwho|1


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d1 Surgxfh wkh uhohydqw frq�ghqfh lqwhuydov/ mxvwli|lqj |rxu fkrlfh ri frq�0ghqfh ohyho/ dqg hydoxdwh |rxu uhvxowv1 Zklfk surfhgxuh zrxog |rx uhfrpphqgwr wkh frxuw dqg zk|B

e1 Frpphqw rq wkh wkhruhwlfdo lpsolfdwlrqv ri wkhvh wzr gl�huhqw dssurdfkhvwr dvvhvvlqj wkh lpsdfw ri glvfulplqdwlrq1

^Frpsxwhu klqw= Lq wkh Glvfgdwd1{ov �oh/ xvh rqo| iruphu hpsor|0hhv +h{w1dsso @ 3,1 Fuhdwh gdwd iudph xvlqj Gdwd/ Vsolw1`

Dqvzhu=d1 Xvh gdwd iudphv ri iruphu hpsor|hhv +h{w1dsso @ 3, dqg kluhg dqg qrw

kluhg +kluh1vwdw @ 4 ) 3 uhvshfwlyho|, iru wkh vshfl�hg djh jurxsv1--- Vxppdu| Vwdwlvwlfv ---Vdodu| ri iruphu hpsor|hhv ohvv wkdq 83 |hduv rog zkr zhuh uhkluhg1Phdq= 945:4/ Q= 493/ Yduldqfh= 553899<9:/ Vwg Ghy1= 47;84<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 81;<8543h7 Xsshu olplw @ 9168;<<3h7

--- Vxppdu| Vwdwlvwlfv ---Vdodu| ri iruphu hpsor|hhv ohvv wkdq 83 |hduv rog zkr zhuh qrw uhkluhg1Phdq= 85;;;/ Q= 58/ Yduldqfh= 534;85:9:/ Vwg Ghy1= 4753:<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 71:35673h7 Xsshu olplw @ 81;:8593h7

--- Vxppdu| Vwdwlvwlfv ---Vdodu| ri iruphu hpsor|hhv juhdwhu wkdq ru htxdo wr 83 |hduv rog zkr zhuh

uhkluhg1Phdq= 96:6</ Q= 77/ Yduldqfh= 5668:<968/ Vwg Ghy1= 485;6<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 81<3<573h7 Xsshu olplw @ 91;6;893h7

569 Hvwlpdwlrq

--- Vxppdu| Vwdwlvwlfv ---Vdodu| ri iruphu hpsor|hhv juhdwhu wkdq ru htxdo wr 83 |hduv rog zkr zhuh

qrw uhkluhg1Phdq= 9:497/ Q= 58/ Yduldqfh= 4;<93<39:/ Vwg Ghy1= 46::3<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 9147;343h7 Xsshu olplw @ :15;7:<3h7

--- Vxppdu| Vwdwlvwlfv iru gdwd lq= Vdodjh1kluhg ---Vdodu|2djh iru uhkluhg iruphu hpsor|hhv1Phdq= 476915/ Wrwdo Q= 53713/ Yduldqfh= 46:45813/ Vwg Ghy1= 6:316<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 46;813;3333 Xsshu olplw @ 47;:1653333

--- Vxppdu| Vwdwlvwlfv iru gdwd lq= Vdodjh1qrwkluhg ---Vdodu|2djh iru iruphu hpsor|hhv qrw uhkluhg1Phdq= 454:155/ Q= 83133/ Yduldqfh= ;;9:91::/ Vwg Ghy1= 5<:1:<<8 ( frq�ghqfh lqwhuydo iru phdq ri qrupdo/ yduldqfh xqnqrzq=Orzhu olplw @ 446518<3333 Xsshu olplw @ 46341;83333

VXPPDU\ WDEOH = <8( Frq�ghqfh Lqwhuydov iru Ydulrxv JurxslqjvUhkluhg Qrw Uhkluhg

? 83 |uv lq '43/333 ^81;<8/ 9168<` ^71:35/ 81;:8`� 83 |uv lq '43/333 ^81<3</ 91;6<` ^9147;/ :15;8`vdodu|2djh lq ' ^46;8/ 47;:` ^4466/ 4635`

H{dplqlqj wkh Wdeoh deryh/ zh vhh wkdw iru wkrvh iruphu hpsor|hhv zkrzhuh uhkluhg wkh frq�ghqfh lqwhuydov duh yhu| vlplodu dfurvv wkh ohvv wkdq 83 dqgwkh juhdwhu wkdq ru htxdo wr 83 djh jurxsv1 Iru wkrvh qrw uhkluhg/ wkh ryhu 83jurxs lqwhuydo lv zhoo wr wkh uljkw ri wkh ohvv wkdq 83 jurxs1 Wklv lv fohdu wkdwiru wkrvh uhkluhg wkhuh lv yluwxdoo| qr gl�huhqfh/ exw iru wkrvh qrw uhkluhg wkhgl�huhqfhv lv vljql�fdqw1

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Zh vhh wkhuhiruh wkdw wkhuh lv d vljql�fdqw gl�huhqfh lq lqwhusuhwdwlrq iruwkhvh uhvxowv1 Wkh lqfuhdvh lq lqfrph shu xqlw ri djh dwwhqv rxw dw wkh kljkhudjh ohyhov/ vr wkdw wkh uhkluhg duh lq idfw sursruwlrqdwho| pruh h{shqvlyh wkdqwkrvh qrw kluhg1 Rqh pljkw frqfoxgh wkdw wkh �up nhsw wkrvh hpsor|hhv zlwkwkh uhodwlyho| kljkhu vdodulhv jlyhq wkhlu djhv1 Wklv uhvxow grhv qrw vxssruw wkhxqlrq srvlwlrq1

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revhuyh krz wkh uhodwlyh iuhtxhqf| ri uhmhfwlrq xqghu wkh dowhuqdwlyh k|srwkhvlvydulhv zlwk wkh vl}h ri wkh gl�huhqfh ehwzhhq qxoo dqg dowhuqdwlyh/ wkh vdpsohvl}h/ dqg wkh � ohyho1 ^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Folfn rq Odev/Srzhu ri d Whvw1 Dffhsw wkh ghidxow ydoxhv lq wkh gldorj1 Uhshdw wkhh{shulphqw vhyhudo wlphv dowhulqj wkh vhwwlqjv lq wkh gldorj wr h{soruhwkh uroh ri srzhu lq k|srwkhvlv whvwv1 �G� uhsuhvhqwv wkh gl�huhqfhehwzhhq wkh qxoo dqg dowhuqdwlyh k|srwkhvhv> doo whvwv duh uljkw0vlghg1`


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^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Folfn rq Odev/Vdpsoh Vl}h/ Ohyho/ dqg Srzhu1 Dffhsw wkh ghidxow hqwulhv lq wkh

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Fkdswhu 45

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5:; Elyduldwh Glvwulexwlrqv

srxqgv/ glylgh hdfk hqwu| lq wkh urz iru 4:918 e| wkh wrwdo ri wkh urz iru 4:9181Sorw wkh Kljk Ghqvlw| Olqh Sorw iru wkh glvwulexwlrq ri khljkw frqglwlrqdo rq dzhljkw ri 4:918 srxqgv1

