charles final year student report

7/25/2019 Charles Final Year Student Report

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Avenue de lArme, B.P : 3900 Kigali, Rwanda Tel: +250 252 57!9!"252 57!9#, $a%: +250 252 57&925"252 57&92

'e()i*e:www.ur.a.rw

SCHOOL OF PURE AND APPLIED SCIENCES

DEPARTMENT OF APPLIED MATHEMATICS

STATISTICS OPTION

Final year Student project Report

Names:NIZEYIMANA Charles S!"#!"$%&

Super'isor( Mr) iru* Taye

Project report submitte to Co!!e"e o# Scie$ces a$ Tec%$o!o"&

U$i'ersit& o# R(a$a i$ partia! #u!#i!me$t o# t%e re)uireme$ts #or t%e First e"ree i$ app!ie

mat%ematics.

ACA+EMIC YEAR !"#&,!"#- a*e:&5"0!"20&5

TOPIC: APPLICATION OF TIME SERIES

ANALYSIS ON THE OCCURRENCE OF

CAR TRAFFIC ACCDENTS IN RWANDA
http://www.ur.ac.rw/http://www.ur.ac.rw/http://www.ur.ac.rw/


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Research Project |University of Rwanda

Application of Time Series on Car Trac Accidents in

Rwanda

Charles NI!"I#ANA

$!C%ARATI&N

-, NIZEYIMANA Charles, ere(/ delare *a*, e%e* were 1*erwi)e india*ed, *i)

d1umen* i) en*irel/ m/ 1wn w1r and a) n1* (een )u(mi**ed in w1le 1r in ar* *1 an/

1*er univer)i*/.

ame 14 *e )*uden*: NIZEYIMANA Charles

igna*ure 14 *e )*uden*........................................

a*e...........".............."20&5

Application of Time series on Car trac accident occurrence in Rwanda Page 1


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Rwanda

Charles NI!"I#ANA

$!$ICATI&N

'i* l1ve and gra*i*ude,

- dedia*e *i) r16e* re1r* *1:

/ Almig*/ 81d,

/ w1le 4amil/,

/ 4riend) and

/ la))ma*e)



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Rwanda

Charles NI!"I#ANA

AC'N&(%!$)!#!NT

Ti) r16e* re1r* a) (een made 1))i(le (/ *e a))i)*ane and en1uragemen* 14 man/

e1le. Al*1ug i*) n1* 1))i(le *1 men*i1n all 14 *em ere (/ *eir name), - w1uld lie *1

ar*iularl/ *an *e 41ll1wing.

-* w1uld n1* ave (een 1))i(le *1 1mle*e *i) r16e* re1r* wi*1u* *e guidane 14 m/uervi)1r riru* Taye, i) r14e))i1nal advie and *e )uervi)i1n 14 *i) w1r, i)

de*ailed 1mmen*) and edi*) were alwa/) *1 *e 1in* and in4luen*ial, - am mu *an4ul *1

im.

- w1uld lie *1 e%re)) m/ areia*i1n *1 *e g1vernmen* 14 Rwanda 8R;, m1re )eiall/

*e


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Rwanda

Charles NI!"I#ANA

A*STRACT

R1ad *ra44i aiden*) are inrea)ing a* a ig ra*e and *i) a) rai)ed ma61r 1nern)

w1rldwide inluding Rwanda. i44eren* re1r*) 1n *ra44i aiden* india*e 1w e1le

ar1und *e w1rld )*ill l1)ing *eir live) and 1*er ge* )eri1u)l/ in6ured due *1 *e *ra44i

aiden*). Ba)ed 1n *e 1u*1me) 14 aiden* redi*i1n m1del), di44eren* 1un*ermea)ure)

will (e imlemen*ed *1 redue *e 4re>uen/ 14 ar *ra44i aiden*). Aiden*?41rea)*ing

m1del) were u)ed *1 m1ni*1r *e e44e*ivene)) 14 vari1u) r1ad )a4e*/ 1liie) *a* ave (een

in*r1dued *1 minimi)e aiden* 1urrene).

Te general 1(6e*ive 14 *i) aer i) *1 iden*i4/ and al/ *e ar1ria*e B1% @enin) *ime

)erie) m1del *1 )*ud/ *e *rend) and a**ern) 14 ar *ra44i aiden*) 1urring in Rwanda a)

well a) mae) a 4ive? /ear 41rea)* 14 ar *ra44i aiden*) *a* will (e e%e*ed *1 1ur in

Rwanda. A m1n*l/ aiden* da*a 4r1m 20&0 *1 20& wa) 1(*ained 4r1m *e *ra44i aiden*

dear*men* 14 Rwanda a*i1nal P1lie. T1)e da*a were deel/ anal/)ed u)ing )*a*i)*ial

)14*ware P and in*erre*ed *1 )ee *e ara*eri)*i (eavi1ur) 14 ar *ra44i aiden*)

1urrene in Rwanda. 1del) were )u()e>uen*l/ devel1ed and AR-A 0, &,&; wa)iden*i4ied a) ar1%ima*el/ ar1ria*e m1del. A 4ive /ear 41rea)* wa) made u)ing *e

ar1ria*e m1del and re)ul*) )1wed *a* ar *ra44i aiden*) w1uld 1n*inue *1 inrea)e

e)eiall/ in eem(er 20&9 *1 #27 in Rwanda.

1re1ver *i) aer 1n*ained *e 1mari)1n 14 *e *rue mean am1ng m1n*l/ ar *ra44i

aiden*) *1 de*ermine *e m1)* )igni4ian* /ear and m1n* in wi m1)* ar *ra44i

aiden*) 1urred (/ u)ing 1ne wa/ AA and *e re)ul*) )1wed *a* *ere i) di44erene

am1ng *e *rue mean 1n /earl/ ar *ra44i aiden*) were *e 1ula*i1n mean

2014 a)

)igni4ian*l/ *e ige)* /earl/ ar *ra44i aiden*) (u* n1 di44erene am1ng *e *rue mean 14

ar *ra44i aiden* (/ m1n*. Te 4inding) 14 *i) )*ud/ draw a**en*i1n *1 *e im1r*ane 14

imlemen*ing e/ r1ad )a4e*/ mea)ure) in 1rder *1 ange *e inrea)ing a**ern) 14 ar

*ra44i aiden*) in Rwanda. Tere41re *e imr1ved and (e**er 1liie) 14 a*i1nal r1ad

)a4e*/ 1mmi))i1n )1uld (e in*r1dued wi* mu ema)i) 1n u(lia*i1n and edua*i1n *1

en)ure ma%imum redu*i1n in =ar *ra44i aiden*). A) 1nlu)i1n B1% @enin) *ime )erie)m1del wa) *e ar1ria*e *ime )erie) m1del 1n ar *ra44i aiden*) 1urring in Rwanda.



