REGRE SI LINEA R IN TRIN S IK M AKALA Hrepository.usd.ac.id/478/2/083114005_full.pdf · REGRE SI LINEA R IN TRIN SIK M AKALA H Dia j uk an Untu k Memenu hi Salah Satu Sy arat Mempe

KISNIRTNI RAENIL ISERGER

HALAKAM

tarayS utaS halaS ihunemeM kutnU nakujaiD akitametaM anajraS raleG helorepmeM

akitametaM idutS margorP

:helO

OKOMTAOWRUP YREH SUNAIROLF

0 :MIN 8 004113 5

AKITAMETAM NASURUJ AKITAMETAM IDUTS MARGORP

NAD SNIAS SATLUKAF IGOLONKET

AMRAHD ATANAS SATISREVINU

ATRAKAYGOY

5102

PLAGIAT MERUPAKAN TINDAKAN TIDAK TERPUJIPLAGIAT MERUPAKAN TINDAKAN TIDAK TERPUJI

i

KISNIRTNI RAENIL ISERGER

HALAKAM

tarayS utaS halaS ihunemeM kutnU nakujaiD akitametaM anajraS raleG helorepmeM

akitametaM idutS margorP

:helO


0 :MIN 8 004113 5

AKITAMETAM NASURUJ AKITAMETAM IDUTS MARGORP

NAD SNIAS SATLUKAF IGOLONKET

AMRAHD ATANAS SATISREVINU

ATRAKAYGOY

5102


ii

NOISSERGER RAENIL YLLACISNIRTNI

A REPAP

stnemeriuqeR eht fo tnemllifluF laitraP sA detneserP margorP ydutS scitamehtaM fo rolehcaB eht niatbO oT

: yb nettirW


tnedutS 0 :DI 8 004113 5

MEHTAM MARGORP YDUTS SCITA SCITAMEHTAM TNEMETRAPED

YGOLONHCET DNA ECNEICS FO YTLUCAF

YTISREVINU AMRAHD ATANAS

ATRAKAYGOY

5102


iii


vi


v

NASILUT NAILSAEK NAATAYNREP

ayaS nakataynem nagned aynhuggnuses awhab ayas gnay halakam silut ini kadit

taumem ayrak uata naigab halet gnay ilaucek ,nial gnaro ayrak naktubesid malad

napituk nad ratfad anamiagabes ,akatsup aynkayal ayrak .haimli

,atrakaygoY 5102 sutsugA 5

siluneP

sunairolF yreH okomtaowruP


iv

NAHABMESREP NAMALAH

ayraK ini silunep nakhabmesrep : adapek

nahuT suseY nad sata airaM adnuB hisak nad tamhar - .hapmilem gnay ayN

audeK ,autgnaro iwD edaM I kapaB otnaW nad ubI tuteK kida ,itnaduS ,pesoYpaneges agraulek atres tahabas - tabahas .aynaumes

hisakamireT sata aumes .aynnagnukud


iiv

NAUJUTESREP NAATAYNREP RABMEL

SIMEDAKA NAGNITNEPEK KUTNU HAIMLI AYRAK ISAKILBUP

nagnatadnatreb gnay ayaS id hawab :ini

amaN sunairolF : yreH okomtaowruP

MIN 500422380 :

nagnabmegnep imeD umli ayas ,nauhategnep nakirebmem adapek naakatsuprep

inU satisrev ayrak amrahD atanaS haimli :ludujreb gnay ayas

KISNIRTNI ISERGER SISILANA

nagneD naikimed ayas kirebmem an adapek naakatsuprep satisrevinU atanaS

kah amrahD kutnu nakhilagnem ,napmiynem malad alolegnem ,nial aidem kutneb

malad kutneb nalakgnap aynnakisubirtsidnem ,atad araces nad ,satabret

kutnu nial aidem uata tenretni id aynnakisakilbupmem nagnitnepek simedaka

apnat ulrep atnimem niji irad ayas nupuam ytlayor adapek ayas amales patet

nakmutnacnem aman ayas iagabes .silunep

naaikimeD ataynrep na ini ayas taub nagned ,aynranebes

.atrakaygoY id taubiD

adaP laggnat : 5102 sutsugA 5

nakataynem gnaY



iiiv

KARTSBA

enil iserger ledoM a tukireb iagabes silutid tapad mumu araces tubesret r 𝑦𝑖 = 𝛽0 + 𝛽1𝑥1𝑖 + 𝛽2𝑥2𝑖 + … + 𝛽𝑘𝑥𝑘𝑖 + 𝜀𝑖

agudneP na om M nagned nakukalid tapad led e T tardauK edot halasaM .licekre ledom nad kisnirtni raenil ledom halada ipadahid gnay ledom akitek lucnum naka

.raenilnon tapad gnay raenilnon iserger ledom utaus halada kisnirtnI raeniL ledoM .nelavike gnay raenil iserger ledom idajnem nakisamrofsnartid ,uti anerak helO

licekreT tardauK edoteM N .nakanugid gnusgnal tapad kadit ledom anerak ,numa ledom nakgnades ,raenil ledom idajnem nakisamrofsnartid tapad kisnirtni raenil

tapad kadit raenilnon kisnirtni raenil ledom naagudnep akam ,nakisamrofnartid.asaib raenil ledom anamiagabes licekret tardauk edotem nakanuggnem tapad

aynraseb tahilem nagned halada kiabret raenil ledom hilimem malad airetirK𝑅2 p gnay rorre radnats ,iggnit gnilap gnay neisifeok irad isnakifingis ,hadner gnila

ismusa nahunemep nad iserger - .ismusa

tardauK edoteM ,kisnirtnI raeniL ,raenilnoN isergeR ,raeniL isergeR :icnuk ataK.licekreT


xi

TCARTSBA

sa nettirw eb nac ledom noisserger raenil ,yllareneG

𝑦𝑖 = 𝛽0 + 𝛽1𝑥1𝑖 + 𝛽2𝑥2𝑖 + … + 𝛽𝑘𝑥𝑘𝑖 + 𝜀𝑖 m eht fo noitamitse ehT melborP .dohteM serauqS tsaeL gnisu yb enod eb nac ledo

cisnirtnI .ledom raenilnon dna ledom raenil cisnirtni gnicaf nehw raeppa lliw hcihw ledom noisserger raenilnon a si ledom raenil otni demrofsnart eb nac

dohtem serauqs tsael eht ,taht fo esuaceB .ledom noisserger raenil tnelaviuqe nacI .yltcerid desu eb ton ,ledom raenil otni demrofsnart eb nac ledom raenil cisnirtn

m raenil cisnirtni os ,demrofsnart eb ton nac ledom raenilnon elihw noitamitse ledo.ledom raenil nommoc sa llew sa ,dohteM serauqS tsaeL eht esu nac

tsehgih eht gniees yb si ledom raenil tseb eht esoohc ot airetirc ehT 𝑅2 eht ,tsewol rorre radnats dna ,tneiciffeoc noisserger fo noitacifingis eht , tnemllifluf eht

fo eht snoitpmussa .ledom eht fo

tsaeL ,raeniL cisnirtnI ,noissergeR raenilnoN ,noissergeR raeniL :sdrow yeK.dohteM serauqS


x

RATNAGNEP ATAK

rukuyS adapeK ahaM gnaY nahuT asE sata alages atnic nad hisak - gnay ayN

hapmilreb aggnihes silunep tapad nakiaseleynem halakam ini kutnu ihunemem

sagut rihka malad hupmenem raleg amrahD atanaSsatisrevinU id )1S( anajraS

.atrakaygoY

amaleS nasilunep halakam silunep ,ini iradaynem kaynab halet gnay kahip

narepreb raseb malad nakirebmem b ,nagnukud nagnibmi nad helO .aynnautnab

silunep ,utianerak nakpacugnem rasebes gnay hisakamiret - aynraseb : adapek

.1 I .rI kapaB halakam gnibmibmep nesod ukales ,.cS.M ,okomtaiwD sirA .g

nasilunep amales silunep ignipmadnem nad gnibmibmem halet gnay

.ini halakam

.2 .H.P cS.M ,.iS.S ,asoR amirP , igolonkeT nad sniaS satlukaF nakeD ukales

.atrakaygoY amrahD atanaS satisrevinU

.3 akitametaM idutS margorP auteK ukales,.D.hP ,.cS.M ,onotraH .G.Y

.atrakaygoY amrahD atanaS satisrevinU

.4 .iS.M ,itawareH ynA .VM nay ijugnep nesod ukales kaynab halet g

.nakusam nakirebmem

.5 .isartsinimda sesorp utnabmem halet gnay ajikuT .Z kapaB

.6 satilisaf nad nahab nakaideynem utnabmem halet gnay DSU naakatsupreP

.halakam nasilunep amales


ix

.7 d satilisaf nakaideynem utnabmem halet gnay narobal ukales olisuS saM i

.muirotarobal

.8 ,silunep aut gnaro ukales ,itnaduS tuteK ubI nad otnaW iwD edaM I kapaB

nautnab nad ,aod ,nagnukud aumes sata agraulek aumes nad ,pesoY kida

.silunep igab

.9 aites nad rabas nagned gnay alyehsraM anailuY takedret nameT

aod ,tagnames nakirebmem malad silunep igab naitahrep nad

.ini halakam nakiaseleynem

.01 nameT - ulales gnay aynnial gnay nad ,kowoW ,oehT ,sutE ,omtA namet

ini halakam nasilunep malad nautnab nad nagnukud nakirebmem

.11 nameT - .amasreb gnaujreb halet gnay akitametaM idorP id namet

.21 ip aumeS .ini halakam asilunep malad utnabmem halet gnay kah

siluneP iradaynem hisam aynada nagnarukek - nagnarukek malad ayrak silut .ini

kitirK naanrupmesek imed nugnabmem gnay naras nad halakam ini nakapurem

natamrohek igab .silunep

,atrakaygoY

siluneP



iix

ISI RATFAD

namalaH

LUDUJ NAMALAH ................................ ................................ .................... i

NAUJUTESREP NAMALAH ................................ ................................ ..... ii i

NAHASEGNEP NAMALAH ................................ ................................ ...... iv

NAMALAH NAATAYNREP NAILSAEK NASILUT ............................... v

NAHABMESREP NAMALAH ................................ ................................ .... iv

KARTSBA ................................ ................................ ................................ .. iiv i

TCARTSBA ................................ ................................ ................................ xi

RATNAGNEP ATAK ................................ ................................ ................. x

ISI RATFAD ................................ ................................ ............................... iix

LEBAT RATFAD ................................ ................................ ....................... vx

RABMAG RATFAD ................................ ................................ .................... ivx

NAULUHADNEP I BAB ................................ ................................ ............ 1

.A halasaM gnakaleB rataL ................................ ................................ ... 1

.B halasaM nasumureP ................................ ................................ .......... 2

.C halasaM nasatabmeP ................................ ................................ ........ 2

.D nasiluneP naujuT ................................ ................................ .............. 2


iiix

.E nasiluneP taafnaM ................................ ................................ ............ 3

.F nasiluneP edoteM ................................ ................................ ............. 3

.G nasiluneP akitametsiS ................................ ................................ ....... 3

IROET NASADNAL II BAB ................................ ................................ ...... 5

.A raeniL isergeR ledoM ................................ ................................ ........ 5

.B edoteM tardauK licekreT ................................ ................................ ... 6

.C tafiS naagudneP tardauK licekreT nad agudneP irad 𝜎2 ..................... 01

.D ijU sisetopiH d mala isergeR adnagreB ................................ .............. 21

)a ijU isnakifingiS isergeR ................................ ......................... 31

)b neisifeoK isanimreteD (𝑹𝟐) ................................ ................... 41

)c naijugneP padahreT neisifeoK isergeR udividnI ..................... 91

)d gnaleS naayacrepeK malad isergeR adnagreB ........................ 02

)e ismusA - isergeR ledoM ismusA ................................ .............. 22

III BAB KISNIRTNI RAENIL LEDOM ................................ ....................... 53

.A aynlucnuM nasagaG kisnirtnI raeniL isergeR ................................ .... 53

)a raenilnoN isergeR ................................ ................................ .. 63

)b macaM - kisnirtnI raeniL ledoM macaM ................................ .. 93

.B pahaT - nakrasadreB ledoM nalanegnePpahaT ataD ............................ 54

V BAB I PUTUNEP ................................ ................................ ....................... 16

.A nalupmiseK ................................ ................................ ...................... 16

.B naraS ................................ ................................ ................................ 16


vix

AKATSUP RATFAD ................................ ................................ .................. 26

NARIPMAL ................................ ................................ ................................ 26


vx

LEBAT RATFAD

1.2 lebaT ................................ ................................ ................................ ....... 7

2 lebaT 2. ................................ ................................ ................................ ....... 41

3.2 lebaT ................................ ................................ ................................ ....... 92

1.3 lebaT ................................ ................................ ................................ ....... 74

2.3 lebaT ................................ ................................ ................................ ....... 05

3.3 lebaT ................................ ................................ ................................ ....... 45


ivx

RABMAG RATFAD

1.3 rabmaG ................................ ................................ ................................ ... 34

2.3 rabmaG ................................ ................................ ................................ ... 34

3.3 rabmaG ................................ ................................ ................................ ... 84

4.3 rabmaG ................................ ................................ ................................ ... 84

5.3 rabmaG ................................ ................................ ................................ ... 94

6.3 rabmaG ................................ ................................ ................................ ... 15

7.3 rabmaG ................................ ................................ ................................ ... 15

8.3 rabmaG ................................ ................................ ................................ ... 35

9.3 rabmaG ................................ ................................ ................................ ... 45

01.3 rabmaG a ................................ ................................ ............................... 65

b01.3 rabmaG ................................ ................................ ............................... 75


1

I BAB

NAULUHADNEP

halasaM gnakaleB rataL .A

notlaG sicnarF riS helo naklanekrepid ilak amatrep iserger sisilana halitsI

2281( - irad igoloroetem ilha nad goloportna gnaroes nakapurem gnay ,)1191

iserger sisilanA .sirggnI halada nad atad asilanagnem kutnu edotem utaus

lebairav aud aratna nagnubuh gnatnet ankamreb gnay nalupmisek libmagnem

lebairaV .hibel uata - ( sabeb kat lebairav halada nakduskamid gnay lebairav 𝑦 )

( sabeb lebairav nad 𝑥 .)

a sabeb lebairav nagned duskamid gnaY aynialin gnay lebairav halad

gnay uata ajagnesid gnay nahaburep tabikA .nakutnetid uata rutaid tapad

nial gnay lebairav padahret huragnepreb tapad ,sabeb lebairav adap idajret

isnegeletni lebairav aratna nagnubuh ,hotnoc iagabeS .sabeb kat lebairav utiay

(𝑥 ( rajaleb lisah lebairav nad ) 𝑦 ) nagned nakledomid tapad iserger naamasrep

apureb 𝑦 = 𝛽1 + 𝛽2𝑥 + 𝜀 mumu araceS . aynah kadit reinil iserger ledom

naksalejnem amatrep edro nagnubuh , ipatet aguj nad laimonilop ledom

aynnial skelpmok hibel gnay nagnubuh . M do tubesret reinil iserger le araces

mumu tukireb iagabes silutid tapad

𝑦𝑖 = 𝛽0 + 𝛽1𝑥1𝑖 + 𝛽2𝑥2𝑖 + … + 𝛽𝑘𝑥𝑘𝑖 + 𝜀𝑖

raenil tubesret ledom anerak raenil iserger ledom nakatakid ini itrepes ledoM

iuhatekid kadit gnay retemarap malad 𝛽𝑗 , 𝑗 = 1,2, … , 𝑘 nad 𝑖 = 1, 2, … , 𝑛 .

agudneP na nagned nakukalid tapad tubesret ledom licekreT tardauK edetoM .


2

raenil ledom halada ipadahid gnay ledom akitek lucnum naka halasaM

.raenilnon ledom nad kisnirtni gnusgnal tapad kadit licekret tardauk edoteM

n ,nakanugid ,numa ak aner nakisamrofsnartid tapad kisnirtni raenil ledom

idajnem ledom aenilnon ledom nakgnades ,raenil tapad kadit r

nakisamrofnartid akam , agudnep na nakanuggnem tapad kisnirtni raenil ledom

licekreT tardauK edoteM asaib raenil ledom anamiagabes .

nasumureP .B halasaM

halada kisnirtni raenil iserger ledom agudnep malad halasam nasumureP

.1 ?kisnirtni raenil iserger nagned duskamid gnay apA

.2 hakgnal anamiagaB - m malad hakgnal agudne ledom raenil iserger

?kisnirtni

.3 aynkadit kiab nakutnenem anamiagaB naagudnep lisah iserger ledom

kisnirtni raenil ?