^Frpsxwhu klqw= Uh0lpsruw Kwzwnhvw +wr uhpryh froxpqv dgghglq 4 ) 5 deryh,1 Rq wkh phqx edu/ folfn rq Gdwd/ Wudqvsrvh> folfnDsso|1 Rshq wkh Remhfw Eurzvhu dqg grxeoh folfn rq gdwd iudphodvw1wudqvsrvh1 Kljkoljkw urz 4 ri odvw1wudqvsrvh/ dqg grxeoh folfn rqwkh Uhpryh Urz exwwrq rq wkh wrroedu1 Uhshdw wkh gluhfwlrqv lq+f, vxevwlwxwlqj [4; +zklfk lv wkh 4:918 srxqg froxpq, iru kw8; dqgqdplqj wkh qhz froxpq frqg4:918 1`

g1 Li |rx pxowlsolhg wkh pdujlqdo suredelolw| wkdw d zrpdq*v khljkw lv 93lqfkhv e| wkh frqglwlrqdo suredelolw| wkdw d zrpdq*v zhljkw lv 4:918 srxqgv jlyhqwkdw wkh fruuhvsrqglqj khljkw zdv 93 lqfkhv/ zkdw suredelolw| zrxog |rx kdyhB

h1 Li |rx glylghg hdfk hqwu| lq wkh urz iru d zhljkw ri 533 srxqgv e| wkhfruuhvsrqglqj urz wrwdo zkdw zrxog |rx kdyhB H{sodlq1

Dqvzhu=d1 Wkh pdujlqdo suredelolw| glvwulexwlrq iru zhljkw lv vkrzq lq Iljxuh 4518=

0 5 10 15 20 25 30 35

0.00

0.02

0.04

0.06

0.08

0.10

0.12

mar

gdis

wt

Iljxuh 4518= Judsk wr H{huflvh 45144 +d,

Wkh phdq/ yduldqfh/ wklug dqg irxuwk vwdqgdugl}hg prphqwv duh 4651;5/83:179/ 1<</ dqg 71;9/ uhvshfwlyho|1 Vhh Iljxuh 45181

e1 Wkh glvwulexwlrq ri zhljkw frqglwlrqdo rq d khljkw ri 8; lqfkhv lv vkrzqlq Iljxuh 45191

f1 Wkh glvwulexwlrq ri khljkw frqglwlrqdo rq zhljkw ri 4:918 srxqgv lv vkrzqlq Iljxuh 451:1

g1 Li |rx pxowlsolhg wkh pdujlqdo suredelolw| wkdw d zrpdq*v khljkw lv 93

H{sorulqj wkh Wrrov 5:<

0 5 10 15 20 25 30 35

0.00

0.04

0.08

0.12

cond

ht58

Iljxuh 4519= Judsk wr H{huflvh 45144 +e,

0 2 4 6 8 10

0.00

0.05

0.10

0.15

0.20

0.25

cond

176.

5

Iljxuh 451:= Judsk wr H{huflvh 45144 +f,

5;3 Elyduldwh Glvwulexwlrqv

lqfkhv e| wkh frqglwlrqdo suredelolw| wkdw d zrpdq*v zhljkw lv 4:918 srxqgvjlyhq wkdw wkh fruuhvsrqglqj khljkw zdv 93 lqfkhv/ |rx zrxog jhw d mrlqw sure0delolw| wkdw d zrpdq kdv khljkw 93 lqfkhv dqg zhljkw 4:918 srxqgv1

h1 Li |rx glylghg hdfk hqwu| lq wkh urz iru d zhljkw ri 533 srxqgv e| wkhfruuhvsrqglqj urz wrwdo/ |rx zrxog jhw wkh frqglwlrqdo suredelolw| glvwulexwlrqri khljkw jlyhq d zhljkw ri 533 srxqgv1

4516 Dssolfdwlrqv

�45145 Remhfwlyh= Wr lqyhvwljdwh wkh frqvwuxfwlrq dqg dqdo|vlv ri frqwrxu sorwv1Wkh gdwd �oh Frvl}h1{ov lq iroghu Plvf surylghv lqirupdwlrq rq vdohv dqg hp0

sor|phqw iru 46; �upv1 Xvlqj |rxu lqwxlwlrq/ zkdw zrxog |rx k|srwkhvl}h derxwwkh vljq dqg pdjqlwxgh ri wkh fruuhodwlrq ehwzhhq vdohv +vdohv, dqg hpsor|phqw+hpso,B Fdq |rx dvvhuw vrphwklqj derxw wkh gluhfwlrq ri fdxvdolw|B Zkdw fdq|rx k|srwkhvl}h derxw wkh vkdsh ri wkh frqwrxu sorwB Uhfrug |rxu k|srwkhvhv/dqg wkhq fdofxodwh wkh fruuhodwlrq1 Frqvwuxfw wkh frqwrxu sorw xvlqj V0Soxv1 Duh|rxu k|srwkhvhv frq�uphg ru uhmhfwhgB

Dqvzhu= Zh pd| k|srwkhvl}h wkdw wkh fruuhodwlrq ehwzhhq vdohv dqg hp0sor|phqw lv srvlwlyh dqg kljk1 Dv wr wkh gluhfwlrq ri fdxvdolw|/ lw lv olnho| wkdwpruh vdohv ohdgv wkh �up wr kluh pruh hpsor|hhv1 Lw lv dovr srvvleoh xqghu vrphflufxpvwdqfhv wkdw klulqj pruh dqwlflsdwhv pruh vdohv1 Ixuwkhu lqyhvwljdwlrq lvqhhghg1 Wkh fdofxodwhg fruuhodwlrq frh!flhqw lv 1:86 dqg wkh frqwrxu sorw lvvkrzq lq Iljxuh 451;1 Rxu lqlwldo k|srwkhvhv duh zhdno| frq�uphg1 Zh qrwhwkdw li zh zhuh wr frqglwlrq rq rqh ri wkh yduldeohv/ wkhq zh revhuyh d glv0wulexwlrq ri ydoxhv iru wkh rwkhu yduldeoh zkhuh wkh orfdwlrq dqg vkdsh ri wkhglvwulexwlrq ghshqgv rq wkh ydoxh wdnhq e| wkh frqglwlrqlqj yduldeoh1

45146 H{sodlq krz wkh xvh ri udqnhg gdwd/ lqvwhdg ri dfwxdo gdwd/ zrxogd�hfw wkh frqvwuxfwlrq dqg dqdo|vlv ri d frqwrxu sorw1 Looxvwudwh e| sorwwlqj wkhfrqwrxu sorwv iru khljkwv ri phq dqg zrphq lq wkh �oh Kxvedqgv1{ov/ lq wkhiroghu Plvf1

Dqvzhu= Wkh frqwrxu sorw xvlqj udqnhg gdwd lv vkrzq lq Iljxuh 451<1Zh fdq frpsduh wklv sorw zlwk wkh rqh xvlqj dfwxdo gdwd lq H{huflvh 45171

Wkh gl�huhqfh lv vwulnlqj1 Udqnv duh qrw xvhixo lq wklv w|sh ri dqdo|vlv1

45147 Lq wkh iroghu Whvwvfru/ lq �oh Svdwvdw1{ov duh wkh yduldeohv svdwpdwkdqg svdwyhue1 H{dplqh wkh frqwrxu sorw ri wkhvh wzr yduldeohv1

^Frpsxwhu gluhfwlrqv= Lq V0Soxv/ lpsruw Svdwvdw1{ov1 Rq wkh phqxedu/ folfn Judsk/ 5G Sorw/ Frqwrxu Sorw1 Folfn RN1 Lq wkh gldorjer{/ vhohfw svdwpdwk iru wkh �{ Froxpq+v,� dqg svdwyhue iru wkh �|Froxpq+v,1� Folfn RN1` \rx pd| zdqw wr wu| wkh Frqwrxu Iloohg sorw1 Li |rxzhuh wr udqgrpl}h wkh rughu ri svdwyhue dqg sorw wkh frqwrxu sorw/ zkdw zrxog|rx h{shfw wr vhhB Wu| lw dqg fkhfn |rxu vxssrvlwlrq1

^Frpsxwhu klqw= Wr udqgrpl}h svdwyhue/ rq wkh phqx edu/ folfnrq Gdwd/ Udqgrp Vdpsoh1 Lq Vdpsolqj Sure1/ vhohfw svdwyhue1 Rshqwkh Remhfw Eurzvhu dqg grxeoh folfn rq gdwd iudph odvw1vdpsoh1 Frs|

Dssolfdwlrqv 5;4

1000 5000 9000 13000sales

50

90

130

170

empl

2.6

2.6

5.2

5.2 7

.8

10.