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Rwanda

Charles NI!"I#ANA

TA*%! &+ C&NT!NTS

Contents

DECLARATION i

DEDICATION ii

AC!NO"LED#E$ENT iii

A%&TRACT i'

TA%LE O( CONTENT&'

DE(INITION O( TER$&'i

LI&T O( ACRON)$&'ii

LI&T O( (I#*RE&'iii

LI&T O( TA%LE& i+

C,AP1INTROD*CTION ON ROAD TRA((IC ACCIDENT&1-

11 %AC!#RO*ND1-

1. T,EORITICAL INTROD*CTION O( TI$E &ERIE& ANAL)&I&/

10#eneral O2ecti'e/

1/ &peci3c O2ecti'es/

14 Researc5 ,6pot5esis4

17 Researc5 8uestions4

19 Prolem &tatement4

C,APTER .: LITERAT*RE RE;IE"7

C,APTER 0: $ET,ODOLO#)uar*er 14 *ra44i aiden*) dear*men* in /arugenge di)*ri*.

Ti) )*ud/ i) a ar* 14 a l1ng *erm r16e* *a* inve)*iga*e) *e 4a*1r) leading *1 *e r1ad

*ra44i aiden*) and 1w *1 reven* *em.

e)i*e (eing a (ig r1(lem, *e r1ad *ra44i aiden*) are reven*a(le. i44eren* 1un*rie)

ar1und *e w1rld inluding Rwanda ave e)*a(li)ed *e r1ad )a4e*/ )*ra*eg/ aiming *1

)*reng*en *e r1ad )euri*/ and 4ig*ing again)* *e *ra44i aiden*).

Te 1verall 1(6e*ive 14 *i) re)ear i) *1 4ind and 4i* *e ar1ria*e m1del *1 *e *ra44i

aiden* and *1 )ee *e m1)* )igni4ian* m1n* and /ear *1 wi *e m1)* ar *ra44i

aiden*) 1urred in Rwanda. Te aim 14 *i) )*ud/ i) *1 de*ermine and 41rea)* a4*er )i%

/ear) *e a**ern 14 ar *ra44i aiden*) 1urrene in Rwanda.

1. T,EORITICAL INTROD*CTION O( TI$E &ERIE& ANAL)&I&

A *ime?)erie) i) a )e>uene 14 numerial da*a *a* u)uall/ 1ur) in uni41rm in*erval) 1ver

a eri1d 14 *ime )u a) 1url/, dail/, weel/, m1n*l/, /earl/ e*. 8enerall/, i* i) a

)e>uene 14 1()erva*i1n) 1rdered (/ a *ime arame*er. T1 al/ *ime )erie) anal/)i), ea

*ime mu)* (e a))1ia*ed *1 a value wi i) *e a)e in *i) re)ear (eau)e *i) )*ud/

will (e (a)ed 1n anal/)i) 14 m1n*l/ average 14 *ra44i aiden*) 1urrene in Rwanda

*r1ug *ime. Te )eial ara*eri)*i) 14 *ime )erie) anal/)i) are *e 4a* *a*

)ue))ive 1()erva*i1n) are u)uall/ deenden* and *a* *e anal/)i) mu)* *ae in*1

a1un* *e *ime 1rder 14 1()erva*i1n). Tere are *w1 )*e) 14 *ime )erie) anal/)i):

Building a m1del *a* rere)en* a *ime )erie) and


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Rwanda

Charles NI!"I#ANA

Te general 1(6e*ive 14 *i) )*ud/ i) *1 iden*i4/ *e ar1ria*e B1% @enin) *ime )erie)

m1del 1n *e 1urrene 14 ar *ra44i aiden*) in Rwanda

1/ &peci3c O2ecti'es

T1 4i* *e ar1ria*e B1% @enin) *ime )erie) m1del 1n *e 1urrene 14 ar

*ra44i aiden*) in Rwanda. T1 41rea)* *e 4u*ure value 14 *e ar *ra44i aiden*) 1urrene in Rwanda.

T1 1mare *e mean) 14 m1n*l/ ar *ra44i aiden*) 1urring in Rwanda (/

/ear and m1n*.

14 Researc5 ,6pot5esis

H0 (Tere i) n1 )igni4iane di44erene am1ng *e mean) 14 m1n*l/ ar *ra44i aiden*)

in Rwanda (/ /ear and m1n*

H1 (Tere i) a )igni4iane di44erene am1ng *e mean) 14 m1n*l/ ar *ra44i aiden*) in

Rwanda (/ /ear and m1n*

17 Researc5 8uestions

'a* i) *e ar1ria*e B1%? @enin) *ime )erie) 1del 41r *e m1n*l/ ar *ra44i

aiden*) 1urrene in RwandaL -) *ere a )*a*i)*ial )igni4ian* di44erene am1ng *e *rue mean) 14 m1n*l/ ar *ra44i

aiden*) 1urrene in RwandaL



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Rwanda

Charles NI!"I#ANA

19 Prolem &tatement

an/ /ear) ag1, man/ Rwandan 1ula*i1n) l1)* *eir live) and 1*er) ge* )eri1u)l/ in6ured

*r1ug *e *ra44i aiden*) and *e r1(lem )*ill er)i)*) *1da/ in Rwanda. T1)e *ra44i

aiden*) are m1)*l/ in4luened (/ *ree di44eren* gr1u 14 4a*1r) )1me rela*ed *1

envir1nmen* %: Adver)e 14 r1ad 1ndi*i1n), )lier/ r1ad), (ad vi)i(ili*/,...;, *1 *e veile

$1r e%amle): Bad man1euvre), eile de4e*),...; and 1*er rela*ed *1 *e driver) $1r

e%amle): ver )eed), Age, ver drining, egligene,...;.G&5H

an/ re)earer) ave )1wn *e im1r*ane 14 r1ad u)er 4a*1r wi 1n*ri(u*e *1 95 14

aiden*) .P11r r1ad u)er (eavi1ur e%i(i*ed (/ *e driver) in )1me devel1ed 1un*rie)

ma/ (e due *1 *e la 14 n1wledge regarding *e r1ad )a4e*/ r1le and regula*i1n), *e

general a**i*ude *1ward) *e r1ad) )a4e*/ ma**er and *e r1(lem 14 al11l in 1*er 1un*rie).

-n *i) r16e*, *e lan will (e *1 iden*i4/ and 4i* *e ar1ria*e B1% @enin) *ime )erie) 1n

*e ar *ra44i aiden*) 1urring in Rwanda.