.C halasaM nasatabmeP

.1 ,ini rihka sagut malaD nasahabmep adap naknaketid naka naagudnep

raenil gnay ledom .kisnirtni

.2 nagned gnusgnal natiakreb gnay aynah sahabid gnay taraysarp iretaM

.kokop iretam

nasiluneP naujuT .D

juT araces iuhategnem kutnu halada ini rihka sagut nasilunep irad nau

ledom naagudnep gnatnet maladnem hibel naanugek nad kisnirtni raenil iserger

.tubesret ledom naagudnep irad


3

nasiluneP taafnaM .E

raenil iserger ledom naagudnep awhab halada ini nasilunep irad taafnaM

nagned natiakreb gnay halasam nakiaseleynem kutnu nakanugid tapad kisnirtni

.kisnirtni raenil

nasiluneP edoteM .F

,aynitrA .akatsup edetom halada ini nasilunep malad iakapid gnay edoteM

kisnirtni raenil ledom naagudnep gnatnet kokop rutaretil adap ucagnem silunep

rutaretil nad kisnirtni raenil nagned natiakreb aguj gnay nial rutaretil atres -

y iretam ianegnem rutaretil .ayniroet nasadnal idajnem gna

nasiluneP akitametsiS .G

NAULUHADNEP .I BAB

.A halasaM gnakaleB rataL

.B halasaM nasumureP

.C halasaM nasatabmeP

.D nasiluneP naujuT

.E nasiluneP taafnaM

.F nasiluneP edoteM

.G nasiluneP akitametsiS

IROET NASADNAL .II BAB

.A raeniL isergeR ledoM

.B eM edot licekreT tardauK

.C irad agudneP nad licekreT tardauK naagudneP tafiS 𝜎2


4

.D adnagreB isergeR nad sisetopiH ijU

M .III BAB LEDO KISNIRTNI RAENIL

.A kisnirtnI raeniL isergeR nasagaG aynlucnuM

.B pahaT - ataD nakrasadreB ledoM nalanegneP pahaT

.VI BAB PUTUNEP

.A nalupmiseK

.B naraS


5

II BAB

IROET NASADNAL

raeniL isergeR ledoM 1.2

kutnu akitsitats kinket irad nalupmuk utaus halada iserger sisilanA

sabeb kat lebairav aratna nagnubuh ikidileynem nad nakledomem 𝑦 nad

sabeb lebairav nanupmih 𝑥1, 𝑥2, ⋯ , 𝑥𝑘 irad isakilpa kaynaB . id iserger sisilana

umli nad napudihek ,akisif uata aimik umli ,kinket kusamret gnadib kaynab

gnay iserger ledom kutneB .imonoke umli nad nemejanam ,laisos umli ,igoloib

kutnebreb gnay raenil iserger ledom halada gnitnep tagnas

𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + … + 𝛽𝑘𝑥𝑘 + 𝜀 )1.2(

sabeb lebairav irad raenil isgnuf nakapurem sabeb kat lebairav anamid

𝑥1, 𝑥2, … , 𝑥𝑘 utiay iserger neisifeok uata iuhatekid kadit gnay retemarap 𝛽0 , 𝛽1

... 𝛽𝑘 nad 𝜀 )talag( iagabes saul tagnas nakanugid raenil iserger ledoM . ledom

kadit gnay isgnuf nad skelpmok gnay isgnuf aparebeb itakednem kutnu siripme

.sabeb lebairav nad sabeb kat lebairav aratna nagnubuh iagabes iuhatekid

itrepes ,amatrep edro nagnubuh aynah kadit itupilem raenil iserger ledoM

naamasrep

𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + … + 𝛽𝑘𝑥𝑘 + 𝜀 )2.2(

.aynnial skelpmok hibel gnay nagnubuh nad laimonilop ledom aguj ipatet

tukireb iagabes silutid tapad raenil iserger ledom nakhaB

𝑦 = 𝛽0 + 𝛽1𝑧1 + 𝛽2𝑧2 + … + 𝛽𝑟𝑧𝑟 + 𝜀 )3.2(

anam id 𝑧𝑖 irad isgnuf nakapurem lebairav 𝑥1, 𝑥2, … , 𝑥𝑘, iserpske kusamret

itrepes 𝑒𝑥𝑖 , �𝑥𝑖 , nad nis −1(𝑥𝑖) iserger ledom tubesid ini ledom awhab nasalA .

halada raenil tubesret ledom anerak retemarap malad raenil 𝛽𝑗 kadit gnay


6

,iuhatekid 𝑗 = 1,2, . . . , 𝑘. gnires gnay nial ledoM isakilpa malad iapmujid

kutnebreb gnay laimonilop ledom halada 𝑦 = 𝛽0 + 𝛽1𝑋 + 𝛽2𝑋2 + 𝜀 )4.2(

kutneb malad ilabmek silutid tapad )2.2( naamasrep malad raenil iserger ledoM

𝑦 = 𝑓(𝒙, 𝜷) + 𝜀 ( 5.2 )

nagneD 𝑓(𝒙, 𝜷) = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + ⋯ + 𝛽𝑘𝑥𝑘 nad 𝒙′ = [𝑥1, 𝑥2, ⋯ , 𝑥𝑘].

raeniL ledoM 1.2 isinifeD

retemarap malad raenil gnay iserger ledom halada raenil iserger ledoM 𝛽𝑗 gnay

,iuhatekid kadit (𝑗 = 1, 2, ⋯ , 𝑘) malad silutid raenil ledom ,mumu araceS .

kutneb 𝑦 = 𝑓(𝒙, 𝜷) = 𝛽𝟎 + 𝛽1𝑥1 + 𝛽2𝑥2 + ⋯ + 𝛽𝑘𝑥𝑘 + ε . in aneraK ial

irad naparah talag nopser lebairav irad naparah ialin ,lon halada ledom

𝐸(𝑦) = 𝐸[𝑓(𝒙, 𝜷) + 𝜀]

= 𝑓(𝒙, 𝜷)

𝑓(𝒙, 𝜷) isgnuf tubesid isatkepske irad ledom gnay aynah nakapurem isgnuf

.iuhatekid kadit gnay retemarap irad raenil

bab adaP ledom adap retemarap agudnem kutnu kinket sahabid naka ,ini

gnales nataubmep radnats edotem aguj sahabid nakA .adnagreb iserger

.licekreT tardauK edoteM atres tubesret ledom kutnu naayacrepek

2.2 licekreT tardauK edoteM

licekreT tardauK edoteM agudnem kutnu nakanugid susuhk araces

ada lasiM .adnagreb raenil iserger ledom adap iserger neisifeok 𝑛 > 𝑘

nagned naklobmisid sabeb kat lebairav irad natamagneP .natamagnep 𝑦1,𝑦2 ,... ,

𝑦𝑛 sabeb kat lebairav paites kutnU . 𝑦 kutnu natamagnep iaynupid , paites


7

lasim ,sabeb lebairav 𝑥 𝑗𝑖 gnay ek natamagnep nakataynem 𝑖 lebairav irad 𝑥 ek

𝑗 lasiM .1.2 lebat adap nakkujnutid ataD . 𝜀 ,talag halada 𝜎2 nakataynem

,isnairav 𝐸(𝜀) atar nakataynem - (rav nad ,talag atar 𝜀 isnairav nakataynem )

awhab nakismusaid ini natamagnep adaP .talag 𝐸(𝜀) (rav nad 0 = 𝜀 = ) 𝜎2 nad

{𝜀𝑖 .isalerokreb kadit gnay kaca lebairav nakataynem }

𝑦1 𝑥 11 𝑥 21 … 𝑥1𝑘

𝑦2 𝑥 12 𝑥 22 … 𝑥2𝑘

⋮ ⋮ ⋮ ⋮

𝑦𝑛 𝑥𝑛1 𝑥𝑛2 … 𝑥 𝑘𝑛

lebaT adnagreB raeniL isergeR kutnu ataD rutkurtS 1.2

lebat adap tapadret gnay natamagnep nakrasadreb silutid naka 1.2 naamasreP

utiay 1.2

𝑦𝑖 = 𝛽0 + 𝛽1𝑥𝑖1 + 𝛽2𝑥𝑖2 + … + 𝛽𝑘𝑥𝑖𝑘 + 𝜀𝑖

= 𝛽0 + ∑ 𝛽𝑖𝑥 𝑗𝑖 + 𝜀𝑖 , 𝑖 = 1, 2, ⋯ , 𝑛𝑘

𝑗=1 )6.2(

uK edoteM kutnu naujutreb 6.2 naamasrep adap nakparetid licekreT tarda

agudnep nakutnenem 𝛽 talag tardauk halmuj aggnihes naikimedes 𝜀𝑖 , utiay 𝑆

.muminim idajnem

𝑆 = ∑ 𝜀𝑖2𝑛

𝑖=1

= ∑ �𝑦𝑖 − 𝛽0 − ∑ 𝛽𝑗𝑘𝑗=1 𝑥 𝑗𝑖 �

2𝑛𝑖=1 )7.2(

isgnuF 𝑆 naklaminimid padahret 𝛽0 , 𝛽1 ... 𝛽𝑘 lasiM . 𝑏0, 𝑏1, … 𝑏𝑘 halada

retemarap igab licekret tardauk agudnep 𝛽0, 𝛽1, ⋯ , 𝛽𝑘 tardauk agudneP .

ihunemem surah tubesret licekret


8

� 𝑆𝜕𝜕𝛽0

� 𝑏0,𝑏1,⋯,𝑏𝑘 = −2 ∑ �𝑦𝑖 − 𝛽0 − ∑ 𝛽𝑗𝑘𝑗=1 𝑥 𝑗𝑖

� = 0𝑛𝑖=1 )a8.2(

nad

� 𝑆𝜕𝜕𝛽𝑗

� 𝑏0,𝑏1,⋯,𝑏𝑘 = −2 ∑ �𝑦𝑖 − 𝛽0 − ∑ 𝛽𝑗𝑘𝑗=1 𝑥 𝑗𝑖

� 𝑥𝑖𝑗 = 0𝑛𝑖=1 )b8.2(

nakisutitsbusnem nad )b8.2( nad )a8.2( naamasrep naanahredeyneP 𝑏0, 𝑏1, … 𝑏𝑘

naklisahgnem ,isulos igabes

𝑛𝑏0 + 𝑏1 � 𝑥𝑖1 + 𝑏2 � 𝑥𝑖2

𝑛

𝑖=1

+ … + 𝑏𝑘 � 𝑥 𝑘𝑖

𝑛

𝑖=1

= � 𝑦𝑖

𝑛

𝑖=1

𝑛

𝑖=1

𝑏0 � 𝑥𝑖1

𝑛

𝑖=1+ 𝑏1 � 𝑥𝑖1

2𝑛

𝑖=1+ 𝑏2 � 𝑥𝑖1

𝑛

𝑖=1𝑥𝑖2 + ∙∙∙ +𝑏𝑘 � 𝑥𝑖1

𝑛

𝑖=1𝑥 𝑘𝑖 = � 𝑥𝑖1 𝑦𝑖

𝑛

𝑖=1

⋮ ⋮ ⋮ ⋮ ⋮

𝑏0 � 𝑥 𝑘𝑖

𝑛

𝑖=1+ 𝑏1 � 𝑥 𝑘𝑖 𝑥𝑖1

𝑛

𝑖=1+ 𝑏2 � 𝑥 𝑘𝑖

𝑛

𝑖=1𝑥𝑖2 + ∙∙∙ +𝑏𝑘 � 𝑥 𝑘𝑖

2𝑛

𝑖=1= � 𝑥 𝑘𝑖 𝑦𝑖

𝑛

𝑖=1

)9.2(

ayntujnales ,lamron licekret tardauk naamasrep tubesid 9.2 naamasreP

awhab nakitahreP .lamron naamasrep tubesid naka tubesret naamasrep

ikilimem lamron naamasrep 𝑝 = 𝑘 + 1 naamasrep kutnu isuloS .naamasrep

utiay iserger neisifeok irad licekret tardauk agudnep idajnem naka lamron

𝑏0, 𝑏1, … 𝑏𝑘 .

naamasrep akij hadum hibel naka lamron naamasrep nakiaseleyneP -

taubid naka gnarakeS .skirtam isaton nagned nakataynid tubesret naamasrep

naamasrep irad skirtam .)9.2( naamasrep nakisatneserperem gnay lamron


9

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎡ 𝑛 � 𝑥𝑖1

𝑛

𝑖=1� 𝑥 21

𝑛

𝑖=1⋯ � 𝑥 𝑘𝑖

𝑛

𝑖=1

� 𝑥𝑖1

𝑛

𝑖=1� 𝑥𝑖

2𝑛

𝑖=1� 𝑥𝑖1 𝑥𝑖2

𝑛

𝑖=1⋯ � 𝑥𝑖1 𝑥 𝑘𝑖

𝑛

𝑖=1⋮

� 𝑥 𝑘𝑖

𝑛

𝑖=1

⋮

� 𝑥 𝑘𝑖 𝑥𝑖1

𝑛

𝑖=1

⋮

� 𝑥 𝑘𝑖 𝑥𝑖2

𝑛

𝑖=1⋯

⋮

� 𝑥 𝑘𝑖2

𝑛

𝑖=1 ⎦⎥⎥⎥⎥⎥⎥⎥⎥⎤

�

𝑏0𝑏1⋮

𝑏𝑘

� =

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎡ � 𝑦𝑖

𝑛

𝑖=1

� 𝑥𝑖1 𝑦𝑖

𝑛

𝑖=1⋮

� 𝑥 𝑘𝑖 𝑦𝑖

𝑛

𝑖=1 ⎦⎥⎥⎥⎥⎥⎥⎥⎥⎤

)01.2(

idajnem ,skirtam isaton nagned silutid akij ini ledoM

𝑿′ 𝒃𝑿 = 𝑿′𝒚 )11.2(

anamid

𝒚 = �

𝑦1𝑦𝟐⋮

𝑦𝒏

� , 𝑿 =

⎣⎢⎢⎡1 𝑥 11

𝑥 21 ⋯ 𝑥1𝑘

1 𝑥 12𝑥 22 ⋯ 𝑥2𝑘

⋮1

⋮𝑥𝑛1

⋮𝑥𝑛2 ⋯

⋮𝑥 𝑘𝑛 ⎦

⎥⎥⎤

, 𝒃 = �

𝑏0𝑏1⋮

𝑏𝑘

�.

mumu araceS 𝒚 narukureb gnay natamagnep rotkev halada (𝑛 × 1) . 𝑿 halada

narukureb gnay skirtam (𝑛 × 𝑝) ,sabeb lebairav halada aynirtne paites nad 𝒃

narukureb rotkev halada (𝑝 × 1) .iserger neisifeok halada aynirtne paites gnay

.skirtam kutneb malad lamron naamasrep nakirebmem )11.2( naamasreP

kitnedi tubesret naamasreP irad molok amaleS .)9.2( naamasrep nagned

skirtam 𝑿 ,raenilok kadit 𝑿′𝑿 tinifed kutnu arac aggnihes ,fitisop

adap isis audek nakilagnem nagned halada lamron naamasrep nakiaseleynem

irad srevni nagned )11.2( naamasrep 𝑿′𝑿 . rdauk agudnep naikimed nagneD ta

irad licekret 𝜷 halada ,b utiay

𝒃 = (𝑿′𝑿)−1𝑿′𝒚 )21.2(

halada iauses gnay iserger ledom agudnep naikimed nagneD

𝒚� = 𝒃𝑿 )31.2(


01

halada )31.2( naamasrep adap ralaks agudneP

𝑦�𝑖 = 𝑏0 + ∑ 𝑏𝑗𝑥 𝑗𝑖𝑘𝑖=1 , 𝑖 = 1, 2, … , 𝑛

lasiM 𝑒𝑖 = 𝑦𝑖 − 𝑦�𝑖 natamagnep aratna hisiles utiay ,laudiser halada 𝑦𝑖 ialin nad

𝑦�𝑖 narukureb gnay laudiser rotkeV . (𝑛 × 1) kutneb malad naklipmatid

𝒆 = 𝒚 − 𝒚� )41.2(

irad agudneP nad licekreT tardauK naagudneP tafiS .3.2 𝝈𝟐

retemarap igab saibkat agudnep naklisahgnem licekret tardauk edoteM 𝜷

aliB .agudid gnay retemarap nagned amas aynnaparah ialin gnay agudnep utiay

𝒃 iracnem nagned nakkujnutid tapad ini tafis ,licekret tardauk agudnep halada

naparah ialin 𝒃 agabes :tukireb i

𝐸(𝒃) = 𝐸[(𝑿′𝑿)−1𝑿′𝒚]

= 𝐸[(𝑿′𝑿)−1𝑋′( 𝜷𝑿 + 𝜺)]

= 𝐸[(𝑿′𝑿)−1𝑿′ 𝜷𝑿 + (𝑿′𝑿)−1𝑿′𝜺]

= 𝜷

aneraK 𝐸 (𝜺) = 𝟎 nad (𝑿′𝑿)−1𝑿′𝑿 = 𝑰 akam 𝒃 irad saibkat agudnep halada

𝜷 isnairav tafiS . 𝒃 tukireb isnairavok skirtam helo nakataynid

𝑣𝑜𝑐 (𝒃) = 𝐸{[𝒃 − 𝐸(𝒃)][𝒃 − 𝐸(𝒃)]′}

skirtam isnairavoK 𝒃 sirtemis skirtam halada (𝑝 × 𝑝) ek sirab nemele gnay 𝑗

ek molok 𝑗 ek silutid aynsuretes kutnu( 𝑗𝑗 irad isnairav halada ) (𝒃𝑗) nemele nad

ek gnay 𝑗𝑖 aratna isnairavok halada 𝑏𝑖 nad 𝑏𝑗 skirtam isnairavoK . 𝒃

𝑣𝑜𝑐 (𝒃) = 𝜎2(𝑿′𝑿)−1 )51.2(


11

.kiabret raenil saibkat agudnep nakapurem aguj licekret tardauk agudneP

,aynitrA 𝒃 isnairav nagned saibkat agudnep malad kiabret gnay halada

atna id muminim .natamagnep irad raenil isgnuf aumes ar

tafiS - nakarikrepmem kutnu nakulrepid aynasaib sata id tafis 𝜎2 kutnU .

talag tardauk halmuj retemarap irad agudnep nakgnabmegnem ( 𝑆𝑆 𝐸) ,

𝑆𝑆 𝐸 = ∑ (𝑦𝑖 − 𝑦�𝑖)2𝑛𝑖=1

= ∑ 𝑒𝑖2𝑛

𝑖=1

= 𝒆′𝒆

itbus nagneD isut 𝒆 = 𝒚 − 𝒚� = 𝒚 − 𝒃𝑿 helorepid ,

𝑆𝑆 𝐸 = (𝒚 − 𝒃𝑿 )′(𝒚 − 𝒃𝑿 )

= 𝒚′𝒚 − 𝒃′𝑿′𝒚 − 𝒚′ 𝒃𝑿 + 𝒃′𝑿′ 𝒃𝑿

= 𝒚′𝒚 − 2𝒃′𝑿′𝒚 + 𝒃′𝑿′ 𝒃𝑿

aneraK 𝑿′ 𝒃𝑿 = 𝑿′𝒚 idajnem rihkaret naamasrep ,

𝑆𝑆 𝐸 = 𝒚′𝒚 − 𝒃′𝑿′𝒚 )61.2(

sabeb tajared ikilimem nad ,talag tardauk halmuj tubesid )61.2( naamasreP

𝑛 − 𝑝 .uti nagned tiakret gnay kutnu susuhk araceS 𝑝 = 2 ,

𝐸( 𝑆𝑆 𝐸) = 𝐸[∑ (𝑦𝑖 − 𝑦�𝑖)2𝑛𝑖=1 ] = 𝐸[∑ (𝑦𝑖 − 𝑏0 − 𝑏1𝑥𝑖)2𝑛

𝑖=1 ]

= 𝐸[∑ (𝑦𝑖 − 𝑦� + 𝑏1�̅� − 𝑏1𝑥𝑖)2𝑛𝑖=1 ]

= 𝐸[∑ [(𝑦𝑖 − 𝑦�) − 𝑏1(𝑥𝑖 − �̅�)]2𝑛𝑖=1 ]

= 𝐸[∑ (𝑦𝑖 − 𝑦�)2 + 𝑏12 ∑ (𝑥𝑖 − �̅�)2 − 2𝑏1 ∑ (𝑥𝑖 − �̅�)(𝑦𝑖 − 𝑦�)𝑛

𝑖=1𝑛𝑖=1

𝑛𝑖=1 ]

aneraK ∑ (𝑥𝑖 − �̅�)(𝑦𝑖 − 𝑦�) = ∑ (𝑥𝑖 − �̅�)2𝑏1𝑛𝑖=1

𝑛𝑖=1 naamasrep aud akam ,

id rihkaret idajnem sata −𝑏12 ∑ (𝑥𝑖 − �̅�)2𝑛

𝑖=1 ,idaJ .