4

Iljxuh 451;= Judsk wr H{huflvh 45145

50 90 130 170rankhh

50

90

130

170

rank

hw

Iljxuh 451<= Judsk wr H{huflvh 45146


wkh qhzo| udqgrpl}hg svdwyhue froxpq wr wkh Svdwvdw gdwd iudph1 Grwkh Frqwrxu judsk xvlqj wkh udqgrpl}hg svdwyhue1`

Dqvzhu= Iurp Iljxuh 45143 zh fdq vhh wkdw wkhuh lv srvlwlyh fruuhodwlrqehwzhhq SVDW pdwk dqg yhuedo vfruhv1 Exw diwhu udqgrpl}lqj wkh vdpsoh/ wkhfruuhodwlrq glvdsshduv dv vkrzq lq Iljxuh 451441

20 40 60psatmath

20

40

60

psat

verb

8.2

16.4 24.6

32.8

41.0

49.2 57.4 65.

6

73.

8


�45148 +Uhihu wr H{huflvh 451471, Uhshdw wkh �uvw sduw ri wkh h{shulphqw/iru vdwpdwk dqg vdwyhue1 H{fhsw iru gl�huhqfhv ri vfdoh duh wkhuh dq| qrwlfhdeohgl�huhqfhv lq wkh frqwrxu sorwvB Fdq |rx h{sodlq wkhvh uhvxowvB

Dqvzhu= Zh fdq frpsduh wkh wzr judskv ehorz/ Iljxuhv 45145/ 45146/ zlwkwkrvh lq wkh odvw h{huflvh1 Wkhuh lv olwwoh gl�huhqfh ehwzhhq wkh frqwrxu sorwv iruVDW vfruhv dqg iru SVDW vfruhv1 Lw vxjjhvwv wkdw wkh VDW dqg SVDW duh yhu|vlplodu whvwv1 Wkhvh judskv dovr uhplqg xv wkdw li zh h{dplqh wkh ydoxhv wdnhqe| rqh yduldeoh jlyhq d vshfl�f ydoxh iru wkh rwkhu/ wkh vkdsh ri wkh glvwulexwlrqri wkh frqglwlrqhg yduldeoh lqfoxglqj lwv orfdwlrq ghshqgv rq wkh ydoxh wdnhq e|wkh frqglwlrqlqj hyhqw1

45149 Frpsduh wkh uhvxowv rewdlqhg li |rx h{dplqh wkh frqwrxu sorwv irusvdwpdwk dqg vdwpdwk1 Vlploduo|/ h{dplqh svdwyhue dqg vdwyhue1 Zkdw lpsuhv0vlrqv gr |rx jhwB Zkdw frqfoxvlrqv derxw wkh uhodwlrqvkls ehwzhhq SVDW dqgVDW gr |rx gudzB

Dqvzhu= E| h{dplqlqj wkh judskv ehorz/ vhh Iljxuhv 45147/ 45148/ zh qrwhwkdw wkhuh lv d vwurqj srvlwlyh fruuhodwlrq ehwzhhq pdwk vfruhv ri SVDW dqgVDW1 Wkhuh lv dovr vwurqj srvlwlyh fruuhodwlrq ehwzhhq yhuedo vfruhv ri SVDWdqg VDW1 Wkhuhiruh edvhg rq wklv h{huflvh dqg wkh odvw wzr/ zh fdq frqfoxgh wkdw

Dssolfdwlrqv 5;6

20 40 60psatmath

20

40

60

psat

verb

rdzd

5.8 11.6 17.4

23.2

29.0

34.8

40.

6 46.4 52

.2


300 400 500 600 700satmath

200

300

400

500

600

700

satv

erb

6.1

12.2

18.3 24.4

36.6

42.7 48.8

54.9



300 400 500 600 700satmath

200

300

400

500

600

700

satv

erbr

dzd

5.4

5.4

10.8

16.2

21.6

27.0

32.4

37.8

43.

2

43.

2

48.

6


d vwxghqw*v SVDW shuirupdqfh lv d jrrg lqglfdwru ri klv2khu VDW shuirupdqfhdqg wkdw wkh uhodwlrqvkls ehwzhhq SVDW pdwk dqg yhuedo vfruhv lv vlplodu wrwkdw iru VDW pdwk dqg yhuedo vfruhv1 Wkh surfhvv ri udqgrpl}dwlrq ri wkh gdwduhplqgv xv wkdw zh duh h{dplqlqj wkh glvwulexwlrq ri sdluv ri udqgrp yduldeohv1

�4514: Lq wkh iroghu Lqwudwh/ xvh wkh �oh Prq|og1{ov zklfk frqwdlqv wkhyduldeohv uhsuhvhqwlqj wkh wkuhh0prqwk dqg wkh vl{0prqwk eloo udwhv +eloo6prdqg eloo9pr uhvshfwlyho|,1 Uhjduglqj wkhvh gdwd dv uhsuhvhqwlqj d vdpsoh iurpwkh mrlqw glvwulexwlrq ri wkuhh0 dqg vl{0prqwk eloo udwhv/ sorw wkh frqwrxuv dqgfrpphqw1 H{dplqh qh{w wkh wkuhh0prqwk eloo udwh dqg wkh �yh0|hdu qrwh udwh+qrwh8|u,1 Frpphqw rq wkh revhuyhg gl�huhqfh1 Fdq |rx h{sodlq wkh gl�hu0hqfhv wkdw |rx revhuyhB

Dqvzhu= Iurp wkh judskv ehorz/ vhh Iljxuh 45149/ 4514:/ zh pd| revhuyhwkdw wkhuh duh yhu| vwurqj srvlwlyh fruuhodwlrqv ehwzhhq wkh wkuhh0prqwk dqgwkh vl{0prqwk eloo udwhv dqg ehwzhhq wkh wkuhh0prqwk eloo udwh dqg wkh �yh0|hduqrwh udwh1 Exw wkh fruuhodwlrq ehwzhhq wkh wkuhh0prqwk eloo dqg vl{0prqwk elooudwhv lv kljkhu1 +1<<: iru wkh iruphu sdlu dqg 1<55 iru wkh odwwhu1, Ehfdxvhwkh wkuhh0prqwk eloo udwh dqg wkh vl{0prqwk eloo udwh duh erwk vkruw whup udwhvdqg wkh �yh0|hdu qrwh udwh lv d orqjhu whup udwh/ wklv uhvxow pljkw kdyh ehhqh{shfwhg1

4514; Xvlqj wkh gdwd lq wkh Hqhuj| iroghu/ frpsduh wkh frqwrxu sorwv irudjulfxowxudo dqg lqgxvwuldo surgxfwlrq dfurvv frxqwulhv1 Iru h{dpsoh/ fdq |rxh{sodlq wkh gl�huhqfhv ehwzhhq Dujhqwlqd dqg wkh Xqlwhg Vwdwhv/ ehwzhhq Nruhddqg Qruzd|B

Dqvzhu= Zkloh iru hdfk frxqwu| lw lv eurdgo| wuxh wkdw erwk lqgxvwuldo dqg

Dssolfdwlrqv 5;8

20 40 60psatmath

300

400

500

600

700

satm

ath

15.2

22.8

30.4

38.0

45.6 53.2 60.8

68.4

Iljxuh 45147= Judsk 4 wr H{huflvh 45148 +Pdwk Vfruhv,

20 40 60psatverb

200

300

400

500

600

700

satv

erb

9.6

19.2

28.