Te g1al 14 *i) )*ud/ i) *1 rea*e a m1del *a* will minimi)e *e err1r (e*ween redi*ed

value 14 *e *arge* varia(le and *e a*ual value 14 *e *ra44i aiden*).



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Rwanda

Charles NI!"I#ANA

C,APT!R /0 %IT!RATUR! R!1I!(

Ti) i) *e review 14 a)* rela*ed li*era*ure availa(le in *e area 14 *i) )*ud/, wi )1w) in

num(er 14 )*udie) arried 1u* (/ )everal re)earer) and di44eren* au*1r). A) a re)ul* i*

review) *e relevan* li*era*ure re)ul*ing 4r1m *e w1r 14 in*ere)*ed re)earer) and u*

41rward in *e (11), re1r*, and an/ 1*er u(li)ed d1umen*) *a* will (e availa(le *1 *e

re)earer. ne 14 *e (e)* wa/) *1 under)*and *e au)e) 14 r1ad *ra44i aiden*) i) *1

devel1 vari1u) aiden* redi*i1n m1del) wi are aa(le 14 iden*i4/ing )igni4ian*

4a*1r) rela*ed *1 uman, veile, r1ad in4ra)*ru*ure, land?u)e, and *e envir1nmen*. $1r

in)*ane,

-n Rwanda (e*ween 2002 and 2005, Te r1du*ive /1u* aged (e*ween &! and 30 /ear) 1ld

1un*ed 50.7 were m1)*l/ liel/ inv1lved in *e *ra44i aiden*) and 7#.7 14 *e male)

were eavil/ a44e*ed and in addi*i1n 1ver 90.2 14 *e *ra44i aiden*) *11 lae in Kigali

i*/.G&!H

-n 20&&, 1ver ,293 aiden*) were regi)*ered wi* 3,! 14 *em min1r and #7 )eri1u).

A *1*al 14 277 *ra44i aiden*) were re1r*ed ar1)) *e 1un*r/ during *e 4ir)* *ree m1n*)

14 *e /ear wi* 72 eren* 14 *em in Kigali, a1rding *1 )*a*i)*i) in *e re1r*.

Te *ra44i 1lie re1r* 4ur*er i*e) *e main au)e) 14 r1ad aiden*) in *e 1un*r/ a) 1ver

)eeding, rele)), driving and, drun driving.

-n Ken/a , (e*ween &97& and &990 a(1u* #0 14 *e dea*) inv1lved *e ede)*rian) wi*

2 and *e a))enger) wi* 3# and 1ver *ree *1u)and e1le are illed in r1ad

aiden*) er /ear and *e 75 14 *e r1du*ive /1u* adul* inv1lved in *ra44i aiden*).Te )*a*i)*i) al)1 )1w) *a* uman 4a*1r), 1*er 4a*1r), eile de4e*) and r1ad



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Rwanda

Charles NI!"I#ANA

envir1nmen* la/ed a ma61r r1le in au)ing *e aiden*) wi* #5.5, !., 5.& and 2.9

re)e*ivel/. Te *ra44i 1lie re1rded *1)e r1ad *ra44i aiden*) in Ken/a r1)e 4r1m 35!2

in &9!5 *1 &32 in &99# wi led *1 *e inrea)ing 14 *e dea*) and in6urie) 4r1m 552 *1

2972 1rre)1nding *1 300 *1 30 re)e*ivel/ 3#45)

R1ad *ra44i aiden* re)ear a) e%*en)ivel/ (een 1n)idered wi*in *e 4ramew1r 14 *ime

)erie) anal/)i)

-n 8ana, m1del) were )u()e>uen*l/ devel1ed 41r aiden* a)e) and AR-A 0,2,&; wa)

iden*i4ied wi* eviden* a) *e (e)* m1del. A $ive? /ear 41rea)* wa) made u)ing *e AR-A0,2,&; m1del and i* )1wed *a* r1ad *ra44i aiden* a)e) w1uld 1n*inue *1 inrea)e.

GH

-n =ina, AR-A *ime )erie) m1del a) (een 41und *1 (e ar1ria*e *ime )erie) m1del 1n

*e r1ad *ra44i aiden*) and *e redi*ed re)ul*) 4r1m AR-A m1del revealed *a* r1ad

*ra44i aiden* a)e) were g1ing *1 inrea)e 4r1m &07,579 *1 0&,53! 1ver *e ne%* 1ne /ear

in =ina G&9H

-n ala/)ia, AR-A m1del wa) u)ed *1 redi* num(er 14 r1ad 4a*ali*ie) 41r *e /ear 20&5

and 2020 and *e re)ul*) )1wed *a* *e redi*ed 4a*ali*ie) 41r *e /ear 20&5 will (e #,7!0

and &0,7&! in 2020.G20H

-n -ran, *e B1%?@enin) *ime )erie) m1del wa) an ae*a(le me*1d 41r redi*i1n 14 r1ad

*ra44i aiden*) and re)ul* )1wn *a*&7!3 dea*) were re1rded (/ *e end 14 @anuar/

were *e redi*i1n dea* wa) 41und *1 (e ,9! (/ *e end 14 @anuar/ in 20&&. G2&H



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Rwanda

Charles NI!"I#ANA

C,APT!R 20 #!T,&$&%&)"

Te )*ud/ a) (een 1ndu*ed in a )/)*ema*i r1edure )*ar*ing 4r1m )ele*i1n 14 *e *1i *1

4inal re1r* reara*i1n. Te in*egral ar* wa) *1 iden*i4/ and 1lle* da*a *1 (e la))i4ied,

anal/Jed, in*erre*ed and re)en*ed in a )/)*ema*i manner *1 4ind *e vi*al 1in*). Te

1verall r1e)) 14 me*1d1l1g/ 41ll1wed in *e )*ud/ i) e%lained 4ur*er:

0 1 &T*D) &ITE AND DATA &O*RCE

Te )*ud/ a) (een 1ndu*ed 1n *e ar *ra44i aiden*) 1urrene in Rwanda. Te da*a

e%e*ed *1 (e u)ed a) (een 1(*ained 4r1m Rwanda a*i1nal P1lie e)eiall/ in *e

dear*men* 14 *e *ra44i aiden* l1a*ed a*


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Rwanda

Charles NI!"I#ANA

wi i) 1miled in 1mu*er. -n *i) re)ear, we e%*ra*ed and u)ed all in41rma*i1n wi

wa) u)e4ul *1 4ul4il all li)*ed )ei4i 1(6e*ive). T1 rea *e )*ud/ 1(6e*ive), *e dear*men*

14 )*a*i)*ial (ulle*in in RP *em)elve) wa) u)ed a) )1ure 14 in41rma*i1n. Te rea)1n 14

11)ing *e)e dear*men*) i) *e r1le *e/ la/ in *ra44i aiden*) 1urrene in Rwanda

and ave *e da*a rela*ed *1 *e )*ud/. Ti) */e 14 me*1d 14 da*a 1lle*i1n i) alled

)e1ndar/ da*a )1ure.