21

∑ (𝑦𝑖 − 𝑦�)2𝑛𝑖=1 = ∑ 𝑦𝑖

2 − 2𝑦�2𝑛𝑖=1

uti anerak helo nad

𝐸[∑ (𝑦𝑖 − 𝑦�1)2𝑛𝑖=1 ] = 𝐸[∑ 𝑦𝑖

2 − 𝑛𝑦�2 − 𝑏11 ∑ (𝑥𝑖 − �̅�)2𝑛

𝑖=1𝑛𝑖=1 ]

= ∑ 𝐸(𝑦𝑖2)𝑛

𝑖=1 − 𝐸𝑛 (𝑦�2) − ∑ (𝑥𝑖 − �̅�)2𝐸(𝑏12)𝑛

𝑖=1

kaca lebairav paites kutnu awhab tataC 𝑈 , 𝐸(𝑈2) = 𝑉(𝑈) + [𝐸(𝑈)]2 akam ,

𝐸[∑ (𝑦𝑖 − 𝑦�1)2𝑛𝑖=1 ] = ∑ {𝑉(𝑦𝑖) + [𝐸(𝑦𝑖)]2} − 𝑛{𝑉(𝑦�) + [𝐸(𝑦�)]2} −𝑛

𝑖=1

∑ (𝑥𝑖 − �̅�)2{𝑉(𝑏1) + [𝐸(𝑏1)]2}𝑛𝑖=1

= 𝑛𝜎2 + �(𝑏0 + 𝑏1𝑥𝑖)2 − 𝑛 �𝜎2

𝑛+ (𝑏𝑜 + 𝑏1�̅�)2�

𝑛

𝑖=1

− �(𝑥𝑖 − �̅�)2 �𝜎2

∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1

+ 𝑏12�

𝑛

𝑖=1

idajnem nakanahredesid gnay

𝐸( 𝑆𝑆 𝐸) = 𝜎2(𝑛 − 2)

S aggnihe agudnep irad saibkat 𝜎2 helo nakirebid

𝜎�2 = 𝑆𝑆 𝐸𝑛−2

)71.2(

4.2 ijU H adnagreB isergeR malad sisetopi

ledom gnatnet sisetopih iju utaus ,adnagreb raenil iserger halasam malaD

naka ini naigab adaP .ledom naitrarebek rukugnem malad utnabmem retemarap

ini rudesorP .gnitnep gnay sisetopih naijugnep rudesorp aparebeb sahabid

talag nakismusagnem 𝜀𝑖 nad lamron isubirtsidreb halada ledom malad

atar nagned nednepedni - natsnok isnairav nad lon atar 𝜎2 ,iuhatekid kadit ipatet

takgnisid 𝜀~ 𝐷𝐼𝑁 (0, 𝜎2) eD . natamagnep ini ismusa nagn 𝑦𝑖 nad lamron

atar nagned nednepedni isubirtsidret - atar 𝛽0 + ∑ 𝛽𝑗𝑥 𝑗𝑖𝑘𝑗=1 isnairav nad 𝜎2


31

isergeR isnakifingiS ijU 1.4.2

amasreb huragnep ijugnem utiay iserger isnakfingis iju macam )aud( 2 adA

i huragnep nad sabeb lebairav iju halada iserger isnakifingis ijU .laudividn

nakutnenem kutnu nopser lebairav aratna reinil nagnubuh ada hakapa 𝑦 nad

sabeb lebairav irad tesbus 𝑥1, 𝑥2, … , 𝑥𝑘 halada iauses gnay sisetopiH .

𝐻0 ∶ 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑘 = 0

𝐻1 ∶ 𝛽𝑗 ≠ 0 kutnu utas ayntikides 𝑗 )81.2(

nakaloneP 𝐻0 sabeb lebairav utas ada aynkadites awhab nakkujnunem )81.2( id

𝑥1, 𝑥2, … , 𝑥𝑘 rudesorP .ledom padahret nakifingis araces isubirtnokreb

latot tardauk halmuj isitrap naktabilem naijugnep ( 𝑆𝑆 𝑇) halmuj idajnem

uk ledom tarda ( 𝑆𝑆 𝑅) talag tardauk halmuj nad ( 𝑆𝑆 𝐸) utiay ,

𝑆𝑆 𝑇 = 𝑆𝑆 𝑅 + 𝑆𝑆 𝐸 )91.2(

lon sisetopih akij gnarakeS 𝐻0 ∶ 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑘 = 0 akam ,raneb halada

𝑆𝑆 𝑅 / 𝜎2 isubirtsidreb 𝑋𝑘2 kutnu sabeb tajared anam id , 𝜒2 nagned amas

v aynkaynab awhab nakkujnutid tapad aguJ .ledom malad sabeb lebaira

𝑆𝑆 𝐸 / 𝜎2 iagabes isubirtsidreb 𝑋𝑛−𝑘−12 nad 𝑆𝑆 𝐸 nad 𝑆𝑆 𝑅 .nednepedni ini itkuB

kutnu iju rudesorp id nakumetid tapad 𝐻0 ∶ 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑘 = 0 halada

gnutihgnem

𝐹0 = 𝑆𝑆 𝑅/𝑘𝑆𝑆 𝐸/(𝑛−𝑘−1) = 𝑀𝑆𝑅

𝑆𝑀 𝐸 )02.2(

kalonem nad 𝐻0 akij 𝐹0 ihibelem 𝐹𝛼,𝑘,𝑛−𝑘−1 aynasaib ini ijU . malad mukgnarid

T itrepes lebat haubes anerak snairav sisilana tubesid ini iju rudesorP .2.2 leba

isisopmoked adap nakrasadid satilibairav latot irad lebairav nopser 𝑦.


41

rebmuSisnairav

halmuJtardauk

tajareDsabeb

ataR - atartardauk

𝐹0

isergeR 𝑆𝑆 𝑅 𝑘 𝑆𝑀 𝑅 𝑆𝑀 𝑅/ 𝑆𝑀 𝐸 talaG 𝑆𝑆 𝐸 𝑛 − 𝑘 − 1 𝑆𝑀 𝐸 latoT 𝑆𝑆 𝑇 𝑛 − 1

2.2 lebaT

anamiD 𝑆𝑀 𝑅 = 𝑆𝑆 𝑅𝑘

nad 𝑆𝑀 𝐸 = 𝑆𝑆 𝐸𝑛−𝑘−1

aneraK . 𝑆𝑆 𝑇 = ∑ 𝑦𝑖2 − �∑ 𝑦𝑖

𝑛𝑖=1 �

2

𝑛=𝑛

𝑖=1

𝒚′𝒚 − (∑ 𝑦𝒊𝒏𝑖=1 )2/𝑛 , naamasrep silutid tapad sata id 61.2 gnalu iagabes

𝑆𝑆 𝐸 = 𝒚′𝒚 − �∑ 𝑦𝑖𝑛𝑖=1 �

2

𝑛− �𝒃′𝑿′𝒚 − �∑ 𝑦𝑖

𝑛𝑖=1 �

2

𝑛�

uata

𝑆𝑆 𝐸 = 𝑆𝑆 𝑇 − 𝑆𝑆 𝑅

helO anerak uti iserger tardauk halmuj halada

𝑆𝑆 𝑅 = 𝒃′𝑿′𝒚 − �∑ 𝑦𝑖𝑛𝑖=1 �

2

𝑛 ( )12.2

halmuJ halada talag tardauk

𝑆𝑆 𝐸 = 𝒚′𝒚 − 𝒃′𝑿′𝒚 )22.2(

halada latot tardauk halmuj naD

𝑆𝑆 𝑇 = 𝒚′𝒚 − �∑ 𝑦𝑖𝑛𝑖=1 �

2

𝑛 )32.2(

2.4.2 ( isanimreteD neisifeoK 𝑹𝟐)

( isanimreted neisifeoK 𝑅2 aynraseb naksalejnem gnay neisifeok halada )

.ledom nagned naksalejid tapad gnay Y isnairav esatneserp neisifeoK

nakirebiD.ledom nakiabek naksalejnem kutnu nakanugid tapad isanimreted

neisifeok pesnok ianegnem narabmag nakirebmem kutnu nneV margaid

.isanimreted


51

margaid adaP V lebairav malad isnairav ilikawem Y narakgnil ,sata id nne

nasirI .X salejnep lebairav malad isnairav ilikawem X narakgnil nad Y sabeb

margaid adaP .naksalejid tapad gnay isnairav naigab nakujnunem V )a( nne

margaiD .isnairav lawa isidnok halada V nem )b( nne nasiri aynada nakujnu

naigabes awhab nakujnunem ini laH .tubesret Y nad X narakgnil audek aratna

gnay nasiri raseb nikameS .X isnairav helo naksalejid tapad Y irad isnairav

margaid adap nakujnutid V gnay Y isnairav alup raseb nikames )e( ,)d( ,)c( nne

lejid tipmihreb uti X narakgnil nad Y narakgnil akiteK .X isnairav helo naksa

margaid adap kapmat itrepes V nesrep 001 awhab nakujnunem ini lah ,)f( nne

.X isnairav helo naksalejid tapad Y isnairav irad 𝑅2 atames - nakapurem atam

snairav aratna nasiri irad naruku nneV margaid rabmag adaP .X isnairav nad Y i

ini ,takgninem X isnairav nad Y isnairav aratna nasiri awhab nakujnunem

.X helo naksalejid tapad gnay Y isnairav isroporp alup takgninem itrareb

whab nakatakid tapad ,tipmihreb X narakgnil nad Y narakgnil akiteK ialin a

𝑅2 = 1 ,aynkilabeS .X helo naksalejid tapad Y isnairav irad nesrep 001 anerak ,

tapad ,nasirireb kadit nad tipmihreb kadit X narakgnil nad Y narakgnil akitek

nakatakid 𝑅2 = 0 .X helo naksalejid tapad kadit Y isnairav aynitra ,

u ,naikimed nagneD gnutihgnem kutn 𝑅2 naamasrep nakanuggnem tapad

𝑌𝑖 = 𝑌�𝑖 + 𝜀�̂�


61

nagnapmis kutneb malad uata

𝑦𝑖 = 𝑦�𝑖 + 𝜀�̂� )42.2(

akam ,)42.2( naamasrep nakhalmujnem nad naktardaukgnem nagneD

tukireb iagabes naamasrep naktapadid

∑ 𝑦𝑖2 = ∑(𝑦�𝑖 + 𝜀�̂�)2 )52.2(

awhab nakitkubid naka ,)72.2( naamasrep nakitkubmem mulebeS ∑ 𝑦�𝑖𝜀�̂� = 0

awhab nakirebid nad 𝑦�𝑖 = �̂�1𝑥𝑖 akam ,

� 𝑦�𝑖𝜀�̂� = � �̂�1𝑥𝑖𝜀�̂�

= �̂�1 � 𝑥𝑖𝜀�̂�

= �̂�1 � 𝑥𝑖(𝑦𝑖 − 𝑦�𝑖)

= �̂�1 � 𝑥𝑖(𝑦𝑖 − �̂�1𝑥𝑖)

= �̂�1 � 𝑥𝑖𝑦𝑖 − �̂�1 � 𝑥𝑖�̂�1𝑥𝑖

= �̂�1�̂�1 � 𝑥𝑖2 − �̂�1

2 � 𝑥𝑖2

= �̂�12 � 𝑥𝑖

2 − �̂�12 � 𝑥𝑖

2

= 0 )62.2(

naamasrep nakirebiD

𝑌� = �̂�0 + �̂�1𝑋� )72.2(

naamasrep irad )41.2( naamasrep nakgnarugnem nagned ayntujnaleS 𝑌𝑖 = �̂�0 +

�̂�1𝑋𝑖 + 𝜀𝑖 urab naamasrep naktapadid

𝑌𝑖 − 𝑌� = (𝛽0 − �̂�0) + 𝛽1(𝑋𝑖 − 𝑋�) + 𝜀𝑖


71

𝑦𝑖 = 𝛽1𝑥𝑖 + 𝜀𝑖

aggniheS 𝑦𝑖 nagned agudid tapad 𝑦�𝑖 = �̂�1𝑥𝑖.

yntujnaleS nakitkubid naka a

∑ 𝑦𝑖2 = ∑(𝑦�𝑖 + �̂�𝑖)2

= ∑ 𝑦�𝑖2 + ∑ 2𝑦�𝑖𝜀�̂� + ∑ 𝜀�̂�

2

= ∑(�̂�1𝑥𝑖)2 + 2 ∑ 𝑦�𝑖𝜀�̂� + ∑ 𝜀�̂�2

= 𝛽12 ∑ 𝑥�𝑖

2 + ∑ 𝜀�̂�2 )82.2(

tapad )82.2( naamasrep malad lucnum gnay tardauk halmuj iagabreB

:tukireb iagabes nakrabmagid

.1 ∑ 𝑦𝑖2 = ∑(𝑌𝑖 − 𝑌�)2 latot tardauk halmuj iagabes tubesid ( 𝑆𝑆 𝑇)

.2 𝛽12 ∑ 𝑥�𝑖

2 tardauk halmuj uata iserger tardauk halmuj iagabes tubesid

iserger helo naksalejid tapad gnay ( 𝑆𝑆 𝑅) nad

.3 ∑ �̂�12 talag tardauk halmuj tubesid ( 𝑆𝑆 𝐸)

pad )42.2( naaamasrep ,nial atak nagneD idajnem gnalu silutid ta

𝑆𝑆 𝑇 = 𝑆𝑆 𝑅 + 𝑆𝑆 𝐸 )92.2(

:iagabes nakisinifedid isanimreted neisifeoK

𝑅2 = 𝑆𝑆 𝑅𝑆𝑆 𝑇

)03.2(

,lebairav aud susak malaD

𝑅2 = 𝛽�12 ∑ 𝑥𝑖

2

∑ 𝑦𝑖2

,lebairav agit susak malaD

𝑅2 = 𝛽�2 ∑ 𝑦𝑖𝑥2𝑖+𝛽�3 ∑ 𝑦𝑖𝑥3𝑖∑ 𝑦𝑖2

susak kutnu naktapadnem atik ,nakisasilareneggnem nagneD 𝑘 − 1 lebairav


81

𝑅2 = 𝛽�2 ∑ 𝑦𝑖𝑥2𝑖+𝛽�3 ∑ 𝑦𝑖𝑥3𝑖+⋯+𝛽�𝑘 ∑ 𝑦𝑖𝑥 𝑖𝑘∑ 𝑦𝑖2

∑ 𝑦𝑖2 = ∑(𝑌𝑖 − 𝑌�)2

= ∑ 𝑌𝑖2 − ∑ 𝑌�2

= ∑ 𝑌𝑖2 − 𝑛𝑌�2

= 𝒚′𝒚 − 𝑛𝑌�2

�̂�2 ∑ 𝑦𝑖𝑥2𝑖 + �̂�3 ∑ 𝑦𝑖𝑥3𝑖 + ⋯ + �̂�𝑘 ∑ 𝑦𝑖𝑥 𝑖𝑘 = 𝒃′𝑿′𝒚 − 𝑛𝑌�2

skirtam isaton malaD 𝑅2 idajnem silutid tapad

𝑅2 =𝒃′𝑿′𝒀 − 𝑛𝑌�2

𝒚′𝒚 − 𝑛𝑌�2

neisifeoK isanimreted adnagreb 𝑅2 nakisinifedid iagabes


= 1 − 𝑆𝑆 𝐸𝑆𝑆 𝑇

)13.2(

𝑅2 satilibairav nagnarugnep aynraseb irad naruku halada 𝑦 nagned helorepid

sabeb lebairav nakanuggnem 𝑥1, 𝑥2, … , 𝑥𝑘 naaskiremep iraD .ledom malad

awhab kapmat ,isnairav satitnedi naamasrep sisilana 0 ≤ 𝑅2 ≤ 1 ialin ,numaN .