8

38.4 48.0 57.6

67.2 76.8

86.4

96.0

Iljxuh 45148= Judsk 5 wr H{huflvh 45148 +Yhuedo Vfruhv,


3 5 7 9 11 13 15bill3mo

3

5

7

9

11

13

15

bill6

mo

5.0

10.0

10.0

15.0

20.0

25.0 30.0

35.0 40.0

45.

0

Iljxuh 45149= Judsk 4 wr H{huflvh 4514: +6 yhuvxv 9 Prqwk Eloo Udwh,

3 5 7 9 11 13 15bill3mo

5

7

9

11

13

note

5yr

3.4

6.8 10

.2 13

.6

17.0 20.4

23.8

Iljxuh 4514:= Judsk 5 wr H{huflvh 4514: +6 Prqwk Eloo Udwh yhuvxv 8 \hdu Qrwh,

Dssolfdwlrqv 5;:

djulfxowxudo surgxfwlrq duh srvlwlyho| fruuhodwhg/ wkhuh duh vrph vxewoh gl�hu0hqfhv ylvleoh lq wkh judskv1 Iru vrph frxqwulhv/ Dxvwudold dqg olnho| wkh XqlwhgVwdwhv/ wkhuh duh wzr shdnv> wkh glvwulexwlrq lv vdlg wr eh �el0prgdo1� Wkh lp0sruw ri wklv lv wkdw wkh glvwulexwlrq ri djulfxowxudo dqg lqgxvwuldo surgxfwlrq duhkhdylo| frqfhqwudwhg durxqg wzr srlqwv/ rqh zlwk uhodwlyho| orz ohyhov ri rxw0sxw dqg rqh zlwk uhodwlyho| kljk ohyhov1 Nruhd lv glvwlqjxlvkhg iru kdylqj yhu|orz ohyhov ri djulfxowxudo rxwsxw iru lwv ohyho ri lqgxvwuldo surgxfwlrq> hyhq dvfrpsduhg wr wkh Xqlwhg Vwdwhv1 Vrph ri wkh glvwulexwlrqv kdyh vwudqjh vkdshv/Qruzd| iru h{dpsoh/ lqglfdwlqj wkdw ehorz d sduwlfxodu ohyho ri djulfxowxudo rxw0sxw/ wkh fruuhvsrqglqj ghfolqh lq wkh uhodwlyh iuhtxhqf| lq lqgxvwuldo surgxfwlrqlv hyhqo| glvwulexwhg> wklv pd| uh hfw wkh suhydohqfh ri kdqglfudiwv lq Qruzd|wkdw duh edvhg rq wkh uxudo hfrqrp|1

4000 6000 8000 10000 12000agrprod

20000

30000

40000

50000

60000

indp

rod

0.3

0.9

1.2

1.5

1.8

2.1

2.4 2.7

3.0

Iljxuh 4514;= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lqDujhqwlqd1

�4514< Lq wkh iroghu Ilupgdwd/ xvh wkh �ohv Dyrq1{ov dqg Fdpsehoo1{ov1 Lqhdfk �oh duh uhfrughg wkh yduldeohv iru orqj0whup ghew +owghew, dqg vdohv1 Li |rxgr d frqwrxu sorw ri wkhvh wzr yduldeohv iru hdfk ri wkhvh �upv/ zkdw frqfoxvlrqvfdq |rx gudz derxw wkh uhodwlrqvkls ehwzhhq orqj0whup ghew dqg vdohv dqg krzlw ydulhv e| w|sh ri �upB

Dqvzhu= Iljxuhv 45157 dqg 45158 vkrz wkh frqwrxu sorwv iru Dyrq dqgFdpsehoo> dqg iru frqwudvw Iljxuhv 45159 wr 45163 vkrz wkh fruuhvsrqglqj sorwviru wkh uhpdlqlqj �upv1 Wkh �uvw dqg prvw lpsruwdqw ohvvrq wr eh ohduqhg iurpwkhvh judskv lv wkdw wkh mrlqw glvwulexwlrq ri vdohv dqg orqj whup ghew lv qrw dvlpsoh dssur{lpdwho| v|pphwulfdo glvwulexwlrq iru dq| ri wkh �upv lqyroyhg/ doowkh judskv ghprqvwudwh frqvlghudeoh luuhjxodulwlhv1 Rqh zrxog eh zhoo dgylvhgqrw wr kd}dug wkh dvvxpswlrq ri elyduldwh Jdxvvldq iru dq| ri wkhvh gdwd1 Rqo|

5;; Elyduldwh Glvwulexwlrqv

4000 6000 8000 10000agrprod

10000

30000

50000

70000

indp

rod

1.2

1.6 2.

0

2.4

2.8

3.2

3.2

3.6

3.6

Iljxuh 4514<= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lqDxvwudold1

5000 10000 15000 20000agrprod

10000

30000

50000

70000

90000

110000

indp

rod 0.6

1.2 1.8

Iljxuh 45153= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lqNruhd1

Dssolfdwlrqv 5;<

1000 1500 2000 2500 3000agrprod

5000

10000

15000

20000

25000

30000

indp

rod

2.4

2.8

3.2

3.6

Iljxuh 45154= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lqQruzd|1

3000 4000 5000 6000 7000 8000agrprod

5000

9000

13000

17000

indp

rod

Iljxuh 45155= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lq wkhSklolsslqhv1

5<3 Elyduldwh Glvwulexwlrqv

0 20000 40000 60000 80000agrprod

0

400000

800000

1200000

indp

rod

0.6

1.2

1.8

2.4

2.4

Iljxuh 45156= Iru H{huflvh 4514;1 Lqgxvwuldo Surgxfwlrq dqg Djulfxowxuh lq wkhXqlwhg Vwdwhv

Fdpsehoo*v sorw lv wkh prvw olnho| wr eh deoh wr surgxfh uhdvrqdeoh hvwlpdwhviru wkh fruuhodwlrq frh!flhqw> wkh uhpdlqlqj fdvhv vkrxog eh dssurdfkhg zlwkfrqvlghudeoh fdxwlrq1 Lq wkhvh vlwxdwlrqv/ d slfwxuh lv wuxo| zruwk d wkrxvdqgzrugv dqg dv pdq| hvwlpdwhv$

45153 Xvlqj wkh vdph gdwd/ li wkh gdwd revhuyhg duh gudzlqjv iurp d mrlqwglvwulexwlrq ri orqj0whup ghew dqg vdohv/ krz zrxog |rx rewdlq dq dssur{lpdwlrqwr d frqglwlrqdo glvwulexwlrq ri vdohv frqglwlrqdo rq orqj0whup ghewB

Dqvzhu= Zh fdq vxe0vdpsoh iurp wkh gdwd +mrlqw glvwulexwlrq, e| vdpsolqjvdohv iru d jlyhq +vpdoo, udqjh ri ydoxhv iru orqj whup ghew1

45154 Uh0h{dplqh wkh iroghu Whvwvfru/ �oh Svdwvdw1{ov1 Krz zrxog |rx rewdlqdq dssur{lpdwlrq wr wkh frqglwlrqdo glvwulexwlrq ri vdwpdwk vfruhv frqglwlrqdorq vdwyhue vfruhvB

Dqvzhu= Vhh wkh dqvzhu wr H{huflvh 451531

45155 Fdvh Vwxg|= Zdv Wkhuh Djh Glvfulplqdwlrq lq d Sxeolf Xwlo0lw|B Pxfk kdv ehhq pdgh ri frqglwlrqdo glvwulexwlrqv lq wklv fkdswhu1 Fohduo|/frqglwlrqlqj ri wkh yduldeohv djh dqg vdodu| duh fulwlfdo lq wklv fdvh1 Ylhzlqjwkh gdwd wkdw |rx kdyh dydlodeoh dv d vhulhv ri frqglwlrqdo glvwulexwlrqv/ vkrz lqvrph ghwdlo krz wkh lqvljkwv rewdlqhg lq wklv fkdswhu dqg lq Fkdswhu < khos |rxwr xqghuvwdqg wkh vwdwlvwlfdo dvshfwv ri wkh sureohp1 H{soruh lq vrph ghswk wkhydulrxv w|shv ri frqglwlrqdo glvwulexwlrqv lqyroyhg1 Lq wkh surfhvv/ vxppdul}hiru d srwhqwldo mxu| wkh uhohydqfh wr wklv fdvh ri dq| dqdo|vlv xvlqj vxfk gdwd1