0. &TATI&TICAL OR $AT,E$ATICAL $ET,OD *&ED TO (*L(ILL T,E O%>ECTI;E&

2./.-. +ittin3 an appropriate time series model

$1r *e 4ir)* )ei4i 1(6e*ive wi wa) *1 4i* *e ar1ria*e B1% @enin) *ime )erie) m1del

41r *e 1urrene 14 *e ar *ra44i aiden*) in Rwanda, *e main me*1d u)ed wa) B1%

@enin) m1delling ar1a. $ir)*l/, *ime l1* 14 )erie) wa) l1**ed. Beau)e, *e da*a were

nei*er )*a*i1nar/ in mean n1r in variane *e di44erene and l1g *ran)41rma*i1n) ave (een

alied *1 *e da*a *1 mae *em )*a*i1nar/ in mean and in variane re)e*ivel/.

B/ *aing *e re4erene 1n *e *ime )e>uene l1* 14 *e )*ud/ 1(*ained 4r1m P, Te

1ie 14 *e ar1ria*e B1% @enin) *ime )erie) m1del wa) 41und *1 (e *e Au*1regre))ive

-n*egra*ed m1ving average m1del 14 1rder ,d, and > GAR-A ,d,>; m1delH. Te

iden*i4ia*i1n 14 1*en*ial m1del wa) d1ne (a)ed 1n a**ern) 14 *e au*11rrela*i1n and ar*ial

au*11rrela*i1n. T1 iden*i4/ *e ar1ria*e B1% @enin) m1del, au*11rrela*i1n and ar*ial

au*11rrela*i1n 1e44iien*) 14 *e )*a*i1nar/ da*a a4*er da*a *ran)41rma*i1n a) (een made;

wa) alula*ed and *en deending 1n *e 1rrel1gram) 14 *e A=$ and PA=$ wi

de*ermined *e ar1ria*e m1del.

Te au*11rrela*i1n a* lag and *e ar*ial au*11rrela*i1n a* lag m were generall/ given (/

*e 41ll1wing 41rmula) re)e*ivel/:

2

& &

9 ;9 ; " 9 ;N k N

k t t t k t t t

t t

r y y y y y y

+

= =

=



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Rwanda

Charles NI!"I#ANA

'ere y t : Time )erie) da*a

y t : mean 14 *ime )erie) da*a

yt+k : lag value) 14 *ime )erie) da*a a* M&, 2, 3,...

D11ing a* A=$ and PA=$ i4 *e au*11rrela*i1n 4un*i1n Nu*) 144 Na* lag > wile ar*ial

au*11rrela*i1n 4un*i1n die) awa/ m1ving average 14 *e 1rder > )1uld (e inluded in *e

m1del werea) wen ar*ial au*11rrela*i1n 4un*i1n Nu*) 144O a* lag wile au*11rrela*i1n

4un*i1n die) awa/ au*1regre))ive m1del 14 1rder )1uld (e al)1 inluded in *e m1del. -4

(1* A=$ and PA=$ die awa/ *i) )ugge)* 1m(ining (1* AR and A; m1del). 'e ave

al)1 *1 *ae in*1 a1un* *e 1rder 14 di44erening (1* )ea)1nal and n1n )ea)1naldi44erening, 41r e%amle i4 *e da*a a) (een *ran)41rmed (/ u)ing n1n )ea)1nal di44erening

and (1* A=$ and PA=$ die awa/, AR-A ,d,>; m1del will (e 4i**ed were :1rder

au*1regre))iveF >: 1rder 14 m1ving average and d: 1rder 14 di44erening.

T1 11)e *e 1rder 14 *e m1del, *e ar1ria*e me*1d i) *e rinile 14 ar)im1n/. Ti)

i) a rule *1 )ee *e )imle)* m1del 1))i(le. $1r e%amle i4 *e m1del *1 11)e i) ARA

,>; u)ing *i) rinile, we ave *1 u)e )mall and > a) 1))i(le. *ar*ing wi* M>M&.

-n *i) wa/, in 4i**ing *e ar1ria*e B1% @enin) *ime )erie) m1del *i) rinile and

iden*i4ia*i1n 14 1*en*ial m1del will ave (een u)ed.

Te in*erre*a*i1n (a)ed 1n *e 1u*u* 14 *e *ime )erie) m1del 1)en will (e nee))ar/ *1

e *e ade>ua*ene)) 14 *e m1del.

=1ndi*i1n 14 *e ade>ua*e m1del

Te re)idual) ave n1 a**ern) eed (/ l1**ing re)idual) again)* *ime



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Rwanda

Charles NI!"I#ANA

Te re)idual) are n1* 1rrela*ed eed (/ e%amining A=$ and PA=$ 14 *e re)idual)

2././. +orecastin3 f4t4re val4e of monthly avera3e trac accident

occ4rrence in Rwanda

A4*er )ele*ing and 4i**ing *e ade>ua*e B1% @enin) *ime )erie) m1del, *e )e1nd )ei4i

1(6e*ive will (e 4ul4illed (/ 41rea)*ing *e 4u*ure value) u)ing *e availa(le *ime )erie) da*a.

Ti) will (e d1ne (a)ed 1n 4inding *e m1del. ine *e 1(*ained m1del i) in *e 4un*i1n 14

lag value) *1 41rea)*, we will 1nl/ )u()*i*u*e *e 1rre)1nding lag value) in *e m1del *1 ge*

*e 4u*ure value) 14 m1n*l/ average aiden* 1urrene in Rwanda.

2./.5. Compare mean of monthly avera3e trac accidents occ4rrence in

Rwanda

T1 4ill *e la)* )ei4i 1(6e*ive, *e )*a*i)*ial me*1d alled 1ne wa/ anal/)i) 14 variane

AA; will (e u)ed. Te me*1d 14 1ne wa/ anal/)i) 14 variane i) u)ed *1 1mare *e

re)1n)e *1 a num(er 14 level) 14 4a*1r. -n *i) re1r* 1ne wa/ AA i) *e ar1ria*e

wen *ere i) 1nl/ 1ne 4a*1r wi i) *ime wi* di44eren* level) wi are /earl/ and

m1n*l/. 'e will 1mare *e re)1n)e varia(le wi i) m1n*l/ ar *ra44i aiden*)

1urrene in Rwanda *1 a num(er 14 di44eren* /ear) and m1n*). Te da*a will (e gr1ued

4ir)*l/ in*1 di44eren* gr1u) wi* a num(er 14 varia(le) 41r ea. T1 al/ *i) *e)*, *e mean

)um 14 )>uare) 41r *e ar *ra44i aiden*) 1urrene and 41r *e err1r )1uld (e de4ined.