raseb 𝑅2 ab itrareb ulales kadit .kiabret gnay halada iserger ledom awh

naknurunem tapad kadit ledom adap lebairav nakhabmaneM 𝑅2 irad sapelret ,

.kitsitats araces kadit uata nakifingis tubesret nahabmat lebairav hakapa

aneraK 𝑅2 sabeb lebairav nakhabmatid akij nurunem tapad kadit aynialin

nakanuggnem akus hibel iserger ledom aparebeb ,ledom malad kitsitats 𝑅2

detsujda( nakiausesid gnay 𝑅2) nakisinifedid , iagabes

𝑅 𝑗𝑑𝑎2 = 1 − 𝑆𝑆 𝐸/(𝑛−𝑝)

𝑆𝑆 𝑇/(𝑛−1) = 1 − �𝑛−1𝑛−𝑝

� (1 − 𝑅2) )23.2(


91

kitsitats ,mumu araceS 𝑅2 lebairav nagned takgninem kadit nakiausesid gnay

.ledom ek nakhabmatid gnay kadit gnay lebairav nahabmanep ada akij ,nakhaB

ialin ,gnitnep 𝑅 𝑗𝑑𝑎2 .gnarukreb naka

udividnI isergeR neisifeoK padahreT naijugneP 3.4.2

opiH gnisam iserger neisifeok gnatnet siset - kutnu kiranem gnires gnisam

gnisam irad ialin nakutnenem malad anugreb naka tubesret ijU .ijuid - gnisam

hibel nikgnum ledom ,hotnoc iagabeS .iserger ledom malad sabeb lebairav

,nahabmat lebairav aynkusam nagned fitkefe nagned nikgnum uata

.ledom malad ada hadus gnay lebairav hibel uata utas nasupahgnep

halmuj nakbabeynem tapad kadit iserger ledom ek lebairav nakhabmaneM

suraH .takgninem asib kadit talag tardauk halmuj nad nurunem iserger tardauk

ep ada hakapa naksutupid kutnu pukuc gnay iserger tardauk halmuj nahabman

,ayntujnaleS .ledom malad nahabmat lebairav nakanuggnem nimajnem

atar naktakgninem tapad ledom kutnu gnitnep kat lebairav nakhabmanem - atar

.ledom naitrarebek ignarugnem aggnihes ,talag tardauk

ijugnem kutnU ,laudividni iserger neisifeok paites irad isnakifingis 𝛽𝑗 ,

pmetid u hakgnal h - :tukireb iagabes hakgnal

.1 nakpateT 𝐻0 ∶ 𝛽𝑗 = 𝛽𝑗0

.2 irad utas halas nakpateT 𝐻1 ∶ �𝛽𝑗 > 𝛽𝑗0 ( 𝑖𝑗𝑢 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑓𝑖𝑡𝑖𝑠𝑜𝑝 )𝛽𝑗 < 𝛽𝑗0 ( 𝑖𝑗𝑢 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑓𝑖𝑡𝑎𝑔𝑒𝑛 )𝛽𝑗 ≠ 𝛽𝑗0 ( 𝑖𝑗𝑢 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑎𝑢𝑑 𝑖𝑠𝑖𝑠 )

�

.3 iju kitsitatS nakpateT 𝑡 = 𝑏𝑗−𝛽𝑗

�𝜎�2𝐶 𝑗𝑗

. )33.2(

anam id 𝐶 𝑗𝑗 lanogaid nemele halada (𝑿′𝑿)−1 nagned iauses 𝑏𝑗 .


02

.4 nakalonep haread nakpateT 𝐻0 nagned iauses 𝐻1 : )2( adap

�𝑡 > 𝑡𝛼 ( 𝑎𝑟𝑒𝑎𝑑 ℎ 𝑛𝑎𝑘𝑎𝑙𝑜𝑛𝑒𝑝 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑓𝑖𝑡𝑖𝑠𝑜𝑝 )𝑡 < 𝑡𝛼 ( 𝑎𝑟𝑒𝑎𝑑 ℎ 𝑛𝑎𝑘𝑎𝑙𝑜𝑛𝑒𝑝 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑓𝑖𝑡𝑎𝑔𝑒𝑛 )

|𝑡| > 𝑡𝛼2 ( 𝑎𝑟𝑒𝑎𝑑 ℎ 𝑘𝑎𝑙𝑜𝑛𝑒𝑝 𝑛𝑎 ℎ 𝑠𝑖𝑠𝑒𝑡𝑜𝑝𝑖 𝑎𝑢𝑑 𝑖𝑠𝑖𝑠 )

�

.5 nagnutihrep nakukaL

.6 nalupmisek tauB

: natataC 𝑡𝛼 sabeb tajared ikilimem 𝑛 − (𝑘 + 1) .

,)33.2( naamasrep malad tubeyneP �𝜎�2𝐶 𝑗𝑗 tubesid gnires , rorre dradnats irad

iserger neisifeok 𝑏𝑗 utiay,

𝑒𝑠 �𝑏𝑗� = �𝜎�2𝐶 𝑗𝑗 )43.2(

naamasrep malad iju kitsitats silunem kutnu amas gnay arac uti anerak helO

halada )33.2(

𝑡0 = 𝑏𝑗

𝑒𝑠 �𝑏𝑗� )53.2(

4.4.2 malad naayacrepeK gnaleS isergeR adnagreB

utnu nakulrepid ini naayacrepek gnaleS k lavretni agudnep nugnabmem

kutnu naayacrepek iserger neisifeok �𝛽𝑗� kutnu rudesorp nagnabmegneP .

talag ismusa nakulremem ini naayacrepek gnales helorepmem {𝜀𝑖} isubirtsidreb

atar nagned nednepedni nad lamron - isnairav nad lon atar 𝜎2 .

gudnep aneraK licekret tardauk a 𝒃 irad raenil isanibmok halada

akam ,natamagnep 𝒃 atar rotkev nagned lamron isubirtsidret - atar 𝜷 skirtam nad

isnairavok 𝜎2(𝑿′𝑿)−𝟏 naidumeK . gnisam - gnisam kitsitats irad

𝑡 = 𝑏𝑗−𝛽𝑗

�𝜎�2𝐶 𝑗𝑗

, 𝑗 = 0, 1, … , 𝑘 )63.2(


12

isubirtsidreB sabeb tajared nagned anam id , ek nemele halada

skirtam irad nad , irad helorepid gnay ,talag snairav agudnep halada

.)71.2( naamasreP

igab naayacrepek gnales nakutnebmeP kitsitats adap nakrasadid

isubirtsidreb gnay t- tneduts sabeb tajared nagned .

id rabmag iraD agudid tapad ,sata

naayacrepek gnales akaM iserger neisifeok kutnu ,

halada ,

)73.2(


22

ismusA 5.2 - isergeR ledoM ismusA

1 ismusA atar ialiN - irad taraysreb atar rusnu talag isalupop 𝜀𝑖 adap gnutnagret ,

naksalejnem gnay lebairav utnetret ialin (𝑥) lon halada

2 ismusA irad taraysreb snairaV 𝜀𝑖 kitsadekomoh uata natsnok halada

3 ismusA talag malad isalerokoto ada kadiT

4 ismusA malad patet( kitsakotsnon halada naksalejnem gnay lebairaV

isubirtsidreb ,kitsakots akij ,uata )gnalureb nalepmaynep irad nednepedni araces

talag 𝜀𝑖

5 ismusA sabeb lebairav aratna id satiraenilokitlum ada kadiT 𝑥

6 ismusA 𝜀 atar nagned lamron araces isubirtsidreb - gnay isnairav nad atar

.2 nad 1 ismusa helo nakirebid

rk tagnas kadit nikgnum ,1 ismusa adap nagnapmiyneP anerak sitkarp iges irad siti

tahilid tapad ini laH .iserger irad pesretni ihuragnepmem aynah nikgnum uti lah

lebairav aud ledom ,lasim : tukireb iagabes 𝑦𝑖 = 𝛽0 + 𝛽1𝑥1 + 𝜀𝑖 lasim nad 𝐸(𝜀𝑖)

adap gnutnagret 𝑥𝑖 atnatsnok nagned amas ipatet lon kadit , 𝑘. nagned ,idaJ

helorepid ,tubesret ledom irad taraysreb naparah libmagnem

𝐸(𝑦𝑖|𝑥𝑖) = 𝛽0 + 𝛽1𝑥1 + 𝐸(𝜀𝑖|𝑥𝑖)

= 𝛽0 + 𝛽1𝑥1 + 𝑘

= 𝛼 + 𝛽1𝑥1


32

anam id 𝛼 = 𝛽0 + 𝑘 awhab tahilret naka ,ihunepid kadit 1 ismusa akij ,idaJ .

narisfkanep 𝛽0 eT .nakukalid tapad kadit rusnu aynketkarp malad anerak ipat

kadit uti lah padahret naitahrep akam ,gnitnep utigeb kadit aynasaib pesretni

neisifeok halada itrareb gnay naraseb ,naujut raseb naigabes kutnU .kaynab ulalret

nagnirimek 𝛽1 sa akij nakhab ,huragnepret kadit patet gnay , kadit 1 ismu

.ihunepret

adaP .satisitsadekoreteh tubesid aguj tapad 2 ismusa padahret naraggnaleP

satisitsadekoreteh ,aynmumu ledom adap idajret gnires - nakanuggnem gnay ledom

atad ssorc - lanoitces tafisreb gnay talag anamid ,utkaw nutnur atad adap irad

ek nahaburep gniries habureb satisitsadekoreteh -i naadarebek irad isneukesnoK .

nad saib kat idajnem licekret tardauk edotem naagudnep halada satisitsadekoreteh

.)9002 ,itarajuG( netsisnok

halaS nagned halada satisitsadekoreteh aynada isketednem arac utas

iju nakanuggnem namraepS knaR hakgnal tukireB . - : aynhakgnal

.1 ialin naktapaD 𝜀𝑖 iserger irad

.2 isalerok ialin naktapaD namraepS knaR aratna |𝜀𝑖| paites nagned

mur nagned ledom malad sabeb lebairav su

𝑟𝑠 = 1 − 6 �∑ 𝑑𝑖

2

𝑛(𝑛2 − 1)�

nagneD 𝑟𝑠 isalerok neisifeok halada namraepS knaR , 𝑑𝑖 hisiles

nad ,gniknar n .natamagnep uata atad aynkaynab halada

.3 kitsitats gnutihgneM 𝑡�𝑡ℎ 𝑔𝑛𝑢𝑡𝑖 � gnisam - isalerok ialin gnisam knaR

namraepS sumur nagned


42

𝑡ℎ 𝑔𝑛𝑢𝑡𝑖 =𝑟𝑠√𝑛 − 2

�1 − 𝑟𝑠2

.4 ijU namraepS knaR

.a sisetopiH

𝐻0 satisitsadekoreteh halasam ada kadit :

𝐻1 satisitsadekoreteh halasam ada :

.b isnakifingis takgnit nautneneP (𝛼 = 0. 50 )

.c naijugnep airetirK

𝐻0 alib amiretid −𝑡 �𝛼2

, 𝑛 − 2� ≤ 𝑡ℎ 𝑔𝑛𝑡𝑖 ≤ 𝑡 �𝛼2

, 𝑛 − 2�

𝐻0 alib kalotid 𝑡ℎ𝑖 𝑔𝑛𝑡 < −𝑡 �𝛼2

, 𝑛 − 2� uata 𝑡ℎ 𝑔𝑛𝑡𝑖 >

𝑡 �𝛼2

, 𝑛 − 2�

.d .nasutupek taubmeM

kadit gnay talag nad isnairav nagned tiakret satisitsadekoreteh halasaM

.natsnok isatagnem kutnu nakanugid gnires amtiragol isamrofsnart edoteM

.satisitsadekoreteh halasam

smusA isalerokotO .talag ratna isalerokoto ada kadit awhab nakatagnem 3 i

lasim ,utnetret edoirep malad talag anam id naadaek utaus halada 𝜀𝑖 isalerokreb ,

lasim ,aynnial edoirep irad talag nagned 𝜀𝑗 . aynada isketednem arac utas halaS

nakanuggnem isalerokoto nibruD iju - iju kitsitats nagned , nostaW

𝑑 =∑ (𝜀𝑡 − 𝜀𝑡−1)2𝑁

𝑡=2

∑ 𝜀𝑡𝑁𝑡=1

𝜀𝑡 .licekret tardauk edotem naagudnep sesorp irad helorepid gnay talag ialin :

𝜀𝑡−1 .utkaw nautas utas kaynabes rudnum gnay talag ialin :


52

ialin naktapadnem haleteS d ialin nakgnidnabmem halada ayntujnales hakgnal , d

ialin nagned - irad sitirk ialin 𝐿𝑑 nad 𝑈𝑑 nibruD kitsitats lebat irad - .nostaW

:naijugnep airetirK

.1 akiJ 𝑑 < 𝐿𝑑 fitisop isalerokoto ada akam ,

.2 akiJ 𝑑 > 4 − 𝐿𝑑 fitagen isalerokoto ada akam ,

.3 akiJ 𝑈𝑑 < 𝑑 < 4 − 𝑈𝑑 isalerokoto ada kadit akam ,

.4 akiJ 𝐿𝑑 ≤ 𝑑 ≤ 𝑈𝑑 uata 4 − 𝑈𝑑 ≤ 𝑑 ≤ 4 − 𝐿𝑑 haread tubesid akam ,

ugarek - .naugar

isamrofsnart nakukalem arac nagned inagnatid tapad isalerokoto halasaM

naamasreP .atad adap amatrep naadebmep 𝑦𝑖 = 𝛽0 + 𝛽1𝑥1𝑖 + 𝜀𝑖 ukalreb nagnubuh

taas adap 𝑖 adap aguj ukalreb surah akam , 𝑖 − 1 naamasrep iaynupmem aggnihes

𝑦𝑖−1 = 𝛽0 + 𝛽1𝑥1𝑖−1 + 𝜀𝑖−1 nagned amatrep naamasrep ignarugnem nagneD .

naamasrep helorepid akam ,audek naamasrep 𝑦𝑖 − 𝑦𝑖−1 = 𝛽1(𝑥1𝑖 − 𝑥1𝑖−1) + 𝑣𝑖 ,

anam id 𝑣𝑖 = 𝜀𝑖 − 𝜀𝑖−1 .

,taraysreb halada iserger ledom kutnu natakednep awhab nakataynem 4 ismusA

lebairav irad utnetret ialin gnutnagret 𝑥 kutnu sitkarp igetats ,uti anerak helO .

ialin ada gnay halasam kutnu awhab nakismusagnem nagned halada itukiid

airav iridnes uti lebairav nupiksem utnetret halada naksalejnem gnay leb


62

.)9002 ,itarajuG( kitsakots aynranebes halada iserger sisilana irad lisah ,idaJ

malad ihunepid naka kadit aynkapmat ,ini ismusA .utnetret ialin adap gnutnagret

dom ,natlumis naamasrep ledom naamasrep utas irad hibel itupilem gnay le

tagnas naamasrep utaus malad talag rusu ,uti itrepes ledom malaD .iserger

naksalejnem gnay lebairav hibel uata utas nagned isalerokreb kutnu nikgnum

p awhab nakitkubid tapad ,ini naadaek malaD.idat naamasrep malad SLO agudne

,saib patet idat nariskanep utiay ,netsisnok kadit aguj ipatet saib aynah kadit

.aggnih kat iapmas takgninem lepmas aynraseb akij nakhab

halitsI .satiraenilokitlum ada kadit awhab nakatagnem 5 ismusA

akumekid ilak amatrep satiraenilokitlum 4391 nuhat adap hcsirF rangaR helo nak

sabeb lebairav aumes uata aparebeb aratna id raenil nagnubuh aynada itrareb gnay

.iserger malad nagned halada satiraenilokitlum aynada isketednem arac utas halaS

gnutihgnem arac airaV rotcaF noitalfnI ecn om adap )FIV( tukireB .iserger led

hakgnal - :aynhakgnal

.1 iserger nakukaL 𝑥𝑖 nagned 𝑥 neisifeok halgnutih nad nial gnay

( isanimreted 𝑅2 .)