Dssolfdwlrqv 5<4

100 300 500 700ltdebt

1500

2000

2500

3000

3500

4000

sale

s

0.4

0.8

0.8

Iljxuh 45157= Iru H{huflvh 4514<1 Frqwrxu Sorw ri Orqj Whup Ghew dqg Vdohviru Dyrq1

100 300 500 700ltdebt

1000

2000

3000

4000

5000

6000

sale

s

Iljxuh 45158= Iru H{huflvh 4514<1 Frqwrxu Sorw ri Orqj Whup Ghew dqg Vdohviru Fdpsehoo1


300 400 500 600 700 800 900 1000ltdebt

4000

6000

8000

10000

12000

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0.5

0.5

0.5

1.0

Iljxuh 45159= Iru H{huflvh 4514<1 Frqwrxu Sorw ri Orqj Whup Ghew dqg Vdohviru 6P1

100 300 500 700 900ltdebt

4000

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Iljxuh 4515:= Iru H{huflvh 4514<1 Frqwrxu Sorw ri Orqj Whup Ghew dqg Vdohviru Gljlwdo1

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1000 1500 2000 2500 3000ltdebt

5000

7000

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0.4

0.4

0 .8

1.2

1.6

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50 100 150 200 250 300ltdebt

500

1000

1500

2000

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500 1000 1500 2000ltdebt

5000

9000

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17000

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1.8 2.4 3.0

3.6

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+Lqwhufhsw, 48;1<966 6<1::;: 61<<95 1333;vdohv 13437 13468 1:99: 17865

Uhvlgxdo vwdqgdug huuru= 7;135 rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 136495I0vwdwlvwlf= 18;:; rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 17865

--- Olqhdu Prgho ---Fdoo= op+irupxod @ lqfrph �vdohv/ gdwd @ Fdpsehoo/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{063715 051:<: 61837 49138 5<;


+Lqwhufhsw, ;155<7 :41;359 14479 1<433vdohv 137;7 13498 51<6;3 3133;;

Uhvlgxdo vwdqgdug huuru= 45<17 rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 16574I0vwdwlvwlf= ;1965 rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 133;:<6

--- Olqhdu Prgho ---Fdoo= op+irupxod @ lqfrph �vdohv/ gdwd @ Gljlwdo/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{04<:3 05<<1: 48134 669 47::


+Lqwhufhsw, 9471:789 73<1:<38 418334 14864vdohv 0139;8 1377: 041866; 14779

Uhvlgxdo vwdqgdug huuru= <4<19 rq 49 ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 145;5I0vwdwlvwlf= 51685 rq 4 dqg 49 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 14779

--- Olqhdu Prgho ---Fdoo= op+irupxod @ lqfrph �vdohv/ gdwd @ Jrrg|hdu/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{068< 065164 5418; 75148 56<15

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+Lqwhufhsw, 0718;39 915:6; 01:634 17:7:vdohv 1398; 13379 4716;6; 13333

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Iljxuh 461:= Iru H{huflvh 4614:1 Uhvlgxdov yv Ilw Sorw1

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Iljxuh 461;= Iru H{huflvh 4614:1 Uhvlgxdov yv Ilw Sorw1

647 Uhjuhvvlrq

Ydoxh Vwg1 Huuru w ydoxh Su+Amwm,+Lqwhufhsw, 6715955 4514838 51;4<; 13446lqfrph 013537 1395: 016596 1:7;3

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+Lqwhufhsw, 4<1839< 818684 618575 13357lqfrph 13;94 13554 61;<<5 13344

Uhvlgxdo vwdqgdug huuru= 471:8 rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 178:<I0vwdwlvwlf= 4815 rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 1334384--- Olqhdu Prgho ---Fdoo= op+irupxod @ ugh{s �lqfrph/ gdwd @ Gljlwdo/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{0::519 085319 07714< 8781; ;;3


+Lqwhufhsw, ;:8196:: 46<19;56 9159;; 13333lqfrph 01547< 147<< 0417675 14:3;

Uhvlgxdo vwdqgdug huuru= 8<317 rq 49 ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1446<I0vwdwlvwlf= 5138: rq 4 dqg 49 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 14:3;--- Olqhdu Prgho ---Fdoo= op+irupxod @ ugh{s �lqfrph/ gdwd @ Jrrg|hdu/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{04491< 08<137 81379 7;1;7 46518


+Lqwhufhsw, 5381377: 6713449 9135;: 13333lqfrph 14955 1446; 417588 14:44

Uhvlgxdo vwdqgdug huuru= :: rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 14347I0vwdwlvwlf= 51365 rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 14:44--- Olqhdu Prgho ---Fdoo= op+irupxod @ ugh{s �lqfrph/ gdwd @ Kdveur/ qd1dfwlrq @ qd1rplw,

Dssolfdwlrqv 648

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+Lqwhufhsw, 518:86 71766; 18;3; 189;8lqfrph 197:5 137<< 451<949 13333

Uhvlgxdo vwdqgdug huuru= 4715; rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1<365I0vwdwlvwlf= 49; rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 41778h0343--- Olqhdu Prgho ---Fdoo= op+irupxod @ ugh{s �lqfrph/ gdwd @ Mrkqvrq/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{0:4158 08; 0461<8 6:1:4 5:5


+Lqwhufhsw, 671;88; 6416<84 414435 15;48lqfrph 1983: 13663 4<1:4<< 13333

Uhvlgxdo vwdqgdug huuru= ;4139 rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1<88;I0vwdwlvwlf= 6;;1< rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 4155<h0346--- Olqhdu Prgho ---Fdoo= op+irupxod @ ugh{s �lqfrph/ gdwd @ Wkuhh1p/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{047417 0<419; 616;; ;:1;5 453


+Lqwhufhsw, 04<<1867: 8;15;95 0617567 13363lqfrph 1;;67 13983 4618;:: 13333

Uhvlgxdo vwdqgdug huuru= <9188 rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1<445I0vwdwlvwlf= 4;719 rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 91995h0344Vlplodu txdolwdwlyh frpphqwv dsso| wr wkhvh uhjuhvvlrqv dv wr wkh odvw vhw1

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--- Olqhdu Prgho ---Fdoo= op+irupxod @ gzdjh �xqhps/ gdwd @ Grpjqs/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{0574 045817 6616 :<1<7 633


+Lqwhufhsw, 54515:<3 5816;34 ;16973 13333xqhps 04518;8: 51:<8; 0718349 13333

Uhvlgxdo vwdqgdug huuru= 45817 rq 8< ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1588:I0vwdwlvwlf= 53159 rq 4 dqg 8< ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 133336564

-100 -50 0 50 100 150 200

-200

-100

010

020

030

0

Fitted : unemp

Res

idua

ls

13

60

59

Iljxuh 46149= Judsk iru H{huflvh 4614<1 Uhvlgxdo yv1 Ilw1

�46153 Wkh lghd ri �zdjh gulyhq� sulfh lqfuhdvhv lv wkdw dq lqfuhdvh lqzdjhv ohdgv wr lq dwlrq1 Krzhyhu/ wkh sureohp lv wu|lqj wr glvwlqjxlvk ehwzhhqlq dwlrq lq �qdo jrrgv sulfhv ohdglqj wr d ghpdqg iru kljkhu prqh| zdjhv dqgzkhwkhu kljkhu prqh| zdjhv ohdg wr lq dwlrq1 Wklv sureohp zh zloo ljqruh1