Te mean )um 14 )>uare) 41r *e ar *ra44i aiden*) A will (e given (/:

Ti) i) e))en*iall/, 6u)* *e variane 14 *e di44erene (e*ween *e mean 14 ea 4a*1r level,

and *e 1verall mean. 'ere we a))ume *a* we ave /earl/ gr1u) wi* n ia)e) in *e i*

/earl/ gr1u, and *e mean 14 *e i* gr1u i)Xi wile *e 1verall mean i)

X and

A: ean )um 14 )>uare).

Te mean )um 14 )>uare) 41r *e err1r will (e de4ined a) 41ll1w):



23/59



Rwanda

Charles NI!"I#ANA

'ere i2 i) *e )amle variane 41r *e i*/earl/ gr1u

Cere *e ull /1*e)i) *1 (e *e)*ed i) *a*, *ere i) n1 di44erene (e*ween *e /earl/ gr1u).

Te Al*erna*ive /1*e)i) i) *a* *ere i) a di44erene. 1*e *a* *e al*erna*ive /1*e)i), in

*e )i*ua*i1n 14 1maring )everal level) 14 ar *ra44i aiden* 1urrene i) alwa/) a *w1

)ided al*erna*ive, a) i* d1e) n1* mae )en)e *1 *r/ *1 )ei4/ in advane were *e di44erene)

lie.

Te ra*i1 14 *e a(1ve *w1 mean )um 14 )>uare) a) an $ di)*ri(u*i1n *a* i) A" a) $

di)*ri(u*i1n; wi* *e *w1 degree) 14 4reed1m a))1ia*ed wi* Awi i) ?& and 41r

wi i) ?K. Cere *e ull /1*e)i) i) re6e*ed i4 *e ?value i) )maller *an *e )ei4ied

)igni4iane level 1r i4 *e *e)* )*a*i)*i $ i) larger *an *e ri*ial value; i.e *ere i)

di44erene am1ng *rue mean 1n /earl/ ar *ra44i aiden* 1urrene in Rwanda.

Ta6le #( The 2eneral one 7ay ANO/A ta6le is as .ollo7s(

1ure 14

varia*i1n

um 14

)>uare)

d.4 ean >uare $?Ra*i1 ig. level

Be*ween

Eear) and

1n*

A K?& A "d.4 A"

'i*in Eear)

and 1n* ?K "d.4

T1*al T ?&

Ta6le #( The 2eneral one 7ay ANO/A ta6le



24/59



Rwanda

Charles NI!"I#ANA

C,APT!R 50 R!SU%T AN$ ANA%"SIS

-n *i) a*er, we ave all rela*ed re)ul*) *1 *e ar *ra44i aiden*) 1urrene in Rwanda in

*e 41rm 14 Ta(le) and $igure) wi r1m* u) *1 n1w and anal/Je *e ar1ria*e *ime

)erie) m1del 14 ar *ra44i aiden*) 1urrene in Rwanda. T1)e re)ul*) al)1 r1vide 1w

*e m1del 4i**ed *e da*a wi i) el4ul in 41rea)*ing )*age and *e re)ul* 14 1maring *e

*rue mean am1ng *e mean) 14 ar *ra44i aiden*) (/ /ear and 1n*.

/1 CAR TRA((IC ACCIDENT&

Cere are *e *a(le) wi rere)en* m1n*l/ and /earl/ ar *ra44i aiden*) 1urrene in

Rwanda 4r1m 20&0 *1 20&.

Ta6le !( Nu*6er o. car tra..ic accidents 6y year and Month

1n* um(er 14 aiden* (/ Eear)

T1*al$ean

20&0 20&& 20&2 20&3 20&

@anuar/ 35 &0 37 59 7!2&3!

/.9.

$e(ruar/ 3#& 3#9 39! 7! ##2&30

/.7

ar 37# && 39# 53& 90220#

//17

Aril 0 372 379 350 7320&

/-.ua*ene)) 14 *e m1del wa) eed (e41re 41rea)*ing )ine 41rea)*ing an* (e made

wi*1u* eing i4 *e m1del 4i**ed i) g11d 1r n1*. Predi*i1n 14 4u*ure value) i) made *1 a

m1del wi 4i)* g11d *e da*a and *e g11dne)) 14 4i**ed m1del were )1wed u)ing A=$ and

Ci)*1gram )uer im1)ed (/ n1rmal urve 14 *e err1r *erm). T1 e i4 *e 4i**ed value) are

l1)e *1 *e 1riginal da*a, mul*ile *ime l1*) ware l1**ed (el1w:

ul*ile *ime l1*) (el1w )1w) 4i**ed value) and m1n*l/ ar *ra44i aiden*)



41/59

$ate

OCT.-1/

>*L.-1/

APR.-1/

>AN.-1/

OCT.-10

>*L.-10

APR.-10

>AN.-10

OCT.-1.

>*L.-1.

APR.-1.

>AN.-1.

OCT.-11

>*L.-11

APR.-11

>AN.-11

OCT.-1-

>*L.-1-

APR.-1-

>AN.-1-

7--

4--

/--

0--

(orecasted

$ont5l6 car trac Accidents



Rwanda

Charles NI!"I#ANA

Fi2ure #!( Ori2inal and .orecasted .or *onthly car tra..ic accidents

$r1m *e a(1ve *ime l1* 4igure&2, 1riginal da*a and 41rea)*ed value) m1ve *1ge*er wi

imlie) *a* *e 4i**ed value) ma* *e 1()erved value) l1)el/. Ti) )1w) *a* *e m1del

4i**ed i) g11d.



42/59

!rror from #onthly car tracAccidents9#odel:-

-.4--.4-4-94

.-

14

1-

4

-

N B4=



Rwanda

Charles NI!"I#ANA

Ci)*1gram 14 41rea)*) err1r 41r m1n*l/ ar *ra44i aiden*) 1urrene in Rwanda.

$igure &3: Ci)*1gram 14 41rea)* err1r 41r m1n*l/ ar *ra44i aiden*)

$igure &: Ci)*1gram 14 41rea)* err1r 41r m1n*l/ ar *ra44i aiden*)

Te Ci)*1gram a(1ve )uer im1)ed (/ n1rmal urve 1n m1n*l/ da*a india*e) *a* *e

urve i) ar1%ima*el/ n1rmall/ di)*ri(u*ed wi* mean Jer1 and *e )*andard devia*i1n 14

0.&37.