.2 FIV gnutiH 𝑏𝑗 = 1(1−𝑅2)

.3 FIV aliB > .satiraenilokitlum ada akam ,01

arac utas halaS nagned halada satiraenilokitlum aynada ignaluggnanem kutnu

naikimed numaN .isarelokreb gnay lebairav utas halas nakgnalihgnem

susak adap nakgnalihid tapad kadit satirenilokitlum - aynlasim ,susuhk susak

kadit raga nakgnalihid tapad kadit satiraenilokitlum mukuh nagned nagnatnetreb

raseb aparebes nagnaretek iatresid surah patet ,naikimed numaN .imonoke


72

.atad malad idajret gnay satiraenilokitlum gnay lebairav nagnalihgneP

iroet nagned nagnatnetreb kadit huajes nakukalid tapad aynah satiraenilokitlum -

nay iroet .aynirasadnem g

talag awhab nakismusagnem iserger ledoM 𝜀 ,lamron isubirtsidreb

𝜀~𝑁(0, 𝜎2) nagned 𝐸(𝜀) = 0 nad 𝑟𝑎𝑣 (𝜀) = 𝜎2 lebairav irad isubirtsid aggnihes ,

sabeb kat 𝒚 naamasrep adap 𝒚 = 𝜷𝑿 + 𝜺 talag isubirtsid itukignem 𝜺 utiay ,

on isubirtsidreb atar ,uti anerak helO .lamr - irad isnairav nad atar 𝑦 tapad

: tukireb iagabes naknurutid

𝐸(𝒚) = 𝐸( 𝜷𝑿 + 𝜺) = 𝐸( 𝜷𝑿 ) + 𝐸(𝜺)

anerak 𝐸(𝜺) = 𝟎 akam ,

𝐸(𝒚) = 𝑿𝐸(𝜷) = 𝜷𝑿

aynisnairav nad

𝑟𝑎𝑣 (𝒚) = 𝑟𝑎𝑣 ( 𝜷𝑿 + 𝜺) = 𝑟𝑎𝑣 ( 𝜷𝑿 ) + 𝑟𝑎𝑣 (𝜺)

= 𝑿2 𝑟𝑎𝑣 (𝜷) + 𝑟𝑎𝑣 (𝜺) = 0 + 𝜎2 = 𝜎2

,idaJ 𝒚 atar nagned lamron isubirtsidreb - atar 𝜷𝑿 isnairav nad 𝜎2 tapad ,

idajnem nakisatonid

𝒚~𝑁( 𝜷𝑿 , 𝜎2) .

utiay ,satilamron iju utas halas nagned isketedid tapad talag nalamroneK

vorogomloK - vonrimS hakgnaL . - naijugnep hakgnal vorogomloK - nrimS vo iagabes

: tukireb


82

.a sisetopih naijugneP

𝐻0: 𝐹(𝑋) = 𝐹0(𝑋) )lamon isubirtsidreb atad(

𝐻0: 𝐹(𝑋) ≠ 𝐹0(𝑋) )lamon isubirtsidreb kadit atad(

.b isnakifingis takgnit nautneneP (𝛼 = 0. 50 )

.c iju kitsitatS

𝐷ℎ 𝑔𝑛𝑢𝑡𝑖 = mumiskam |𝐹𝑛 − 𝐹0(𝑋)|

anam id

𝐹𝑛(𝑋) halada lepmas atad nakrasadreb fitalumuk fitubirtsid isgnuf

𝐹0(𝑋) hawab id fitalumuk fitubirtsid isgnuf halada 𝐻0𝑃(𝑍 < 𝑍𝑖)

.d naijugnep airetirK

𝐻0 akij kalotid 𝐷ℎ 𝑔𝑛𝑢𝑡𝑖 < 𝐷(𝛼,𝑛) anam id , 𝑛 .natamagnep aynkaynab halada

.e K nalupmise

bid tukireb hotnoc adaP sisilana nagned sisilanaid naka gnay atad nakire

sahabid halet gnay nautnetek iagabreb nakitahrepmem nagned iserger

.aynmulebes

1.2 hotnoC

anam id iduts haubes nakrabmaggnem )5991( yremogtnoM nad sreyM

niag rotsisnart nad rotime aratna udapret tiukris takgnarep haubes malad

( rotkelok EFh tapad gnay lebairav aud nagned amasreb nakropalid )

( rotime utkaw nautnenep ,napadnegnep sesorp adap nakiladnekid 𝑥1 malad ,

( rotimesisod nad ,)tinem 𝑥2 noi malad , × 01 41 saleb tapmE .) gnay natamagnep

ledom iracnem kutnu abocid nakA .3.2 lebat adap nakkujnutid nad helorepid

nakanuggnem raenil iserger niag rotime utkaw nad sabeb kat lebairav iagabes

.sabeb lebairav iagabes rotime sisod nad


92

isavresbO 𝑥1 𝑥2 𝑦

1 591 00.4 4001

2 552 00.4 6361

3 591 06.4 258

4 552 06.4 6051

5 522 02.4 2721

6 522 01.4 0721

7 522 06.4 9621

8 591 03.4 309

9 552 03.4 5551

01 522 00.4 0621

11 522 07.4 6411

21 522 03.4 6721

31 522 27.4 5221

41 032 03.4 1231

3.2 lebaT

ledom nugabid nakA 𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝜀

: helorepid tubesret ledom nakrasadreB


03

𝑿 =

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡1111111

591552591552522522522

44

4.64.64.24.14.6

1111111

591552522522522522032

4.34.34

4.74.3

4. 274.3 ⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤

, 𝒚 =

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡

40016361

2586051272107219621

309555106216411672152211231 ⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤

𝑿′𝑿 = �41 5513 06 . 27

5513 524617 38631 .506 . 27 38631 .5 462 . 4842

�

𝑿′𝒚 = �59471

021100483757 .3

�

(𝑿′𝑿)−1 = �03 . 695742 −0. 217140 −4. 549987

−0. 217140 0. 481000 0. 830000−4. 549987 0. 830000 1. 934201

�

irad licekret tardauk agudneP 𝜷 halada

𝒃 = �− 025 .101 . 2187

− 251 . 51�

halada sata id ledom agudnep naikimed nagneD 𝑦� = − 025 .1 + 01 . 2187 𝑥1 −

251 . 51 𝑥2 .

gnutignem kutnU 𝑆𝑆 𝐸 nakulrepid

𝒚′𝒚 = [ 98872522 ]

nad

𝒃′𝑿′𝒚 = [ 76441522 .9].

akaM

𝑆𝑆 𝐸 = 𝒚′𝒚 − 𝒃′𝑿′𝒚


13

= 98872522 − 76441522 .9 = 12431 .1

d na irad saibkat agudnep 𝜎2 halada

𝜎�2 = 𝑆𝑆 𝐸𝑛−𝑝

= 12431 .141 −3

= 0221 .1

ialin helorepid haleteS 𝑆𝑆 𝐸 ialin iracid naka , 𝑆𝑆 𝑅 nad 𝑆𝑆 𝑇 : utiay ,

𝑆𝑆 𝑅 = 𝒃′𝑿′𝒚 − �∑ 𝑦𝑖41

𝑖=1 �2

𝑛

= 76441522 .9 − ( 59471 )2

41= 669156 .1

nad

𝑆𝑆 𝑇 = 𝒚′𝒚 − �∑ 𝑦𝑖41

𝑖=1 �2

𝑛

= 98872522 − ( 59471 )2

41= 783566 .2

ialiN 𝑅2 nad 𝑅 𝑗𝑑𝑎2 gnutihid tapad : nagned


= 669156 .1783566 .2

= 0. 8979

nad 𝑅 𝑗𝑑𝑎2 = 1 − (𝑛−1)

(𝑛−𝑝)(1 − 𝑅2)

= 1 − ( 31 )( 11 )

(1 − 0. 8979 ) = 0. 2679

atreS 𝑆𝑀 𝑅 = 𝑆𝑆 𝑅𝑘

= 669156 .12

= 389523

naD 𝑆𝑀 𝐸 = 𝑆𝑆 𝐸𝑛−𝑝

= 12431 .111

= 0221 .1 = 𝜎2

helorepid aggnihes

𝐹0 = 𝑆𝑀 𝑅𝑆𝑀 𝐸

= 3895230221 .1

= 762 . 771

,3 ,2 ismusa adap nakukalid naka ,ismusa naijugnep ,ayntujnaleS 6 nad ,5

.SSPS margorp nakanuggnem ismusa naijugnep malad SSPS irad lisah aumeS

.1.2 laos hotnoc naripmal adap tahilid tapad


23

amraepS isalerok iju nagned satisitsadekoreteh ismusa ijU ialin nakkujnunem n

0 halada SSPS irad helorepid gnay isnakifingis ialiN.160. 0. 160 > 0. 50 ,

ismusa iju( satisitsadekoreteh ada kadit naklupmisid tapad akam

iju naigab 1.2 laos hotnoc naripmal adap tahilid tapad satisitsadekoreteh

.)satisitsadekoreteh

ijU ialin helorepidnagnutihrep iraD.3 ismusa adap 𝑑 = 1. 296 hotnoc naripmal(

ialin helorepid ,lebat iraD .)isalerokoto iju naigab 1.2 laos 𝑈𝑑 = 1. 7055 nad

𝐿𝑑 = 0. 4509 helorepid aggnihes . 4 − 𝐿𝑑 = 3. 6490 nad 4 − 𝑈𝑑 = 2. 3944 .

,idaJ 1. 7055 < 1. 296 < 2. 3944 ada kadit akam .isalerokoto

laos hotnoc naripmal( 1=FIV ialin nakkujnunem ,satiraenilokitlum naijugneP

.satiraenilokitlum ada kadit akam ,)satiraenilokitlum iju naigab 1.2

iju nakanuggnem nagned satilamron ijU vorogomloK - vonrimS nakkujnunem

naijugnep isnakifingis ialin ismusa iju naigab 1.2 naripmal tahil( 468.0

.)lamron ialiN 0. 468 > 0. 50 .lamron araces isubirtsidreb ada gnay atad akam ,

ismusa padahret nahunemep lisah iraD - atad sisilana akam ,sata id ismusa

.dilav idajnem iserger nagned sisetopih iju nakukalid ayntukireB padahret

.aynnaayacrepek gnales nad iserger neisifeok

hakgnal nakrasadreb laudividni iserger neisifeok naijugneP - 3.4..2 adap hakgnal

:tukireb iagabes halada

𝐻0: 𝛽1 = 0

𝐻1: 𝛽1 ≠ 0


33

nakalonep hareaD |𝑡| > 𝑡0. 502 , 11 = |𝑡| > 2. 102 .

𝐶 11 = 0. 481000 nad 𝑏1 = 01 . 2187

𝑡 =𝑏1

�𝜎�2𝐶 11=

01 . 2187

�( 0221 .1)(0. 481000 )=

01 . 21870. 3474

= 22 . 37

𝐻0: 𝛽2 = 0

𝐻1: 𝛽2 ≠ 0


𝐶 22 = 1. 934201 nad 𝑏2 = − 251 . 51

𝑡 =𝑏2

�𝜎�2𝐶 22=

− 251 .5

�( 0221 .1)(1. 934201 )=

− 251 .563 . 86

= −4. 51

ialin audek aneraK 𝑡 utiay ,nakalonep haread irad raseb hibel 7. 469296 >

2. 262 nad |−4. 51 | > 2. 262 akam , 𝐻𝑜 kalotid awhab naklupmisid tapad akaM .

𝛽1 ≠ 0 itrareb gnay 𝑥1 gnay ledom padahret nakifingis araces isubirtnokreb

nad ,nakirebid 𝛽2 ≠ 0 itrareb gnay 𝑥2 padahret nakifingis araces isubirtnokreb

.nakirebid gnay ledom

eP nakutnebm retemarap kutnu naayacrepek gnales 𝛽1 gnales nakanugid naka

,%59 naayacrepek 𝑏1 = 01 . 2187 , 𝜎�2 = 0221 .1 nad 𝑒𝑠 (𝑏1) = 0. 3474 akam ,

𝑏1 − 𝑡0. 520 , 11 𝑒𝑠 (𝑏1) ≤ 𝛽1 ≤ 𝑏1 + 𝑡0. 520 , 11 𝑒𝑠 (𝑏1)


43

01 .7 218 − 2. 102 (0. 3474 ) ≤ 𝛽1 ≤ 01 . 2187 + 2. 102 (0. 3474 )

01 . 2187 − 1. 9340 ≤ 𝛽1 ≤ 01 . 2187 + 1. 9340

9. 3737 ≤ 𝛽1 ≤ 11 . 1528

retemarap kutnU 𝛽2 id naka , ,%59 naayacrepek gnales nakanug 𝑏2 = − 251 . 51 ,

𝜎�2 = 0221 .1 nad 𝑒𝑠 (𝑏2) = 63 . 86 akam ,

𝑏2 − 𝑡0. 520 , 11 𝑒𝑠 (𝑏2) ≤ 𝛽2 ≤ 𝑏2 + 𝑡0. 520 , 11 𝑒𝑠 (𝑏2)

− 251 . 51 − 2. 102 ( 63 . 86 ) ≤ 𝛽2 ≤ − 251 . 51 + 2. 102 ( 63 . 86 )

− 251 . 51 − 08 . 86237 ≤ 𝛽2 ≤ − 251 . 51 + 08 . 86237

− 232 . 388 ≤ 𝛽2 ≤ − 17 . 3714


53

III BAB

KISNIRTNI RAENIL LEDOM

kisnirtnI raeniL isergeR nasagaG aynlucnuM .A

sahabid halet aynmulebes bab adaP ajrek akgnarek gnay nakanugid tapad

ihunemem kutnu nahutubek nugnabmem ledom arap igab silana .atad ,numaN

anam id isautis kaynab adA .isautis aumes kutnu iauses kadit raenil iserger ledom

lebairav sabeb kat lebairav nad kutneb malad nagnubuhreb gnilas sabeb isgnuf

raenilnon aggnihes , raenilnon iserger ledom nakulrepid . naikimed nagneD

e etemarap isamits ledom isnerefni nad r naktabilem nagned kococ hibel ledom

adapirad raenilnon iserger raenil edoteM akitek ,aynlasiM . licekreT tardauK

naklisahid gnay lamron naamasrep ,raenilnon iserger ledom adap nakparetid

tafisreb acemem kutnu tilus gnires nad raenilnon nakh ayn mumu gnay natakedneP .

halada nagned tardauk halmuj naklaminimem gnusgnal sesorp iulalem talag

isareti . iD s uti gnipma iroet - ukalreb gnay iroet kadit raenil iserger ledom malad

malad ek nakukalrebid tapad .raenilnon iserger ledom

nakapurem gnay kisnirtni raenil ledom nasagag sahabid naka ini bab adaP

isamrofsnartid tapad aynhuggnuses numan raenilnon ”aynkapmat” gnay ledom

malad iakapid asaib gnay nalupmisek nakiranep sesorp aggnihes raenil idajnem

akparetid tapad raenil ledom .n


63

)a raenilnoN isergeR

kadit reinil iserger ledom anam id isautis kaynab adA kococ . iagabeS

,hotnoc gnaroes silana gnusgnal araces nauhategnep ikilimem irad

lebairav aratna nagnubuh sabeb kat nad sabeb lebairav , gnay nikgnum

lasareb adnem gnay iroet irad aratna raneb gnay nagnubuH .anemonef iras

lebairav nad nopser sabeb lebairav uata ,laisnerefid naamasrep halada

isulos irad .laisnerefid naamasrep surah ledom idaJ b malad kutne

.raenilnon

gnay ledom gnarabeS kadit gnay retemarap malad raenil kadit

id iuhatek tubesid ledom ,hotnoc iagabeS .raenilnon iserger ledom

𝑦 = 𝛽1𝑒𝛽2𝑥 + 𝜀 .3( 1)

retemarap malad reinil kadit 𝛽1 nad 𝛽2 ,mumu araceS . tubesret ledom

tid tapad iagabes silu tukireb

𝑦 = 𝑓(𝐱, 𝜷) + 𝜀 .3( 2)

anam id 𝜷 rotkev halada 𝑝 × 1 nad ,iuhatekid kadit gnay retemarap irad ɛ

halada kadit gnay talag nagned isalerokreb 𝐸(𝜀) = 0 nad 𝑟𝑎𝑣 (𝜀) = 𝜎2 .

ketkarp malaD , ,lamron isubirtsidreb talag awhab nakismusaid gnires

.raenil iserger malad itrepes K anera

E(𝑦) = E[𝑓(𝐱, 𝜷) + 𝜀]

= 𝑓(𝐱, 𝛃) .3( 3)

𝑓(𝐱, 𝛃) tubesid isgnuf isatkepske irad .raenilnon iserger ledom i laH in

isgnuf gnarakes awhab ilaucek ,raenil iserger susak nagned pirim tagnas

.retemarap irad raenilnon isgnuf halada naparah iserger ledom malaD


73

naparah isgnuf irad laisrap nanurut irad utas halas aynkadites ,raenilnon

irad utas aynkadites adap gnutnagret retemarap nagned nagnubuhes

,reinil iserger malaD .retemarap nanurut ini nakub isgnuf irad retemarap

.iuhatekid kadit gnay isartsuli iagabeS , dna nakia raenil iserger ledom

( naamasrep malad 2.2 isatkepske isgnuf gnay ,) ayn halada

𝑓(𝒙, 𝜷) = 𝛽0 + � 𝛽𝑗𝑥𝑗

𝑘

𝑗=1

nanuruT isgnuf irad laisrap isatkepske tukireb iagabes halada

𝜕ƒ (𝐱 ,𝛃)𝑗𝛽𝜕

= 𝑥𝑗, , . . . ,1 ,0 = j k

anamid kutnu 𝑥0 = 1 .pesretni ilikawem gnay ymmud lebairav halada

laisrap nanurut awhab nakitahreP nakapurem nakub tubesret irad isgnuf

iserger ledom nakitahrep gnarakeS .iuhatekid kadit gnay retemarap

aenilnon r

𝑦 = 𝑓(𝒙, 𝜷) + 𝜀

= 𝛽1𝑒𝛽2𝑥 + 𝜀 .3( 4)

nanuruT ad laisrap naparah isgnuf ir padahret 𝛽1 nad 𝛽2 halada

𝜕ƒ (𝑥 ,𝜷)𝜕𝛽1

= 𝑒𝛽2𝑥

𝜕ƒ (𝑥 ,𝜷)𝜕𝛽2

= 𝛽1 𝑥 𝑒𝛽2𝑥

aneraK nanurut laisrap tubesret kadit gnay retemarap irad isgnuf halada

iuhatekid 𝛽1 nad 𝛽2 akam , ledom halada tubesret .raenilnon

ledom haburem kutnu raenil isamrofsnart nakhutubid gnadakreT

isgnuf aynah ilakgnires ,numaN .raenil ledom idajnem raenilnon iserger


83

hilimem akitek nakitahrepid gnay isatepske isamrofnart iagabeS .tubesret

ledom nakitahrep ,hotnoc

𝑦 = 𝑓(𝑥, 𝜷) + 𝜀

= 𝛽1𝑒β2x + 𝜀 )5.3(

halada isatepske isgnuf anerak ,gnarakeS 𝐸(𝑦) = 𝑓(𝑥, 𝜷) = 𝛽1𝑒β2x ,

arac nagned nakraenilid hadum nagned tapad tubesret isatepske isgnuf

tubesret isgnuf irad amtiragol taubmem

nl 𝐸(𝑦) = nl 𝛽1 + 𝛽2𝑥

iagabes iserger ledom idajnem gnalu silutid tapad tubesret isgnuf idaJ

tukireb

nl (𝑦) = nl 𝛽1 + 𝛽2𝑥 + 𝜀

𝑦∗ = 𝛼0 + 𝛼1𝑥 + 𝜀 )6.3(

anamid 𝑦∗ = nl (𝑦) kutnu nakanugid tapad raenil iserger agudnep edotem ,

retemarap agudnem 𝛼0 nad 𝛼1.

natakednep adap nakitahrepid surah hibel gnay naitiletek takgniT

urab gnay ledom nagned raenil retemarap agudnep ,mumu araceS .ini

nelavike naka kadit )6.3( naamasrep adap retemarap irad licekret tardauk

d ilsa ledom adap raenilnon retemarap agudnep nagned .)5.3( naamasrep ira

nakisakilpmignem ilsa gnay licekret tardauk raenilnon ledom aneraK

isasilaminim halmuj talag tardauk adap 𝑦 gnay ledom adap anamid ,

tardauk halmuj naklaminimem atik isamrofsnartid talag amtiragol adap

irad 𝑦 .