Vwdwlvwlfdoo|/ zkdw zh revhuyh lv wkh uhodwlrqvkls ehwzhhq wkh fsl dqg prqh|zdjhv +vhh wkh yduldeoh zdjh,1 Frqvlghu wkh uhjuhvvlrq ri �fsl� rq �zdjh1�Xvlqj wkh �oh iroghu Jqs/ vxeiroghu Grpjqs/ Grpjqs1{ov/ iroorz wkh frpsxwhugluhfwlrqv lq H{huflvh 4614:1 Frpphqw rq wkh uhohydqfh ri |rxu uhvxowv wr wkhlvvxh ri wkh uhodwlrqvkls ehwzhhq wkh fsl dqg prqh| zdjhv1

Dssolfdwlrqv 654

Dqvzhu= Hyhq wkrxjk wkh hvwlpdwhg ydoxh ri wkh vorsh frh!flhqw/ 1343;/ lvyhu| vpdoo/ wkh vwdqgdug huuru/ 13336/ lv hyhq vpdoohu1 Vr wkh srvlwlyh uhodwlrqvklslv vwdwlvwlfdoo| vljql�fdqw1 Zh fdqqrw krzhyhu frqfoxgh dq|wklqj derxw gluhfwlrqri fdxvdolw|1 Dq h{dplqdwlrq ri wkh U5 ydoxh lqglfdwhv wkdw qrw yhu| pxfk riwkh yduldwlrq lv dffrxqwhg iru e| wkh prgho1

46154 Zrunhg1 Remhfwlyh= Wr looxvwudwh xvh ri wkh uhjuhvvlrq urxwlqh1 Lqd zhljkw uhgxfwlrq surjudp dw Q\X/ d qxpehu ri vwxghqwv ri erwk vh{hv zhuhhquroohg1 Lw lv uhdvrqdeoh wr suhvxph wkdw zhljkw dqg khljkw duh srvlwlyho| fruuh0odwhg/ exw wkh uhodwlrqvkls ehwzhhq khljkw dqg idw lv qrw vr reylrxv1 Lq wkh iroghuPlvf/ �oh Frohv1{ov duh wkh yduldeohv kw iru khljkw/ wkh uhjuhvvru yduldeoh/ dqgwkh yduldeohv suhzw dqg suhidw/ wkh suhsurjudp zhljkw dqg idw phdvxuhphqwv1Uhjuhvvlqj hdfk ri wkhvh odwwhu wzr yduldeohv rq khljkw/ dqg frpphqw rq wkhgl�huhqfhv ehwzhhq wkh uhjuhvvlrqv1

^Frpsxwhu gluhfwlrqv= Vwduw V0Soxv1 Lpsruw �oh[�ohvqPlvfqFrohv1{ov1 Rq wkh phqx edu/ folfn Vwdwlvwlfv/ Uhjuhvvlrq/

Olqhdu1 Lq wkh gldorj/ vhohfw Gdwd Iudph/ Frohv1 Lq Irupxod/ nh| lqsuhzw �kw 1 Folfn rq wkh Sorw wde> lq Sorwv fkhfn rqo| Uhvlgxdovyv Ilw1 Folfn Dsso|1 Wkh uhvxowv duh lq wkh Judsk zlqgrz dqg wkhUhsruw zlqgrz1 Uhshdw iru suhidw1`

Lw lv dv sodxvleoh wr uhjuhvv kw rq suhzw dv wkh rwkhu zd| durxqg1 Wu|uhjuhvvlqj kw rq suhzw/ xvlqj wkh vdph olqhdu uhjuhvvlrq frpsxwhu lqvwuxfwlrqv1Rqfh djdlq wkh whpswdwlrq wr odeho d vljql�fdqw uhjuhvvlrq uhvxow dv �fdxvdo� lvsrwhqwldoo| plvohdglqj1 Grhv khljkw �fdxvh� suhsurjudp zhljkw/ ru suhsurjudpzhljkw �fdxvh� khljkwB Wkh wrrov wkdw |rx kdyh vr idu gr qrw hqdeoh |rx wrghflgh wklv lvvxh1

Dqvzhu=--- Olqhdu Prgho ---Fdoo= op+irupxod @ suhzw �kw/ gdwd @ Frohv/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{06418: 04<1:6 09157; <19<: 4341<


+Lqwhufhsw, 0471:;87 433167:7 0147:6 1;;6;kw 516;4< 4186<6 4187:7 14646

Uhvlgxdo vwdqgdug huuru= 5;194 rq 66 ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 139:98I0vwdwlvwlf= 516<7 rq 4 dqg 66 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 14646--- Olqhdu Prgho ---Fdoo= op+irupxod @ suhidw �kw/ gdwd @ Frohv/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{04713< 061645 1:<8 8183< 4615;

Frh!flhqwv=

655 Uhjuhvvlrq

Ydoxh Vwg1 Huuru w ydoxh Su+Amwm,+Lqwhufhsw, 861:847 5818397 5143:7 1375;kw 01775< 16<46 0414653 31598;

Uhvlgxdo vwdqgdug huuru= :15:6 rq 66 ghjuhhv ri iuhhgrp

Pxowlsoh U0Vtxduhg= 136:6;

I0vwdwlvwlf= 415;4 rq 4 dqg 66 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 1598;

Wkhuh lv yhu| olwwoh hylghqfh ri fruuhodwlrq lq hlwkhu fdvh/ shukdsv vxusulvlqjo|vr iru wkh yduldeoh �suhzw/� l1h1 wkh lghd wkdw wdoohu shrsoh duh rq dyhudjh khdylhuwkdq vkruwhu1 Exw olwwoh uholdqfh fdq eh sodfhg rq wkh ydoxhv wdnhq e| wkh srlqwhvwlpdwhv1

125 130 135 140 145 150 155

-20

020

4060

8010

0

Fitted : ht

Res

idua

ls

2230

10

Preweight Regressed on Height

Iljxuh 4614:= Judsk iru H{huflvh 461541 Uhvlgxdo yv Ilw1

Dssolfdwlrqv 656

23 24 25 26 27

-15

-10

-50

510

Fitted : ht

Res

idua

ls30

139

Prefat Regressed on Height

Iljxuh 4614;= Judsk iru H{huflvh 461541 Uhvlgxdo yv Ilw1

�46155 Hfrqrplf wkhru| whoov xv wkdw dv |rxu lqfrph ulvhv/ frqvxpswlrqri +qrupdo, frpprglwlhv lqfuhdvhv1 Wkh lqwxlwlrq lv wkdw wkh pruh lqfrph |rxkdyh/ wkh juhdwhu txdqwlwlhv ri doo frpprglwlhv |rx frqvxph1 Xvh wkh gdwd frq0wdlqhg lq wkh �oh Irrg1{ov lq wkh Plvf iroghu wr h{soruh wkh k|srwkhvlv wkdw dv|rxu lqfrph +|, ulvhv/ wkh txdqwlw| ri irrg |rx frqvxph +tg, ulvhv1 Vhh wkhfrpsxwhu gluhfwlrqv lq H{huflvh 461541 Fdq |rx uhodwh wkh uhvxow ri |rxu k|0srwkhvlv whvw wr frpprq vhqvhB Zkdw gl!fxowlhv gr |rx dqwlflsdwh iurp |rxuvwdwlvwlfdo dqdo|vlvB

Dqvzhu=--- Olqhdu Prgho ---Fdoo= op+irupxod @ tg �|/ gdwd @ Irrg/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=Plq 4T Phgldq 6T Pd{06167: 01:;4 13:978 4146; 41<84