Te A=$ 14 41rea)* err1r 41r m1n*l/ ar *ra44i aiden*).


134S,$& De7& 80&

Me(! 80


43/59

Lower

Con3dence Limit

*pper

Con3dence Limit

Coecient

!rror from #onthly car trac accidents



Rwanda

Charles NI!"I#ANA



44/59

17141/101.111-=


45/59

$ate

$AR.-1=

$A).-1*L.-19

&EP.-17

NO;.-14

>AN.-14

$AR.-1/

$A).-10

>*L.-1.

&EP.-11

NO;.-1-

>AN.-1-

1@4--

[email protected]

1@---

94-

4--

.4-

*CL fromAccidents$odel1

LCL fromAccidents$odel1

(orecasted

$ont5l6 cartrac accidents



Rwanda

Charles NI!"I#ANA

Fi2ure #%( Ti*e plot o. ori2inal: Forecast: ;pper and


46/59



Rwanda

Charles NI!"I#ANA

ul*ile *ime )erie) l1* )1w) *a* *e 4i**ed value) and *e 1riginal da*a m1ve and l1)e

*1ge*er wi de)ri(e *e ade>ua*e m1del. 'e r1eed *1 41rea)* in 4ive /ear) *e num(er

14 m1n*l/ ar *ra44i aiden*) e)eiall/ in eem(er )ine *e m1del are ae*ed.

1n*l/ ar *ra44i aiden*) in ne%* 5/ear) e)eiall/ in eem(er will (e #27 and *eir

1rre)1nding redi*i1n in*erval i) 3#3, &575;.

Ta6le &( Ta6le o. .orecasted Car tra..ic accidents 6y Year and Month

1n*l/$1rea)*e

d

$1rea)*ed in /ear)20&5 20&! 20&7 20 20&9

@anuar/ 5# 59! !# 70 7!!

$e(ruar/ 552 !00 !52 709 77&

ar 55! !0 !57 7& 777

Aril 5!0 !0# !!2 7&9 7#2

a/ 5! !&3 !!! 72 7#7

@une 5!7 !&7 !7& 729 793

@ul/ 57& !2& !75 73 79#Augu)* 575 !2! !#0 70 #0

e*em(er 579 !30 !#5 75 #&0

*1(er 5# !3 !90 750 #&5

1vem(er 5## !39 !95 755 #2&

eem(er 592 !3 !99 7!0 #27

=1mared *1 *e 4ive /ear) ag1, =ar *ra44i aiden*) will inrea)e 1ver *e ne%* 4ive /ear).



47/59



Rwanda

Charles NI!"I#ANA

5.2. CPAR! #!AN &+ #&NT,%" CAR TRA++IC ACCI$!NTS &CURR!NC!

IN R(AN$A.

T1 4ul4il *e )ei4i 1(6e*ive wi i) *1 1mare *e *rue mean 14 ar *ra44i aiden*)

1urrene in Rwanda ,*e *eni>ue 14 1ne wa/ anal/)i) 14 variane ne wa/ AA;

wa) u)ed *r1ug /ear 20&0 *1 20&.

Time wa) iden*i4ied a) *e indeenden* varia(le wi i) a )ingle 4a*1r wi* 4ive gr1u)

/earl/; and wi* *welve gr1u) m1n*l/; and *e deenden* varia(le wa) 41und *1 (e

m1n*l/ ar *ra44i aiden*) 1urrene in Rwanda. ne wa/ AA wa) u)ed )ine we are

dealing wi* 1ne 4a*1r wi* di44eren* gr1u. Te mean )um 14 )>uare) 41r 4a*1r A i) given

(/ *e 41ll1wing 41rmula:

Ti) i) *e variane 14 *e di44erene (e*ween *e mean 14 ea 4a*1r level, and *e

1verall mean. 'e a))ume *a* we ave gr1u) wi*ni( i=1,2, ,5 ) a)e) in *e i*gr1u,

and *e mean 14 *e i*gr1u i) Xi , wile *e 1verall mean i)

X in 1mari)1n 14

m1n*l/ ar *ra44i aiden*) 1urrene in Rwanda. Te mean )um 14 )>uare) 41r *e err1r

i) de4ined a) 41ll1w):

'ere i2 i) *e )amle variane 41r *e i*/earl/ gr1u)

Te ra*i1 14 *e a(1ve *w1 mean )um 14 )>uare) a) an $ di)*ri(u*i1n *a* i) A" a) $

di)*ri(u*i1n; wi* *e *w1 degree) 14 4reed1m a))1ia*ed wi* Awi i) ?& and 41r

wi i) ?K, were i) *e 1verall 1()erva*i1n) grand *1*al;. Cere *e ull /1*e)i) i)



48/59



Rwanda

Charles NI!"I#ANA

re6e*ed i4 *e ?value i) )maller *an *e )ei4ied )igni4iane level 1r i4 *e *e)* )*a*i)*i $

i) larger *an *e ri*ial value; i.e *ere i) di44erene am1ng *rue mean 1n /earl/ ar *ra44i

aiden* 1urrene in Rwanda.

5.2.-. CPAR! #!AN &+ "!AR%" CAR TRA++IC ACCI$!NTS &CURR!NC!

IN R(AN$A.

$r1m *a(le 21n*l/ ar *ra44i aiden*); *ere i) /1*e)i) *1 (e *e)*ed. Ti) /1*e)i)

mu)* (e *e)*ed u)ing 1ne wa/ AA )ine *ere i) 1nl/ 1ne 4a*1r wi* di44eren* level).

T1)e /1*e)e) are *e 41ll1wing:

H0:

2010=

2011=

2012=

2013=

2014 Tere i) n1 di44erene am1ng *e *rue mean 1n /earl/

ar *ra44i aiden*);

H0:

2010

2011

2012

2013

2014 Tere i) di44erene am1ng *e *rue mean 1n /earl/ ar

*ra44i aiden*);

'ere

2010 ,

2011 ,

2012 ,

2013 ,

2014 rere)en* *e 1ula*i1n mean 14 /earl/ ar

*ra44i aiden*). Te re)ul* 14 1ne wa/ AA anal/)i) eled in maing 1nlu)i1n. uare) d.4

ean

>uare $ ig.