93

m adap nakitahreP )5.3( naamasrep adap ilsa raenilnon ledo

rutkurts iaynupmem talag amtiragol aggnihes ,nahalmujnep tafisreb gnay

.3( naamasrep irad 5 naklisahgnem kadit ) akij ,numaN .)6.3( naamasrep

rutkurts talag akam nailakrep tafisreb

𝑦 = 𝑓(𝑥, 𝜷)(1 + 𝜀)

= 𝛽1𝑒β2x𝜀∗ )7.3(

anerak tapet halada amtiragol libmagnem nad

nl (𝑦) = nl 𝛽1 + 𝛽2𝑥 + nl ε∗

𝑦∗ = 𝛼0 + 𝛼1𝑥 + 𝜀∗∗ )8.3(

anamid 𝑦∗ = nl (𝑦) nad 𝜀∗∗ = nl ε∗

akij ,gnarakeS talag halada urab gnay 𝜀∗∗ reb nagned lamron isubirtsid

isnairav natsnok , akam ledom nalupmisek nakiranep radnats rudesorp

.nakisakilpaid tapad raenil iserger

idajnem nakisamrofsnartid tapad gnay raenilnon iserger ledom utauS

tubesid nelavike gnay raenil iserger ledom aenil ledom kisnirtni r .

)b macaM - kisnirtnI raeniL ledoM macaM

.1 fitakilpitluM ledoM

𝒀 = 𝜶 𝑿1𝛽 𝑿𝟐

𝛾 𝑿3𝛿 𝜺 )9.3(

anamid 𝜶, 𝛽, 𝛾, 𝛿 nad iuhatekid kadit gnay retemarap halada 𝜀

nakanuggnem nagneD .fitakipitlum tafisreb gnay talag halada


04

amtiragol sisabreb 𝑒 ledom akam ,)9.3( naamasrep adap ,)nl( ,

raenil kutneb idajnem habureb tubesret

nl 𝑌 = nl 𝛼 + 𝛽 nl 𝑋1 + 𝛾 nl 𝑋2 + 𝛿 nl 𝑋3 + nl 𝜀 )01.3(

rudesorp aggnihes raenil kutneb idajnem halet )01.3( naamasreP

.nakukalrebid tapad ukab raenil ledom isamitse

.2 M laisnenopskE ledo

𝒀 = 𝒆𝜷𝟎+𝜷𝟏𝑿𝟏+𝜷𝟐𝑿𝟐. 𝜺 )11.3(

arac nagned raenil kutneb idajnem haburid tapad )11.3( naamasreP

kutneb helorepid aggnihes saur audek nakamtiragolem

𝒏𝒍 𝒀 = 𝜷𝟎 + 𝜷𝟏𝑿𝟏 + 𝜷𝟐𝑿𝟐 + 𝒏𝒍 𝜺 aggnihes nakiranep sesorp

.nakukalrebid tapad raenil ledom malad nalupmisek

.3 lakorpiseR ledoM

𝒀 = 𝟏𝜷𝟎+𝜷𝟏𝑿𝟏+𝜷𝟐𝑿𝟐+ 𝜺

)21.3(

nakilabek isarepo nagned isamrofsnartid sata id naamasrep aliB

helorepid naka )srevni(

𝟏𝒀

= 𝜷𝟎 + 𝜷𝟏𝑿𝟏 + 𝜷𝟐𝑿𝟐 + 𝜺 laD . lebairav nakilabek ,ini lah ma

.nopser lebairav iagabes nakanugid surah sabeb

.4 timuR hibeL gnay laisnenopskE ledoM

𝒀 = 𝟏𝟏+𝒆𝜷𝟎+𝜷𝟏𝑿𝟏+𝜷𝟐𝑿𝟐+ 𝜺 )31.3(

naidumek nad 1 ignarugnem ,nakilabek isamrofsnartnem nagneD

am ,saur audek nakamtiragolem helorepid ak

𝒏𝒍 �𝟏𝒀

− 𝟏� = 𝜷𝟎 + 𝜷𝟏𝑿𝟏 + 𝜷𝟐𝑿𝟐 + 𝜺 .


14

isaretiret isamrofsnart lisah hotnoc nakapurem sata id naamasreP

gnay raenilnon ledom habugnem kutnu sabeb kat lebairav padahret

.raenil ledom idajnem timur hibel

.5 laisnenopskE nahubmutreP ledoM

𝑌𝑖 = 𝛼𝑒𝛽𝑋𝑖𝜀𝑖 )41.3(

id ialum nahubmutrep isgnuF 𝑌𝑖 = 𝛼 anamid 𝑋 = 0 takgninem nad

irad fitaler gnay ujal nagned nagned laisnenopske araces

ek amas gnay nahubmutrep 𝛽(𝛼 > 0, 𝛽 > 0 nanurunep ledoM .)

gned ipatet amas gnay kutneb ikilimem laisnenopske akgnaj na

adap ialumid nanurunep ledoM .fitagen laisnenopske utkaw 𝑌𝑖 = 𝛼

anamid 𝑋 = 0 nagned amas fitaler gnay ujal nagned nurunem nad

𝛽 nagned raenil idajnem sata id laisnenopske isgnuf audeK .

,nahubmutrep ledom kutnu ,akaM .amtiragol isamrofsnart

𝑌𝑖∗ = 𝛼∗ + 𝛽𝑋𝑖 + 𝜀𝑖

∗ )51.3(

anam iD 𝑌𝑖∗ , 𝛼 nad , 𝜀𝑖

∗ iauses gnay ialin irad imala amtiragol halada

.ilsa ledom malad

.6 laimoniloP srevnI ledoM

kutneb ikilimem ini ledoM

𝑌𝑖 = 𝑋𝑖𝛼+𝛽𝑋𝑖+𝜀𝑖

)61.3(

abmag malad nakisartsuliid ,ini isgnuF isgnuf halada ,2.21 r

irad kian notonom 𝑋 totmisa itakednem tabmal tagnas gnay

𝑌 = 1 𝛽⁄ . 𝑌 id ,srevni isarepo nagned isamrofsnartid anam

𝑌∗ = 1 𝑌⁄ idajnem sataid naamasrep akam ,


24

𝑌𝑖∗ = 𝛽 + 𝛼 � 1

𝑋𝑖� + 𝜀𝑖

∗ )71.3(

,akaM 𝑌∗ d utas tajaredreb laimonilop halada mala 1 𝑋⁄ nagned

pesretni 𝛽 nagnirimek nad 𝛼 ialiN . 𝑋 surah lon nagned amas

.ajrekeb tapad tubesret isamrofsnart raga iradnihid

.7 kitsigoL ledoM

𝑌𝑖 = 𝛼1+𝛾𝑒−𝛽𝑋𝑖𝜀𝑖

)81.3(

ialum kitsiretkarak nahubmutrep avruk nakirebmem ini isgnuF

𝑌 = 𝛼 (1 + 𝛾)⁄ id 𝑋 = 0 ek totmisa nad 𝑌 = 𝛼 aggnihes 𝑋

raenil tubesid isgnuF .)2.3 nad 1.3 rabmag( raseb nikames idajnem

ialin aynah akij kisnirtni 𝛼 ,susak malad itrepes ,iuhatekid

gnay udividni isroporp halada nedneped lebairav akitek ,aynlasim

t iskaer nakkujnunem akiJ .natabognep padahre 𝜎 ledom ,iuhatekid

kutneb malad reanil ini

𝑌∗ = 𝑛𝑙 �𝛼𝑌

− 1� )91.3(

idajnem ledom naD

𝑌𝑖∗ = 𝛾∗ − 𝛽𝑋𝑖 + 𝜀𝑖

∗ )02.3(

anam iD 𝛾∗ = 𝑛𝑙 (𝛾) nad 𝜀𝑖∗ = 𝑛𝑙 (𝜀𝑖) .


34

1.3 rabmaG

2.3 rabmaG

.8 laimonilop ledoM

sabeb kat lebairav aratna nakismusaid raenil nagnubuh haubeS

nahaburep ujal nakkujnunem )tupni( sabeb lebairav nad )nopser(

raneb gnay nagnubuh ilikawem kadit nikgnum nad natsnok - raneb

harad narila malad tabo isartnesnok ,hotnoc iagabeS .iadamem

it nikgnum imonoke lebairav aparebeB .utkaw padahret raenil kad

nert nagned nakgnubuhid isalfni skedni itrepes utkaw nutnur

.utkaw padahret raenil kadit nikgnum gnay oturb kitsemod kudorp

nagned nurunem tapad euk gnaggnamem kutnu utkaw nupikseM

nevo uhus naktakgninem kadit nikgnum aynnagnarugnep ipatet ,

malad nahaburep takgnit ,ini hotnoc aumes malaD .reinil araces

y

y

x

x


44

atar - sabeb kat lebairav irad atar (𝑌) lebairav padahret natsnok kadit

sabeb (𝑋).

gnay ledom irad raenil nasaulrep irad anahredes gnilap hotnoC

naktabilem laimonilop ledom halada nednepedni lebairav utas

,)tardauk( audek naturu

𝐸(𝑌) = 𝛽0 + 𝛽1𝑋 + 𝛽2𝑋2 )12.3(

ukus taumem tardauk ledoM 𝑋2 nad 𝑋 ini ledom natatac iagabeS .

anam id adnagreb iserger ledom irad susuhk susak halada 𝑋1 = 𝑋

nad 𝑋2 = 𝑋2 . kutneb irad iggnit edro laimoniloP

𝐸(𝑌) = 𝛽0 + 𝛽1𝑋 + 𝛽2𝑋2 + 𝛽3𝑋3 + ⋯ + 𝛽𝑝𝑋𝑝 )22.3(

aguj nad nopser nagnubuh satilibiskelf natakgninep naknikgnumem

anam id iserger ledom irad susuhk susak 𝑋𝑖 = 𝑋𝑖 , 𝑖 = 1, ⋯ , 𝑝 .

dom tubesid 22.3 naamasrep adap ledoM tajared laimonilop le 𝑝

aynnakadebmem gnay laimonilop ledom irad gnitnep kepsa haubeS

atar awhab halada aynnial iserger ledom irad - lebairav atar

nupikseM .laggnut sabeb lebairav irad isgnuf halada nedneped

apad mumu iserger ledom malad nednepedni lebairav t

isgnuf nakismusaid kadit aynasaib ,nial amas utas nagnubuhreb

ledom malad "nednepedni" lebairav awhab atkaF .nial amas utas

laggnut sabeb lebairav irad isgnuf halada anahredes laimonilop

ledom ,aynlasim ,nakitahreP .retemarap isaterpretni ihuragnepmem

𝐸(𝑌) = 𝛽0 + 𝛽1𝑋1 + 𝛽2𝑋2 )32.3(

,ini ledom malaD 𝛽1 atar malad nahaburep iagabes nakrisfatid - atar

nautas rep nahaburep idajret alib nedneped lebairav irad 𝑋1 kutnu

irad patet ialin paites 𝑋2 ,aguJ( 𝛽2 atar malad nahaburep halada - atar

lebairav irad nahaburep nautas rep nedneped 𝑋2 ialin paites adap

irad patet 𝑋1 akij ,numaN .) 𝑋2 = 𝑋12 nahaburep naidumek , 𝑋1


54

ialin habugnem naka aguj nautas utas rasebes 𝑋2 ledom malaD .

atar nahaburep ujal ,12.3 naamasrep ,aud tajared - lebairav atar

agabes nedneped irad isgnuf i 𝑋 tubesid nagnirimek id X uata

nanurut adap 𝑋 padahret 12.3 naamasrep nanurut ,suluklak iraD . 𝑋

halada

𝐸𝑑 (𝑌)𝑋𝑑

= 𝛽1 + 2𝛽2𝑋 )42.3(

nagnirimek ,aynitrA 𝐸(𝑌) lebairav ialin adap gnutnagret

retemaraP .nednepedni 𝛽1 adap aynah nagnirimek halada 𝑋 = 0 .

retemaraP 𝛽2 nahaburep natapecek hagnetes halada 𝐸(𝑌) ,uata

nagnirimek malad nahaburep takgnit hagnetes halada uti ,amas

𝐸(𝑌) .

lebairav utas malad laimonilop ledom paites awhab nakitahreP

nagned ilikawem tapad ,isnemid aud kifarg adap gnukgnel tolp

anerak ,iggnit hibel gnay isnemid gnaur malad naakumrep adapirad

sabeb lebairav irad isgnuf iagabes paggnaid nedneped lebairav

.laggnut

tas sata iridret tapad ledom awhab tahilid tapad ,8 iapmas 1 ledom iraD : natataC u

isamrofnart ,naikimed nagneD .sabeb lebairav utas irad hibel nad sabeb lebairav

ledom padahret raenil - anahredes raenil ledom naklisahgnem naka tubesret ledom

nautnetek itukignem sisilana sesorp ,uti anerak helO .adnagreb raenil ledom nad

esret ledom adeb .tub

.B pahaT - ataD nakrasadreB ledoM nalanegneP pahaT

.1 tolp rettacs nakanuggnem nagned atad rabmaggneM

.2 rabmag itakednem gnilap gnay kisnirtni raenil ledom utas halas hilimeM

raenil iserger ledom idajnem atad nakisamrofsnartnem nad 1 romon adap

d nelavike gnay .lawa atad nagne


64

.3 : nakrasadreb kiab gnilap gnay ledom ijugneM

𝑅2 iggnit gnilap gnay ialin ikilimem

𝑒𝑠 hadner gnilap gnay

iserger neisifeok irad isnakifingiS

ismusa irad nahunemeP - .naayacrepek gnales ismusa

hotnoc adaP - c utas ada aynah ,tukireb hotnoc naka gnay 3.3 hotnoc utiay hotno

.ledom naagudnep nakukalid naka aynah aynnialeS .pakgnel araces sisilanaid

1.3 hotnoC

iraD .4791 adap akubid ,ijas tapec nanakam iadek ,sesuohkaetS s`lliB raiL

4791 nuhat - ,isareporeb gnay sesuohkaets halmuj 8891 𝑦𝑡 naklasiM .tatacid ,

𝑡 = 1 ,4791 nuhat kutnu 𝑡 = 2 anam id ,aynsuretes nad ,5791 nuhat kutnu 𝑡

nuggnem nigni naahasurep kutnu silana gnaroeS .utkaw skedni halada atad naka

T malad nakijasid( ini igab nahubmutrep takgnit nakarikrepmem kutnu )1.3 leba

.naahasurep

T nuha T tY tY nl 4791 1 11 598793.2 5791 2 41 750936.2 6791 3 61 985277.2 7791 4 22 240190.3 8791 5 82 502233.3 9791 6 63 915385.3 0891 7 64 146828.3 1891 8 76 396402.4 2891 9 28 917604.4 3891 01 99 21595.4 4891 11 911 321977.4 5891 12 651 658940.5


74

6891 13 752 670945.5 7891 14 482 479846.5 8891 15 304 739899.5

1.3 lebaT

ledom awhab ayacrep silana ,inis iD

𝑦𝑡 = 𝛽𝑜(𝛽1𝑡)𝜀𝑡 kutnu 𝑡 = 0,1,2, … , 41

awhab nakkujnunem ini ledoM .tapet nikgnum

𝑦𝑡 = [𝛽0(𝛽1𝑡−1)]𝛽1𝜀𝑡 ≈ (𝑦𝑡−1)𝛽1𝜀𝑡

awhab nakatagnem ini laH 𝑦𝑡 ratikes idajnem nakparahid 𝛽1 ilak 𝑦𝑡−1 iagabeS .

irad aynranebes ialin akij ,hotnoc 𝛽1 akam ,3,1 halada 𝑦𝑡 idajnem nakparahid

ilak 3,1 ratikes 𝑦𝑡−1 awhab nakatagnem ini laH . 𝑦𝑡 ratikes idajnem nakparahid

001 (𝛽1 − 1)% = 001 (1.3 − 1)% = 03 %.

tubes atiK 001 (𝛽1 − 1)% uhat kadit atik aneraK .naahasurep nahubmutrep ujal

irad aynranebes ialin 𝛽1 naayacrepek lavretni nad isamitse kitit helorepid naka ,