+Lqwhufhsw, ;31<7<: 51<454 5:1:<:: 13333| 15364 135<: 91;7;7 13333

Uhvlgxdo vwdqgdug huuru= 4185< rq 4; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 1:55:I0vwdwlvwlf= 791< rq 4 dqg 4; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 513;h0339Wklv uhjuhvvlrq prgho h{sodlqv idu pruh ri wkh gdwd wkdq wkh suhylrxv wzr1

Wkh frh!flhqw lv srvlwlyh/ dqg wkh hvwlpdwhg ydoxh ri wkh frh!flhqw vhhpv wr ehuhdvrqdeoh1 Krzhyhu/ wkhuh lv d gl!fxow| khuh1 Krz gr zh nqrz zkhwkhu zh duh

657 Uhjuhvvlrq

h{dplqlqj revhuydwlrqv iurp wkh frqglwlrqdo glvwulexwlrq ri irrg frqvxpswlrqjlyhq lqfrph dorqhB Wkdw lv/ lq wkh dfwxdo gdwd wkh txdqwlw| ri irrg frqvxphgfrxog zhoo kdyh ehhq d�hfwhg e| yduldwlrqv lq rwkhu yduldeohv/ iru h{dpsoh/ wkhuhodwlyh sulfhv ri irrg wr gxudeoh jrrgv/ ru zh pljkw eh revhuylqj wkh frqglwlrqdoglvwulexwlrq ri lqfrph jlyhq irrg frqvxphg1

96 98 100 102 104 106

-3-2

-10

12

Fitted : y

Res

idua

ls

16

15

14

y = per capita disposable income divided by cost of living index

Iljxuh 4614<= Judsk iru H{huflvh 461551 Uhvlgxdo yv Ilw1

46156 Wkh �oh Sv|fkro1{ov lq iroghu Plvf frqwdlqv gdwd rq Lqwhooljhqfh Txr0wlhqw phdvxuhv dqg khljkw +phdvxuhg lq lqfkhv, iru 83 lqglylgxdov1 H{soruh wkhk|srwkhvlv wkdw vkruwhu shrsoh duh vpduwhu wkdq wdoohu shrsoh1 Krz grhv wklvk|srwkhvlv gl�hu iurp wkh k|srwkhvlv wkdw vpduwhu shrsoh duh vkruwhu wkdq ohvv0lqwhooljhqw shrsohB Zrxog |rxu whvwlqj surfhgxuh gl�hu ehwzhhq wkh wzr k|srwkh0vhvB Whvw erwk ri wkhvh k|srwkhvhv/ dqg h{sodlq dq| gl�huhqfhv lq wkh uhvxowv|rx rewdlq1

Dqvzhu= Zkloh wkh fruuhodwlrq ehwzhhq LT dqg khljkw zloo eh wkh vdph/qdpho| 0146</ zkhwkhu zh frqvlghu LT frqglwlrqdo rq khljkw/ ru khljkw frqgl0wlrqdo rq LT wkhuh lv d gl�huhqfh lq wkh edvlf dvvxpswlrqv xqghuo|lqj wkh uh0juhvvlrq dqdo|vlv1 Uhfdoo wkh glvfxvvlrq rq frqglwlrqdo glvwulexwlrqv lq Fkdswhu451

Li zh frqvlghu wkh k|srwkhvlv wkdw �vkruwhu shrsoh duh vpduwhu wkdq wdoohushrsoh� zh duh h{dplqlqj wkh frqglwlrqdo phdq ri LT rq khljkw1 Wkh hvwlpdwhgvorsh frh!flhqw lv 0187 dqg wkh hvwlpdwhg vwdqgdug huuru lv 188/ vr dw dq| uhdvrq0deoh ohyho ri vljql�fdqfh zh zrxog dffhsw wkh qxoo k|srwkhvlv ri qr uhodwlrqvkls/hyhq wkrxjk wkh vljq ri wkh frh!flhqw lv qhjdwlyh1

Wkh dowhuqdwlyh irupxodwlrq/ vpduwhu shrsoh duh vkruwhu/ lpsolhv d uhjuhvvlrqri khljkw rq LT dqg suhvxphv wkdw zh froohfwhg revhuydwlrqv rq khljkw iru jlyhq

Dssolfdwlrqv 658

ydoxhv ri LT1 Wklv uhjuhvvlrq |lhogv d vorsh frh!flhqw hvwlpdwh ri 01369 zlwk dvwdqgdug huuru ri 136:1 Zh frph wr wkh vdph vwdwlvwlfdo frqfoxvlrq/ d }hur vorshfrh!flhqw dv d qxoo lv dffhswhg dw dq| uhdvrqdeoh ohyho ri vwdwlvwlfdo vljql�fdqfh1

--- Olqhdu Prgho ---Fdoo= op+irupxod @ khljkw �lt/ gdwd @ Sv|fkro/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=

Plq 4T Phgldq 6T Pd{0:1839 0518:9 0413:: 515:6 4314:


+Lqwhufhsw, 9<173;3 71879: 4815988 13333lt 01368; 1369< 01<9<3 166:7

Uhvlgxdo vwdqgdug huuru= 71535 rq 7; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 134<4<I0vwdwlvwlf= 1<6< rq 4 dqg 7; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 166:7

--- Olqhdu Prgho ---Fdoo= op+irupxod @ lt �khljkw/ gdwd @ Sv|fkro/ qd1dfwlrq @ qd1rplw,Uhvlgxdov=

Plq 4T Phgldq 6T Pd{05;198 0:1;3< 01::68 ;19:7 :51;4


+Lqwhufhsw, 4891;:<; 69137;6 71684< 13334khljkw 018693 18864 01<9<3 166:7

Uhvlgxdo vwdqgdug huuru= 49159 rq 7; ghjuhhv ri iuhhgrpPxowlsoh U0Vtxduhg= 134<4<I0vwdwlvwlf= 1<6< rq 4 dqg 7; ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 166:7�46157 +Uhihu wr H{huflvh 461561, Frqvlghu zkhwkhu wkh h�hfwv ri wkh h{hu0

flvh surjudp/ li dq|/ zhuh juhdwhu ru ohvv iru zhljkw ru idw1 Zh pljkw vshfxodwhwkdw zlwk odujh ydoxhv iru suhzw zh zrxog kdyh kljk ydoxhv iru srvwzw/ exw wkdwd uhjuhvvlrq ri wkh odwwhu rq wkh iruphu zrxog lqglfdwh d vorsh frh!flhqw zlwkd ydoxh ohvv wkdq rqh> wkdw lv/ hyhq wkrxjk khdylhu shrsoh duh vwloo khdylhu diwhuwkh surjudp/ wkh| duh ohvv vr1

Uxq d uhjuhvvlrq ri srvwzw rq suhzw> dqg frpphqw rq wkh dssduhqw h�hf0wlyhqhvv ri wkh h{huflvh surjudp1 Vhh wkh frpsxwhu gluhfwlrqv lq H{huflvh 461541Frpsduh wkhvh uhvxowv zlwk wkrvh rewdlqhg e| uhjuhvvlqj srvwidw rq suhidw1 Lvwkh surjudp pruh h�hfwlyh iru idw ru zhljkw uhgxfwlrqB Krz zrxog |rx ghflghwklv lvvxhB +Klqw= Uhphpehu wkdw uhjuhvvlrq frh!flhqwv kdyh xqlwv ri phdvxuh0phqw dwwdfkhg1,

Dqvzhu= Iru wkh uhjuhvvlrq

srvwzw @ �3 . �4 � suhzw. %>

wkh hvwlpdwhg �3 lv lqvljql�fdqwo| gl�huhqw iurp }hur/ zklfk phdqv wkhuh lv qrgl�huhqfh ehwzhhq zhljkwv ehiruh dqg diwhu wkh surjudp1 Wkh hvwlpdwhg �4 lv