Be*ween /ear) &599!.000 39#7.000 &&.2!5 .000'i*in /ear) &9!#3.250 55 3539.!95

T1*al 35&79.250 59 Ta6le -( One 7ay ANO/A ta6le o. yearly car tra..ic accidents



49/59



Rwanda

Charles NI!"I#ANA

Te re)ul* a(1ve all1w) u) *1 *e)* we*er *ere i) a )igni4ian* di44erene in 1ula*i1n

mean 14 m1n*l/ ar *ra44i aiden*) 1r n1*. Te ?value )ig.; in *e 1u*u* wi i) 0.000 i)

)maller *an level 14 )igni4iane wi i) 5. Tere41re, *i) )ugge)*) re6e*ing *e null

/1*e)i) C0;. -n re6e*ing *e null /1*e)i) i* mean) *a* *ere i) )igni4ian* di44erene

in /earl/ ar *ra44i aiden*). B/ 1maring *e value 14 $?alula*ed wi i) &&.2!5 and

*e value 14 $ 4r1m *e *a(le wi* degree 14 4reed1m ?&, ?K; M,55; wi i) 2.5 we

1(*ain *a* $?alula*ed $?*a(ula*ed, *ere41re, we re6e* C0 wi i) *e )ame 1nlu)i1na) *a* 1(*ained u)ing P?value *a* *ere i) )igni4ian* di44erene in /earl/ ar *ra44i

aiden*);.

/011 $*LTIPLE CO$PARI&ON&

Sine *ere i) di44erene am1ng *e *rue mean 1n /earl/ ar *ra44i aiden*) 1urrene in

Rwanda, generall/, we w1uld lie *1 n1w wi mean) are )igni4ian*l/ di44eren*. Ti) wa)

d1ne (/ 1maring all air wi)e) (e*ween air) 14 *e /ear. 'e de*ermine we*er 1r n1* Jer1

i) inluded in *e 1n4idene in*erval). Tue/) me*1d wa) u)ed 41r all air wi)e

1mari)1n) )ine i* i) 1mm1nl/ u)ed r1edure wi i) m1re 1wer4ul *an B1n4err1ni

me*1d. Te general 41rm, all1wing 41r di44eren* )amle )iJe) 41r *rea*men* i and 6 i):

, ,9 ; 9&" &" ; " 2i j k n k i jY Y q MSE n n +

'ereq , k , nk i) *e )*uden*iJed range 4r1m *e *a(le

Te di44erene am1ng *e mean) 14 ar *ra44i aiden*) i) )1wn in *e 41ll1wing:



50/59



Rwanda

Charles NI!"I#ANA

Ta(le9.Eearl/ 1mari)1n 14 ar *ra44i aiden*) 1urrene in Rwanda

EARDE

=PAR-

-$$R=

A

P?

AD


51/59



Rwanda

Charles NI!"I#ANA

A1rding *1 *e a(1ve *a(le, a* 95 1n4idene in*erval

2010

=2011

=2012


52/59



Rwanda

Charles NI!"I#ANA

Ta6le 8)One 7ay ANO/A ta6le o. *onthly car tra..ic accidents

ANO/A

1ure 14

varia*i1n um 14 >uare) d.4 ean >uare $ ig.

Be*ween

1n*253&!.&33 && 230&.!7 .33! .973

'i*in 1n* 329&57.!00 # !#57.50

T1*al 3573.733 59

Ta6le 4( One 7ay ANO/A ta6le o. *onthly car tra..ic accidents

Te re)ul* a(1ve, *e ?value )ig; i) .973 wi i) grea*er *an level 14 )igni4iane 14

5.Tere41reF *i) mean) *e ae*ane 14 *e null /1*e)i) n1 )igni4ian* di44erene in

1ula*i1n mean 14 m1n*l/ ar *ra44i aiden*) (/ m1n*. -n ae*ing *e null /1*e)i) i*

mean) *a* *ere i) n1 )igni4iane di44erene in m1n*l/ ar *ra44i aiden*). B/ 1maring

*e value 14 $?alula*ed wi i) 0.335 and *e value 14 $ 4r1m *e *a(le wi* degree 14

4reed1m ?&, ?K; M&&,#; wi i) .... we 1(*ain *a* $?alula*ed Q $?*a(ula*ed, *ere41re,

we ae* C0wi i) *e )ame 1nlu)i1n a) *a* 1(*ained u)ing P?value *a* *ere i) n1

)igni4ian* di44erene in mean 14 m1n*l/ ar *ra44i aiden*)

C,APT!R ;0 $ISCUSSI&N< C&NC%USI&N AN$

R!C#AN$ATI&N

41 DI&C*&&ION

Ti) )e*i1n di)u))ed *e main re)ul*) 1(*ained in revi1u) a*er and 1mare) *1)e

re)ul*) wi* re)ul*) 1(*ained (/ 1*er) w1rldwide. Te da*a anal/Jed are m1n*l/ ar *ra44i

aiden*) 1urrene in Rwanda. uring *e anal/)i), *e ar1ria*e (1% @enin) *ime )erie)

m1del wa) 41und *1 (e AR-A 0,&,&;.


53/59



Rwanda

Charles NI!"I#ANA

1n*l/ =ar *ra44i aiden*) in *e ne%* 5/ear) e)eiall/ in eem(er 20&9 will (e #27 and

wa) 41und u)ing 4i**ed m1del. Te /earl/ 1mari)1n 14 ar *ra44i aiden* 1urrene in

Rwanda u)ing 1ne wa/ an1va )1wed a )igni4ian* di44erene am1ng *e mean) 14 /earl/ ar

*ra44i aiden*) in Rwanda and u)ing Tue/) me*1d 41r all air wi)e 1mari)1n) were

41und *a* *e 1ula*i1n mean

2014 a) )igni4ian*l/ *e ige)* /earl/ ar *ra44i

aiden*).

-n 1mari)1n wi* 1*er rela*ed )*ud/, *e re)ul* )1wed *a* generall/ AR-A *ime )erie)

m1del a) (een 41und *1 (e ar1ria*e *ime )erie) m1del 1n *e ar *ra44i aiden*) and *e

redi*ed re)ul*) 4r1m AR-A m1del w1rldwide revealed *a* ar *ra44i aiden* a)e) were

g1ing *1 inrea)e 1ver *e ne%* )i% /ear 4r1m AR-A 0,&,&; in Rwanda, &07,579 *1 0&,53!