.ini nahubmutrep takgnit kutnu %59

mutreP T malad nakirebid ini atad nahub b ,1.3 leba ilsa amtiragol nagned amasre

irad 𝑦𝑡 ilsa kaets ataD .nuhat paites kutnu (𝑦𝑡) utkaw padahret tolpid (𝑡) adap

.3.3 rabmaG


84

3.3 rabmaG

anam id laisnenopske natakgninep nakkujnunem ini tolP laH .1 irad raseb hibel

ledom awhab nakkujnunem ini

id edoirep utkaw halada nednepedni lebairav anam alop nagned kococ nikgnum ,

( kaets irad ilsa amtiragoL .atad .4.3 rabmaG adap tolpid )

4.3 rabmaG

aratna nagnubuh awhab nakkujnunem ini tolP nad nagneD .raenil halada

helorepid ,sata id ledom nagned kimtiragol isamrofsnart nakparenem

0

001

002

003

004

005

0 5 01 51 02

01234567

0 5 01 51 02

tY nL

t

tY

t


94

anamid , nad , akam ,

em haloid aidesret halet gnay atad akam ,tubesret naagudnep iraD nakanuggn

)1.3 hotnoc naripmal tahil( halada helorepid gnay lisaH .SSPS

oN ledoM neisiffeoK agudneP radnatSrorrE

1 raeniL 699.0 2 amtiragoL 3 srevnI

4 kitardauK 699.0 5 kibuK

699.0

6 htworG 789.0 7 laisnenopskE 789.0 8 citsigoL

789.0

5.3 rabmaG

nLy


05

halada kiabret gnay ledom akam ,SSPS nagned atad nahalognep iraD

𝑌 = 2. 741 + 0. 32 𝑥 + 0. 200 𝑥2

2.3 hotnoC

,namalagnep huragnep iuhategnem nigni aragen utaus nakajaprep nemetrapeD 𝑥 ,

,utkaw utaus adap 𝑦 natapadnep kutneb ,GV A0401 TS isignem kutnu nakulrepid ,

atar - nalisahgnep nagned gnaro nalibmes ,ini lah nakukalem kutnU .aragen atar

atar - gnisaM .kaca araces hilipid pukuc gnay atar - isignem kutnu atnimid gnisam

d( utkaw nakropalem nad GV A401 TS rilumrof kutnu nakulrepid gnay )maj mala

nikgnum atiK .isi ai tapad gnay rilumrof aynkaynab nad rilumrof ipakgnelem

itrepes ledom isapisitnagnem

𝑦 = 𝛽0 + 𝛽1 �1𝑥

� + 𝜀

gnay utkaw nakbabeynem tapad sigol araces utkaw ek utkaw irad rajaleb anerak

isignem kutnu nakhutubid .totpmisa ialin hara ek nurunem GV A401 TS rilumrof

,uti anerak helO 𝑥 .lihatsum halada lon nagned amas

.2.3 lebat malad nakirebid kajap rilumrof naabocrep malad helorepid gnay ataD

gnaro Y X 1 8 1 2 7.4 8 3 7.3 4 4 8.2 61 5 9.8 1 6 8.5 2 7 2 21 8 9.1 5 9 3.3 3

2.3 lebaT


15

anam iD Y nad rilumrof isignem kutnu utkaw halada X aynkaynab halada

.isiid tapad gnay rilumrof ialin nakkujnunem 6.3 rabmaG 𝑦 nad 𝑥 awhab kapmaT .

id nanurunep nagnurednecek 𝑦 ialin ayntakgninem nagned 𝑥 gnay alop malad

nok .naklusuid gnay ledom nagned netsis

rabmag haubeS 𝑦 padahret 1 / 𝑥 awhab nakitahreP .7.3 rabmaG adap nakkujnutid

isamitsE .raenil gnay nalipmanep ikilimem ini tolp 𝛽0 nad 𝛽1 nagned

6.3 rabmaG

7.3 rabmaG

0

1

2

3

4

5

6

7

8

9

01

0 5 01 51 02

y

x

0

1

2

3

4

5

6

7

8

9

01

0 2.0 4.0 6.0 8.0 1 2.1

y

x/1


25

𝒚 =

⎣⎢⎢⎢⎡8.04.73.7

⋮3.3⎦

⎥⎥⎥⎤ nad 𝑿 =

⎣⎢⎢⎢⎡111⋮1

1. 0000. 5210. 052

⋮0. 333 ⎦

⎥⎥⎥⎤

irad audek molok ,inis iD 𝑿 .namalagnep natamagnep slakorpiser isireb

lisaH .SSPS nakanuggnem nagned haloid atad ,sataid naagudnep nakrasadreB

,)2.3 hotnoc naripmal tahil( SSPS margorp nagned helorepid gnay

oN ledoM neisiffeoK agudneP radnatSorrE r 𝑅 𝑗𝑑𝑎

2

1 raeniL 𝑌 = 2. 850 + 6. 453 𝑥 920.1 538.0 2 amtiragoL 𝑌 = 7. 614 + 2. 511 nl (𝑥) 774.1 066.0

3 srevnI 𝑌 = 6. 663 − 0. 113 �1𝑥

� 070.2 233.0

4 kitardauK 𝑌 = 2. 333 + 4. 364 𝑥 + 1. 507 𝑥2 001.1 118.0

5 kibuK 𝑌 = 3. 304 − 9. 953 𝑥 + 04 . 934 𝑥2

− 62 . 720 𝑥3 531.1 997.0

6 htworG 𝑌 = 0. 378 𝑒1. 092 𝑥 213.0 786.0 7 laisnenopskE 𝑌 = 2. 393 𝑒1. 092 𝑥 213.0 786.0

8 citsigoL 𝑌 =1

1 + 𝑒−(0. 814 +0. 572 𝑥) 213.0 786.0


35

8.3 rabmaG

halada kiabret gnay ledom akam ,SSPS nagned atad nahalognep nakrasadreB

.

aneraK awhab nakifingis gnay itkub helorepmem atik ,fitisop ialinreb .

akiJ naamasrep , awhab nakatagnem , atar( - utkaw atar

padahret nurunem naka )rilumrof naisignep nakiaseleynem kutnu rasebes .

gnay itkub helorepmem atik akaM atar awhab nakatagnem kutnu nakifingis - atar

namalagnep nakianek nagned gnarukreb tubesret rilumrof isignem kutnu utkaw

.nasisignep

3.3 hotnoC

anamid ,mizne iskaer natapecek irad atad naktahilrepmem )8891( sttaW nad setaB

turalep irebid natural nicimorup gnatnet ataD .isartnesnok aparebeb adap

margaid nad 3.3 lebat adap nakkujnutid isartnesnok nad iskaer natapecek

y


45

naamasrep agudid naka ,ini hotnoc iraD .9.3 rabmag adap nakkujnutid aynracnep

d aynnatapecek nad tartsbus isartnesnok nakgnubuhgnem gnay iserger na .

tartsbus isartnesnok natapecek mpP ( nim/stnuoc 2)

20.0 74 67 60.0 79 701 11.0 321 931 22.0 251 951 65.0 191 102 01.1 002 702

3.3 lebaT

9.3 rabmaG

sileahciM ledom nakanuggnem sttaW nad setaB - aimik akitenik kutnu netneM

)52.3(

sileahciM ledom irad isatepske isgnuf awhab nakitahreP .tubesret atad adap -

tukireb iagabes hadum araces raenil idajnem taubid tapad netneM


55

1𝑓(𝑥𝑖,𝜷)

= 𝛽2+𝑥𝑖𝛽1𝑥𝑖

= 1𝛽1

+ 𝛽2𝛽1

1𝑥𝑖

= 𝛼0 + 𝛼1𝑧𝑖

anamid 𝑧 = 1𝑥𝑖

iserger ledom nagned iauses tubesret naamasrep uti babes helO .

raenil

𝑦�𝑖∗ = 𝛼0 + 𝛼1z𝑖 + 𝜀𝑖

nagned 𝑦𝑖∗ = 1

𝑦𝑖 atapecek irad kilabret nagnidnabrep halada .itamaid gnay n

hakgnal nagned gnutihid tapad iauses gnay licekret tardauk agudneP - hakgnal

8.2 naamasrep nakrasadreb tukireb

𝑿 =

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡1111

0505

61 . 766661 . 7666

11111111

9. 9090909. 9090904. 4545454. 4545451. 4175871. 4175870. 1909090. 190909 ⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤

𝒚 =

⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡0. 7721200. 8513100. 9030100. 6439000. 0318000. 4917000. 9756000. 9826000. 6325000. 5794000. 0005000. 138400 ⎦

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤

𝑿′

= � 1 1 105 05 61 . 7666

1 1 161 . 7666 9. 909090 9. 909090

1 1 14. 454545 4. 454545 1. 7587

1 1 11. 7587 0. 90909 0. 90909 �

𝑿′𝑿 = � 21 561 . 7599561 . 7599 0775 . 965791 �

(𝑿′𝑿)−1 = �0. 514831 −0. 89300−0. 89300 0. 882000 �


65

margaid nakkujnunem a01.3 rabmaG racnep halet gnay atad irad

aparebeb tapadret aneraK .iauses gnay surul sirag iatresid nagned isamrofsnartid

isnairav awhab 9.3 rabmag irad tahilid hadum nagned tapad ,atad irad nahaburep

nakkujnunem a01.3 rabmag adap ipatet ,natsnok itakednem nopser atad irad

ab irad huaj nakisamrofsnartid gnay alaks adap isnopser atad irad isnairav awh

.natsnok

a01.3 rabmaG


75

b01.3 rabmaG

( )01.3 rabmaG srevni nagned natapecek srevni irad rabmaG )a(

mulebes( ilsa atad irad avruk agudneP )b( .nicimorup atad irad isartnesnok

.)isamrofsnartid

tukireb iagabes halada retemarap aratna nagnubuh ,ayntujnaleS

𝛼0 =1𝛽1

nad

𝛼1 =𝛽2

𝛽1

igab agudnep nakisutitbusnem nagned ,uti babes helO 𝛽1 nad 𝛽2 helorepid

0, 701500 =1𝑏1

nad

0, 2742000 =𝑏2

𝑏1


85

retemarap agudneP 𝛽1 nad 𝛽2 halada ilsa raenilnon ledom nakanuggnem nagned

𝑏1 = 591 . 18

nad

𝑏2 = 0. 14840

nakgnidnasid gnay ilsa alaks irad raenilnon ledom nakkujnunem b01.3 rabmaG

atad narabes itakednem tubesret avruk awhab nakitahreP .atad narabes nagned

atad kutnu ilaucek .hadner hibel gnurednec gnay iggnit isartnesnok adap

gnutihid naka ayntujnaleS 𝑅2 nad 𝑅 𝑗𝑑𝑎2 .launam araces nakukalid nagnutihreP .

: tukireb iagabes halada helorepid gnay lisaH

𝒚′𝒚 = 0. 121100

𝒃′𝑿′𝒚 = 0. 580100

𝑆𝑆 𝐸 = 𝒚′𝒚 − 𝒃′𝑿′𝒚 = 0. 121100 − 0. 580100 = 3. 95 E − 50

𝑆𝑆 𝑅 = 𝒃′𝑿′𝒚 −(∑ 𝑦𝑖

21𝑖=1 )𝟐

𝑛= 0. 580100 −

0. 7401021

= 0. 872212000

𝑆𝑆 𝑇 = 𝒚′𝒚 − �∑ 𝑦𝑖21

𝑖=1 �2

𝑛= 0. 121100 − 0. 74010

21= 0. 842000

𝜎2 = 𝑆𝑆 𝐸𝑛−𝑝

= 3. 95 E− 5001

= 3. 32585 E − 60


= 0. 8722120000. 842000

= 0. 15558

𝑅 𝑗𝑑𝑎2 = 1 − (𝑛−1)

(𝑛−𝑝)(1 − 𝑅2) = 1 − 11

01(1 − 0. 15558 ) = 0. 160148


95

5 nad ,3 ,2 ismusa adap nakukalid naka ,ismusa naijugnep ,ayntujnaleS

.SSPS margorp nakanuggnem ismusa naijugnep malad SSPS irad lisah aumeS

3.3 hotnoc naripmal adap tahilid tapad

agned satisitsadekoreteh ismusa ijU ialin nakkujnunem namraepS isalerok iju n

529.0 halada SSPS irad helorepid gnay isnakifingis ialiN . 0. 529 > 0. 50 akam ,

adap tahilid tapad satisitsadekoreteh ismusa iju( ada kadit satisitsadekoreteh

.)satisitsadekoreteh iju naigab 3.3 laos hotnoc naripmal

ialin helorepid ,3 ismusa adap ijU 𝑑 = 2. 337 naigab 3.3 laos hotnoc naripmal(

ialin helorepid ,lebat iraD .)isalerokoto iju 𝑈𝑑 = 1. 4133 nad 𝐿𝑑 = 0. 8079 ,

helorepid aggnihes 4 − 𝐿𝑑 = 3. 2920 nad 4 − 𝑈𝑑 = 2. 6866 ,idaJ . 2. 6866 <

2. 337 < 3. 2920 akam 𝑑 ugar haread adap adareb - naklupmisid tapad kadit( ugar

.)isalerokoto aynkadit uata ada

laos hotnoc naripmal( 1=FIV ialin nakkujnunem ,satiraenilokitlum naijugneP

.satiraenilokitlum ada kadit akam ,)satiraenilokitlum iju naigab 3.3

atilamron ijU iju nakanuggnem nagned s vorogomloK - vonrimS nakkujnunem

naijugnep isnakifingis ialin .)lamron ismusa iju naigab 1.2 naripmal tahil( 707.0

ialiN 0. 707 > 0. 50 .lamron araces isubirtsidreb ada gnay atad akam ,

ismusa padahret nahunemep lisah iraD - sata id ismusa nagned atad sisilana akam ,

neisifeok padahret sisetopih iju nakukalid ayntukireB .dilav idajnem iserger

.aynnaayacrepek gnales nad iserger


06

hakgnal nakrasadreb laudividni iserger neisifeok naijugneP - 3.4..2 adap hakgnal

:tukireb iagabes halada

𝐻0: 𝛽1 = 0

𝐻1: 𝛽1 ≠ 0


ialin aneraK 𝑏1 = 0. 2742000 , 𝐶 11 = 0. 882000 akam ,

𝑡 =𝑏1

�𝜎�2𝐶 11=

0. 2742000

�(3. 32585 𝐸 − 60 )(0. 882000 )=

0. 27420003. 33312 𝐸 − 50

= 7. 469296

ialin aneraK 𝑡 utiay ,nakalonep haread irad raseb hibel 7. 469296 > 2. 262 akam ,

𝐻𝑜 awhab naklupmisid tapad akaM .kalotid 𝛽1 ≠ 0 itrareb gnay 𝑥1 isubirtnokreb

.nakirebid gnay ledom padahret nakifingis araces

nakutnebmeP retemarap kutnu naayacrepek gnales 𝛽1 id naka gnales nakanug

,%59 naayacrepek 𝑏1 = 0. 2742000 , 𝜎�2 = 3. 585 32 𝐸 − 60 nad 𝑒𝑠 (𝑏1) =

3. 33312 𝐸 − 50 akam ,

𝑏1 − 𝑡0. 520 , 11 𝑒𝑠 (𝑏1) ≤ 𝛽1 ≤ 𝑏1 + 𝑡0. 520 , 11 𝑒𝑠 (𝑏1)

0. 2742000 − 2. 822 (3. 33312 𝐸 − 50 ) ≤ 𝛽1 ≤ 0. 2742000 + 2. 822 (3. 33312 𝐸 − 50 )

0. 2742000 − 7. 92951 𝐸 − 50 ≤ 𝛽1 ≤ 0. 2742000 − 7. 92951 𝐸 − 50

0. 671000 ≤ 𝛽1 ≤ 0. 397813000


16

I BAB V

NEP PUTU

.A nalupmiseK

nad ikidileynem kutnu nakanugid gnay kinket halada iserger sisilanA

.lebairav ratna lanoisgnuf nagnubuh nakledomem tapad aumes kadit numaN

nakiaselesid gnusgnal araces nagned licekret tardauk edotem gnadakret anerak

tapadret .kisnirtni raenil ledom tubesid gnay ledom licekret tardauk edotoM

aguj nad retemarap padahret raenil gnay ledom malad nakanugid tapad aynah

malad raenil kutneb idajnem nakisamrofsnartid tapad gnay ledom padahret

m ,akaM .retemarap rtni raenil ledo isamrofsnart sesorp iulalem surah kisni

ledom iracnem kutnu nakanugid tapad licekret tardauk edotem ayapus raenil

.naknigniid gnay

.B naraS

naanugeK .saul araces kisnirtni raenil sahabid aynah ini halakam malaD

kisnirtni raenil araces sahabid muleb naanugek akij kiab tagnas nakA .liated

itilenep helo sahabid kisnirtni raenil - gnatnet sahabmem nigni gnay nial itilenep

.ini kiskirtni raenil


26

AKATSUP RATFAD

.5991 .ihduB ayteS ,iduB raeniL rabajlA : atrakaJ . .amatU akatsuP aidemarG

.2991 .yrraH ,htimS nad namroN ,reparD napareT isergeR sisilanA : atrakaJ . .amatU akatsuP aidemarG

.9002 .C nwaD ,retroP ,.N radomaD ,itarajuG scirtemonocE cisaB ehT : kroY weN .wargcM - .CNI ,seinapmoC lliH

.0102 .sugA ,otnairI A ,rasaD pesnoK : kitsitatS aynnagnabmegneP nad ,isakilp . .anacneK : atrakaJ

.6891 .D sinneD ,ylrekcaW ,.L drahciR ,reffaehcS ,.mailliW ,llahnedneMsnoitacilppA htiw scitsitatS lacitamehtaM ,secivreS srehsilbuP s’yaJ : notsoB .