659 Uhjuhvvlrq

100 120 140 160 180iq

55

60

65

70

75

heig

ht

Iljxuh 46153= Iru H{huflvh 461561 Vfdwwhu Gldjudp dqg Uhjuhvvlrq= Khljkw rqLT1

56 61 66 71 76height

100

120

140

160

180

200

iq

Iljxuh 46154= Iru H{huflvh 461561 Vfdwwhu Gldjudp dqg Uhjuhvvlrq= LT rqKhljkw1

Dssolfdwlrqv 65:

htxdo wr rqh vwdwlvwlfdoo|1 Vr lqlwldoo| khdylhu shrsoh gr qrw orvh pruh zhljkwwkdq wkh rwkhuv1

Li zh uhjuhvv srvwidw rq suhidw/ a�3 @ �4=;; dqg lwv vwdqgdug huuru lv =<31 Vrshrsoh pd| kdyh orvw vrph idw diwhu wkh surjudp/ exw wkh uhvxow lv gxelrxv1 Wkhhvwlpdwhg �4 lv vwloo htxdo wr rqh vwdwlvwlfdoo|1 Vr wkhuh lv qr gl�huhqfh dv wr wkhidw orvv ehwzhhq khdylhu shrsoh dqg rwkhuv1 Rxu pdlq frqfoxvlrq lv wkdw wkhuhlv yhu| olwwoh fkdqjh lq zhljkw ru idw iurp wklv surjudp1

--- Olqhdu Prgho ---

Fdoo= op+irupxod @ srvwzw �suhzw/ gdwd @ Frohv/ qd1dfwlrq @ qd1rplw,

Uhvlgxdov=

Plq 4T Phgldq 6T Pd{0451<5 041699 013584: 5166 ;1397

Frh!flhqwv=

Ydoxh Vwg1 Huuru w ydoxh Su+Amwm,+Lqwhufhsw, 0187:6 61375; 014:<< 1;8;7suhzw 41336: 13545 7:157:7 13333

Uhvlgxdo vwdqgdug huuru= 61949 rq 66 ghjuhhv ri iuhhgrp

Pxowlsoh U0Vtxduhg= 1<;87

I0vwdwlvwlf= 5565 rq 4 dqg 66 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 3

--- Olqhdu Prgho ---

Fdoo= op+irupxod @ srvwidw �suhidw/ gdwd @ Frohv/ qd1dfwlrq @ qd1rplw,

Uhvlgxdov=

Plq 4T Phgldq 6T Pd{061;85 01:874 157;: 1<656 614:5

Frh!flhqwv=

Ydoxh Vwg1 Huuru w ydoxh Su+Amwm,+Lqwhufhsw, 041;::; 1<369 0513:;4 13789suhidw 1<<:3 1367; 5;19446 13333

Uhvlgxdo vwdqgdug huuru= 417;7 rq 66 ghjuhhv ri iuhhgrp

Pxowlsoh U0Vtxduhg= 1<945

I0vwdwlvwlf= ;4;19 rq 4 dqg 66 ghjuhhv ri iuhhgrp/ wkh S ydoxh lv 3

65; Uhjuhvvlrq

10 15 20 25 30 35

-4-2

02

Fitted : prefat

Res

idua

ls

29

2719

Iljxuh 46156= Judsk iru H{huflvh 461571 Uhvlgxdov yv Ilw1

100 120 140 160 180 200 220

-10

-50

5

Fitted : prewt

Res

idua

ls

7

8

6

Iljxuh 46155= Judsk iru H{huflvh 461571 Uhvlgxdov yv Ilw1

46158 Dprqj wkh phpehuv ri |rxu fodvv/ dvn wkh vwxghqwv wr surylgh d phd0vxuh ri/ dup ohqjwk/ khljkw/ ru vkrh vl}h1 Eh yhu| vshfl�f derxw zkdw |rx zdqwphdvxuhg dqg krz1 Dvn wkhp wr dftxluh wkh vdph lqirupdwlrq iurp wkhlu sdu0hqwv1 Iru hdfk sdlu ri prwkhuv dqg gdxjkwhuv dqg idwkhuv dqg vrqv/ uhshdw wkh

Dssolfdwlrqv 65<

fdofxodwlrqv wkdw jdyh ulvh wr wkh �uhjuhvvlrq idoodf|� wkdw zdv glvfxvvhg lq wkhwh{w1 Frpsduh wkh er{0dqg0zklvnhu sorwv ri wkh wzr vhwv ri phdvxuhphqwv1 Frp0phqw1


46159 Frqvlghu wkh iroorzlqj h{shulphqw1 Slfn d frxuvh zlwk pxowlsoh vhf0wlrqv1 Lq hdfk vhfwlrq/ kdyh wkh vwxghqwv sod| d idlu jdph> wkdw lv/ wkh suredelolw|ri orvlqj lv 18 dqg wkh suredelolw| ri zlqlqj lv 181 Lq rqh vhfwlrq/ sudlvh wkh zlq0qhuv dqg fulwlfl}h wkh orvhuv> dqg lq wkh rwkhu vhfwlrq/ gr wkh rssrvlwh> dqg lqd wklug vhfwlrq/ gr qhlwkhu1 Uhsod| wkh jdph lq hdfk vhfwlrq1 Frpsduh wkh rxw0frphv lq wkh wkuhh fdvhv1 Zkdw frpphqwv fdq |rx pdnh derxw wkh h!fdf| risudlvh dqg eodph lq d�hfwlqj shuirupdqfh lq wkhvh vlwxdwlrqv dqg wkh uhohydqfhri wkh vwdwlvwlfv wkdw |rx fdofxodwhB


4615: Frqvlghu wklv d frpsdqlrq h{shulphqw wr H{huflvh 461591 Udqgrpo|vhohfw kdoi wkh vwxghqwv wr sod| d jdph wkdw lv eldvhg lq wkhlu idyru> wkdw lv/ wkhlusuredelolw| ri zlqqlqj lv 19/ vr wkdw wkh suredelolw| ri wkh rssrqhqw zlqqlqj lvrqo| 171 Wkhvh suredelolwlhv uhsuhvhqw wkh �lqqdwh fdsdelolwlhv� ri wkh wzr w|shvri vwxghqwv1 Sod| d vhtxhqfh ri jdphv iru hdfk sdlu ri vwxghqwv/ dqg uhfrug wkhqxpehu ri zlqv iru hdfk1 Gr wklv wzlfh> |rx qhhg qrw/ exw |rx pd|/ sudlvh dqgeodph wkh vwxghqwv rq wkhlu shuirupdqfh lq wkh �uvw urxqg1 Uhshdw wkh dqdo|vlvwkdw jdyh ulvh wr wkh uhjuhvvlrq idoodf|/ dqg frq�up wkdw wkh frqfoxvlrqv |rxfdph wr krog lq wklv fdvh dv zhoo1 Qrz/ vhohfw wkh jrrg vwxghqwv dqg fdofxodwhwkhlu dyhudjh shuirupdqfh lq erwk wuldov dqg vhohfw wkh srru vwxghqwv dqg fdofxodwhwkhlu shuirupdqfh lq wkh wzr wuldov1 Whvw zkhwkhu wkh phdq vfruhv duh wkh vdphiru hdfk jurxs dfurvv wkh wzr wuldov1 Frpphqw rq |rxu uhvxowv1


�4615; Fdvh Vwxg|= Zdv Wkhuh Djh Glvfulplqdwlrq lq d SxeolfXwlolw|B

\rxu �up/ Iruhqvlf Hfrqrplf Frqvxowdqwv/ kdv ehhq dvnhg wr uhsuhvhqw wkhghihqgdqwv lq wklv fdvh1 \rx kdyh ehhq dvnhg wr h{sodlq wr |rxu froohdjxhv wkhehqh�wv iurp xvlqj uhjuhvvlrq dqdo|vlv1

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687 Uhwurvshfwlyh

Dqvzhu= Iru vwxghqw glvfxvvlrq


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lv q. 41+m, d{6.e{5.f{.g

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