1ver *e ne%* 1ne /ear in =inaG&9H and al)1 in 8ana, AR-A 0,2,&; wa) iden*i4ied wi*

eviden* a) *e (e)* m1del. A )i%? /ear 41rea)* wa) made u)ing *e AR-A 0, 2, &; m1del

and i* )1wed *a* ar *ra44i aiden* a)e) w1uld 1n*inue *1 inrea)e. GH

4. CONCL*&ION

Time )erie) Anal/)i) 14 *e ar *ra44i aiden*) da*a 4r1m @anuar/ 20&0 *1 eem(er 20&

)1wed *a* *e a**ern) 14 ar *ra44i aiden*) are inrea)ing in Rwanda. AR-A 0,&,&; i)

iden*i4ied *1 (e ar1%ima*el/ *e )ui*a(le m1del 41r ar *ra44i da*a. Predi*i1n 4r1m AR-A

0, &, &; m1del revealed *a* ar *ra44i aiden*) will 1n*inue *1 inrea)e 1ver *e ne%* 4ive

/ear). Te 4inding) 14 *i) )*ud/ draw a**en*i1n *1 *e im1r*ane 14 imlemen*ing e/ r1ad

)a4e*/ mea)ure) in 1rder *1 ange *e inrea)ing a**ern) 14 ar *ra44i aiden*) in Rwanda.Tere41re *e imr1ved and (e**er 1liie) 14 a*i1nal r1ad )a4e*/ 1mmi))i1n )1uld (e

in*r1dued wi* mu ema)i) 1n u(lia*i1n and edua*i1n *1 en)ure ma%imum redu*i1n

in =ar *ra44i aiden*).



54/59



Rwanda

Charles NI!"I#ANA

40 RECO$$ANDATION

eending 1n re)ul* 1(*ained, *i) )*ud/ iglig*) re1mmenda*i1n) wi inlude *e

advie) *1 Rwanda a*i1nal P1lie RP;.

T1 minimiJe *e 1urrene 14 *e ar *ra44i aiden*), *e 41ll1wing mea)ure) w1uld (e

*aen a) re1mmenda*i1n):

T1 edua*e *e u(li r1ad u)er e)eiall/ *e driver) and ede)*rian) 1n 1w *1 a(ide

(/ *e l1w in 1rder *1 redue *ra44i aiden*). T1 imlemen* and imr1ve r1ad )a4e*/ amaign

en)i*iJe *e r1ad u)er) *1 u)e 1rre*l/ *e e)*a(li)ed u(li aring /ard and

inrea)e in num(er 14 u(li aring /ard 41ll1wing a 1mlain* (/ *a%i 1era*1r)

*a* *e /ard) availa(le are in)u44iien*



55/59



Rwanda

Charles NI!"I#ANA

T1 en41re *e rule) and l1w) *1 en)ure )euri*/ and a))1ia*i1n 14 *e *ran)1r*er)

)1uld ar*iia*e *1 41rmaliJe enal*ie) *1 mem(er) w1 vi1la*e *ra44i rule) and

regula*i1n a) a wa/ 14 enaning r1ad )euri*/ Regular in)e*i1n 14 veile) (/ -= 1*1r veile in)e*i1n en*er; and

*enial 1n*r1l er*i4ia*e i))ued a4*er *e in)e*i1n Te maring 14 divider) and )eed (reaer mu)* (e d1ne. -mmedia*e *1 rem1ve all *e

aged and damaged veile) 144 4r1m *e r1ad will de4ini*el/ (e a wel1ming )*e. 81vernmen* and 8) )1uld rea*e u(li awarene)) *1 reven* r1ad *ra44i

aiden* (/ 1rganiJing )eminar), r1ad drama e*

REFERENCES

&. Te %41rd Advane Dearner) i*i1nar/ &9#9;

2. Peden , ur4ield R, lee* , 1an , C/der AA, @arawan d).; 200. '1rld

re1r* 1n r1ad *ra44i in6ur/ reven*i1n. 8eneva: '1rld Ceal* rganiJa*i1n.

3. =a*er , 'aler P d).; &99#. '1rld i)a)*er) Re1r*. %41rd


56/59



Rwanda

Charles NI!"I#ANA

5. '1rld Ceal* rganiJa*i1n &9#. R1ad *ra44i aiden*) in devel1ing 1un*rie).

Tenial Re1r* erie) 1. 73. 8eneva.

!. lee* A, Brane = 200. R1ad )a4e*/: A new u(li eal* ri1ri*/. a4e*/ iene

1ni*1r, &: &?3.

7. S-RTA a*a(a)e, 1vem(er 2009 ? Ri) -ndia*1r)S. = -n*erna*i1nal Tra44i a4e*/

a*a and Anal/)i) gr1u -RTA;.

G**:""www.in*erna*i1nal*ran)1r*41rum.1rg"ir*ad"d4"ri).d4.

#. **:""www.6aan*1da/.1m"a*eg1r/"na*i1nal"view"*ra44i?aiden*?dea*)?i*?57?/earl1w?

(el1w?5000?in?2009

9. **:""www.d4*.g1v.u"gr")*a*i)*i)"da*a*a(le)u(lia*i1n)"aiden*)"a)ual*ie)mr"

rrg(mainre)ul*)2009

&0. an*ul/a , Rei R 2002. Te negle*ed eidemi: r1ad *ra44i in6urie) in

devel1ing 1un*rie). B@, 32: &&39?&&&.

&&.ew *ime), *andard @1urnal,1l.&,um(er &0

&2. '1rld Ceal* rganiJa*i1n gl1(al )*a*u) re1r* 1n r1ad )a4e*/ 20&3

&3. 'C?Rwanda (urden 14 di)ea)e 20&0 re1r*

&. P1lie magaJine n1 005.

&5. 1lv1 Tru), ur1ean Aiden* Re)ear and a4e*/ Re1r* 20&31

&!:East and Central African Journal of Surgery, Vol. 1, No. 1, Marc!"A#ril $%%&, ##. '"

'( ,. Twagira/eJu, R. Te*eli, A. B1nane, . RugwiJang1ga, Kigali


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&7. -n6ur/ =1n*r1l and a4e*/ Pr1m1*i1n 2003;, 1l.&0, 1.&?2, 53?!&H

.Avugla R., Adu?P1u K.A, Carri) 20&;. Te alia*i1n 14 AR-A m1del) *1 r1ad

*ra44i aiden* a)e in 8anaH.

&9. Euan?Euan Pa e* al., 20&3;

Euan, E.P., u? @un, U., Ui?(in, T., eng?6ing, =., and Eue, 8. 20&3;. NAu*1regre))ive

-n*egra*ed 1ving Average 1del in redi*ing r1ad *ra44i in6ur/ in =inaO. U1ngua Diu

ing Bing ue Ua Ui 20&3 @ulF 37;:73!?9.

20. R1a/u arani e* al., 20&2;. R1a/u, ., ari4a All/ana, ..R., @amila, .., and

'1ng, .. 20&2;. Predi*ing ala/)ian r1ad 4a*ali*ie) 41r /ear 2020. Kuala Dumur:

ala/)ian -n)*i*u*e 14 R1ad a4e*/ Re)ear 2020, RR!;20&2

2&.@1urnal 14 A)ian ien*i4i Re)ear, 20&3, 3;:25?30



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charles final year student report

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