.CNI

gniniV & ,.C alguoD ,yremogtnoM ,.H dnomyaR ,sreyM .2002 .yerffoeG .G , ehT dna gnireenignE ni snoitacilppA htiW :sledoM raeniL dezilareneG

secneicS .CNI ,snoS & yeliW nhoJ : kroY weN .

nhoJ ,sgnilwaR .8991 .A divaD ,yekciD ,.G yrtsaS ,alutnaP ,.O noissergeR deilppAlooT hcraeseR A .sisylanA regnirpS : kroY weN . - .CNI ,kroY weN galreV

.9891 .F .A .G ,rebeS noissergeR raenilnoN : adanaK . .CNI ,snoS & yeliW nhoJ

,nimaY S ,.nayfo R hca .1102 .yreH ,nawainruK nad .A neiL ,hcam nad isergeR ,sweiVE ,SSPS erawtfoF nagneD isakilpA :adnA namaggneG malaD isaleroK

SCIHPARGTATS nad ,BATINIM .tapmE abmelaS : atrakaJ .

.8002 .onramuS ,nniaZ rasaD akirtemonokE .aggnalrE : atrakaJ .


NARIPMAL


naripmal hotnoc 1.2

satisitsadekoreteh ismusa ijU stneiciffeoC a

ledoM

stneiciffeoC dezidradnatsnU

dezidradnatS

stneiciffeoC

t .giS B rorrE .dtS ateB

1 )tnatsnoC( - 863.36 875.37 - 168. 704.

1x - 061. 281. - 912. - 088. 793.

2x 642.92 740.41 915. 280.2 160.

.a 2SER :elbairaV tnednepeD

isalerokoto ismusa ijU

yrammuS ledoM b

ledoM R erauqS R R detsujdA

erauqS

eht fo rorrE .dtS

etamitsE

nibruD - nostaW

1 099. a 089. 679. 59929.43 296.1

1x ,2x ,)tnatsnoC( :srotciderP .a

y :elbairaV tnednepeD .b

ismusa ijU satiraenilokitlum

stneiciffeoC a

ledoM dezidradnatsnU

stneiciffeoC

dezidradnatS

stneiciffeoC

t .giS ytiraenilloC

scitsitatS

B rorrE .dtS ateB ecnareloT FIV

1

noC(

tnats

)

- 770.025 701.291

- 707.2 020.

1x 187.01 474. 379. 037.22 000. 000.1 000.1

x2 - 941.251 576.63 - 871. - 941.4 200. 000.1 000.1

y :elbairaV tnednepeD .a


naripmal hotnoc 1.2

lamron ismusa ijU

enO - vorogomloK elpmaS - tseT vonrimS

dezidradnatsnU

laudiseR

N 41

sretemaraP lamroN b,a naeM 0000000.

noitaiveD .dtS 85088031.23

emertxE tsoM secnereffiD etulosbA 161.

evitisoP 161.

evitageN - 411.

vorogomloK - Z vonrimS 106.

2( .giS .pmysA - )deliat 468.

.lamroN si noitubirtsid tseT .a

.atad morf detaluclaC .b


1.3 hotnoc naripmal

raeniL

yrammuS ledoM

R erauqS R erauqS R detsujdA etamitsE eht fo rorrE .dtS

899. 699. 699. 670.

.x si elbairav tnednepedni ehT

AVONA

serauqS fo muS fD erauqS naeM F .giS

noissergeR 774.81 1 774.81 969.9323 000.

laudiseR 470. 31 600.

latoT 155.81 41


stneiciffeoC

stneiciffeoC dezidradnatsnU dezidradnatS

stneiciffeoC

t .giS

B rorrE .dtS ateB

x 752. 500. 899. 129.65 000.

)tnatsnoC( 070.2 140. 154.05 000.

amtiragoL

yrammuS ledoM

R erauqS R detsujdA erauqS R eht fo rorrE .dtS

etamitsE

929. 368. 258. 244.


AVONA

serauqS fo muS Df erauqS naeM F .giS

noissergeR 900.61 1 900.61 868.18 000.

laudiseR 245.2 31 691.

latoT 155.81 41



1.3 hotnoc naripmal

stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

)x(nl 763.1 151. 929. 840.9 000.

)tnatsnoC( 285.1 303. 312.5 000.

srevnI

yrammuS ledoM


337. 735. 105. 318.


AVONA


noissergeR 659.9 1 659.9 060.51 200.

laudiseR 495.8 31 166. latoT 155.81 41


stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x / 1 - 034.3 488. - 337. - 188.3 200.

)tnatsnoC( 488.4 782. 420.71 000.

kitardauK

yrammuS ledoM


899. 799. 699. 270.

tnednepedni ehT .x si elbairav


1.3 hotnoc naripmal

AVONA


noissergeR 884.81 2 442.9 383.3871 000.

laudiseR 260. 21 500. latoT 155.81 41


stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x 032. 810. 298. 254.21 000.

2 ** x 200. 100. 901. 715.1 551.

)tnatsnoC( 741.2 460. 284.33 000.

kibuK

yrammuS ledoM


899. 799. 699. 570.


AVONA


noissergeR 984.81 3 361.6 338.2901 000.

laudiseR 260. 11 600. latoT 155.81 41


stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x 832. 350. 629. 764.4 100.

2 ** x 000. 800. 520. 250. 069.

3 ** x E044.5 - 500 000. 250. 371. 668.

)tnatsnoC( 431.2 201. 159.02 000.


1.3 hotnoc naripmal

htworG

yrammuS ledoM


499. 889. 789. 430.

ehT .x si elbairav tnednepedni

AVONA


noissergeR 571.1 1 571.1 737.0301 000.

laudiseR 510. 31 100.

latoT 091.1 41


stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x 560. 200. 499. 501.23 000.

)tnatsnoC( 068. 810. 509.64 000.

.)TYnl(nl si elbairav tnedneped ehT

laisnenopskE

yrammuS ledoM


499. 889. 789. 430.


AVONA


noissergeR 571.1 1 571.1 737.0301 000.

laudiseR 510. 31 100. latoT 091.1 41



1.3 hotnoc naripmal

stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x 560. 200. 499. 501.23 000.

)tnatsnoC( 463.2 340. 115.45 000.

.)TYnl(nl si elbairav tnedneped ehT

kitsigoL

yrammuS ledoM


499. 889. 789. 430.


AVONA


noissergeR 571.1 1 571.1 737.0301 000.

laudiseR 510. 31 100.

latoT 091.1 41


stneiciffeoC


stneiciffeoC

t .giS

B rorrE .dtS ateB

x 739. 200. 073. 126.594 000.

)tnatsnoC( 324. 800. 115.45 000.

.)TYnl / 1(nl si elbairav tnedneped ehT


1.3 hotnoc naripmal


naripmal 3 hotnoc .2










3.3 hotnoc naripmal

satisitsadekoreteh ismusa ijU

stneiciffeoC a

ledoM

stneiciffeoC dezidradnatsnU

dezidradnatS

stneiciffeoC

t .giS B rorrE .dtS ateB

1 )tnatsnoC( 669.42 098.5 932.4 200.

x - 001.1 844.11 - 030. - 690. 529.

2SER :elbairaV tnednepeD .a

ismusa ijU isalerokoto

yrammuS ledoM b

ledoM R erauqS R R detsujdA

erauqS

eht fo rorrE .dtS

etamitsE

nibruD - nostaW

1 529. a 658. 148. 98100. 337.2

x ,)tnatsnoC( :srotciderP .a

y :elbairaV tnednepeD .b

satiraenilokitlum ismusa ijU

stneiciffeoC a

ledoM dezidradnatsnU

stneiciffeoC

dezidradnatS

stneiciffeoC

t .giS ytiraenilloC

scitsitatS

B rorrE .dtS ateB cnareloT

e

FIV

1

noC(

)tnats 500. 100.

552.7 000.

X 000. 000. 529. 007.7 000. 000.1 000.1

.a y :elbairaV tnednepeD


3.3 hotnoc naripmal

lamron ismusa ijU

enO - vorogomloK elpmaS - tseT vonrimS

dezidradnatsnU

laudiseR

N 21

sretemaraP lamroN b,a naeM 0000000.

noitaiveD .dtS 41644064.92

secnereffiD emertxE tsoM etulosbA 302.

evitisoP 311.

evitageN - 302.

vorogomloK - Z vonrimS 307.

2( .giS .pmysA - )deliat 707.

.lamroN si noitubirtsid tseT .a

.atad morf detaluclaC .b


Direproduksi oleh: Junaidi (http://junaidichaniago.wordpress.com) dari: http://www.standford.edu Page 2

Tabel Durbin-Watson (DW), α = 5%

k=1 k=2 k=3 k=4 k=5

n dL dU dL dU dL dU dL dU dL dU

6 0.6102 1.4002

7 0.6996 1.3564 0.4672 1.8964

8 0.7629 1.3324 0.5591 1.7771 0.3674 2.2866

9 0.8243 1.3199 0.6291 1.6993 0.4548 2.1282 0.2957 2.5881

10 0.8791 1.3197 0.6972 1.6413 0.5253 2.0163 0.3760 2.4137 0.2427 2.8217

11 0.9273 1.3241 0.7580 1.6044 0.5948 1.9280 0.4441 2.2833 0.3155 2.6446

12 0.9708 1.3314 0.8122 1.5794 0.6577 1.8640 0.5120 2.1766 0.3796 2.5061

13 1.0097 1.3404 0.8612 1.5621 0.7147 1.8159 0.5745 2.0943 0.4445 2.3897

14 1.0450 1.3503 0.9054 1.5507 0.7667 1.7788 0.6321 2.0296 0.5052 2.2959

15 1.0770 1.3605 0.9455 1.5432 0.8140 1.7501 0.6852 1.9774 0.5620 2.2198

16 1.1062 1.3709 0.9820 1.5386 0.8572 1.7277 0.7340 1.9351 0.6150 2.1567

17 1.1330 1.3812 1.0154 1.5361 0.8968 1.7101 0.7790 1.9005 0.6641 2.1041

18 1.1576 1.3913 1.0461 1.5353 0.9331 1.6961 0.8204 1.8719 0.7098 2.0600

19 1.1804 1.4012 1.0743 1.5355 0.9666 1.6851 0.8588 1.8482 0.7523 2.0226

20 1.2015 1.4107 1.1004 1.5367 0.9976 1.6763 0.8943 1.8283 0.7918 1.9908

21 1.2212 1.4200 1.1246 1.5385 1.0262 1.6694 0.9272 1.8116 0.8286 1.9635

22 1.2395 1.4289 1.1471 1.5408 1.0529 1.6640 0.9578 1.7974 0.8629 1.9400

23 1.2567 1.4375 1.1682 1.5435 1.0778 1.6597 0.9864 1.7855 0.8949 1.9196

24 1.2728 1.4458 1.1878 1.5464 1.1010 1.6565 1.0131 1.7753 0.9249 1.9018

25 1.2879 1.4537 1.2063 1.5495 1.1228 1.6540 1.0381 1.7666 0.9530 1.8863

26 1.3022 1.4614 1.2236 1.5528 1.1432 1.6523 1.0616 1.7591 0.9794 1.8727

27 1.3157 1.4688 1.2399 1.5562 1.1624 1.6510 1.0836 1.7527 1.0042 1.8608

28 1.3284 1.4759 1.2553 1.5596 1.1805 1.6503 1.1044 1.7473 1.0276 1.8502

29 1.3405 1.4828 1.2699 1.5631 1.1976 1.6499 1.1241 1.7426 1.0497 1.8409

30 1.3520 1.4894 1.2837 1.5666 1.2138 1.6498 1.1426 1.7386 1.0706 1.8326

31 1.3630 1.4957 1.2969 1.5701 1.2292 1.6500 1.1602 1.7352 1.0904 1.8252

32 1.3734 1.5019 1.3093 1.5736 1.2437 1.6505 1.1769 1.7323 1.1092 1.8187

33 1.3834 1.5078 1.3212 1.5770 1.2576 1.6511 1.1927 1.7298 1.1270 1.8128

34 1.3929 1.5136 1.3325 1.5805 1.2707 1.6519 1.2078 1.7277 1.1439 1.8076

35 1.4019 1.5191 1.3433 1.5838 1.2833 1.6528 1.2221 1.7259 1.1601 1.8029

36 1.4107 1.5245 1.3537 1.5872 1.2953 1.6539 1.2358 1.7245 1.1755 1.7987

37 1.4190 1.5297 1.3635 1.5904 1.3068 1.6550 1.2489 1.7233 1.1901 1.7950

38 1.4270 1.5348 1.3730 1.5937 1.3177 1.6563 1.2614 1.7223 1.2042 1.7916

39 1.4347 1.5396 1.3821 1.5969 1.3283 1.6575 1.2734 1.7215 1.2176 1.7886

40 1.4421 1.5444 1.3908 1.6000 1.3384 1.6589 1.2848 1.7209 1.2305 1.7859

41 1.4493 1.5490 1.3992 1.6031 1.3480 1.6603 1.2958 1.7205 1.2428 1.7835

42 1.4562 1.5534 1.4073 1.6061 1.3573 1.6617 1.3064 1.7202 1.2546 1.7814

43 1.4628 1.5577 1.4151 1.6091 1.3663 1.6632 1.3166 1.7200 1.2660 1.7794

44 1.4692 1.5619 1.4226 1.6120 1.3749 1.6647 1.3263 1.7200 1.2769 1.7777

45 1.4754 1.5660 1.4298 1.6148 1.3832 1.6662 1.3357 1.7200 1.2874 1.7762

46 1.4814 1.5700 1.4368 1.6176 1.3912 1.6677 1.3448 1.7201 1.2976 1.7748

47 1.4872 1.5739 1.4435 1.6204 1.3989 1.6692 1.3535 1.7203 1.3073 1.7736

48 1.4928 1.5776 1.4500 1.6231 1.4064 1.6708 1.3619 1.7206 1.3167 1.7725

49 1.4982 1.5813 1.4564 1.6257 1.4136 1.6723 1.3701 1.7210 1.3258 1.7716

50 1.5035 1.5849 1.4625 1.6283 1.4206 1.6739 1.3779 1.7214 1.3346 1.7708

51 1.5086 1.5884 1.4684 1.6309 1.4273 1.6754 1.3855 1.7218 1.3431 1.7701

52 1.5135 1.5917 1.4741 1.6334 1.4339 1.6769 1.3929 1.7223 1.3512 1.7694

53 1.5183 1.5951 1.4797 1.6359 1.4402 1.6785 1.4000 1.7228 1.3592 1.7689

54 1.5230 1.5983 1.4851 1.6383 1.4464 1.6800 1.4069 1.7234 1.3669 1.7684

55 1.5276 1.6014 1.4903 1.6406 1.4523 1.6815 1.4136 1.7240 1.3743 1.7681

56 1.5320 1.6045 1.4954 1.6430 1.4581 1.6830 1.4201 1.7246 1.3815 1.7678

57 1.5363 1.6075 1.5004 1.6452 1.4637 1.6845 1.4264 1.7253 1.3885 1.7675

58 1.5405 1.6105 1.5052 1.6475 1.4692 1.6860 1.4325 1.7259 1.3953 1.7673

59 1.5446 1.6134 1.5099 1.6497 1.4745 1.6875 1.4385 1.7266 1.4019 1.7672

60 1.5485 1.6162 1.5144 1.6518 1.4797 1.6889 1.4443 1.7274 1.4083 1.7671

61 1.5524 1.6189 1.5189 1.6540 1.4847 1.6904 1.4499 1.7281 1.4146 1.7671

62 1.5562 1.6216 1.5232 1.6561 1.4896 1.6918 1.4554 1.7288 1.4206 1.7671

63 1.5599 1.6243 1.5274 1.6581 1.4943 1.6932 1.4607 1.7296 1.4265 1.7671

64 1.5635 1.6268 1.5315 1.6601 1.4990 1.6946 1.4659 1.7303 1.4322 1.7672

65 1.5670 1.6294 1.5355 1.6621 1.5035 1.6960 1.4709 1.7311 1.4378 1.7673

66 1.5704 1.6318 1.5395 1.6640 1.5079 1.6974 1.4758 1.7319 1.4433 1.7675

67 1.5738 1.6343 1.5433 1.6660 1.5122 1.6988 1.4806 1.7327 1.4486 1.7676

68 1.5771 1.6367 1.5470 1.6678 1.5164 1.7001 1.4853 1.7335 1.4537 1.7678

69 1.5803 1.6390 1.5507 1.6697 1.5205 1.7015 1.4899 1.7343 1.4588 1.7680

70 1.5834 1.6413 1.5542 1.6715 1.5245 1.7028 1.4943 1.7351 1.4637 1.7683


Diproduksi oleh: Junaidi (http://junaidichaniago.wordpress.com), 2010 Page 1

Titik Persentase Distribusi t (df = 1 – 40)

Pr 0.25 0.10 0.05 0.025 0.01 0.005 0.001

df 0.50 0.20 0.10 0.050 0.02 0.010 0.002

1 1.00000 3.07768 6.31375 12.70620 31.82052 63.65674 318.30884

2 0.81650 1.88562 2.91999 4.30265 6.96456 9.92484 22.32712

3 0.76489 1.63774 2.35336 3.18245 4.54070 5.84091 10.21453

4 0.74070 1.53321 2.13185 2.77645 3.74695 4.60409 7.17318

5 0.72669 1.47588 2.01505 2.57058 3.36493 4.03214 5.89343

6 0.71756 1.43976 1.94318 2.44691 3.14267 3.70743 5.20763

7 0.71114 1.41492 1.89458 2.36462 2.99795 3.49948 4.78529

8 0.70639 1.39682 1.85955 2.30600 2.89646 3.35539 4.50079

9 0.70272 1.38303 1.83311 2.26216 2.82144 3.24984 4.29681

10 0.69981 1.37218 1.81246 2.22814 2.76377 3.16927 4.14370

11 0.69745 1.36343 1.79588 2.20099 2.71808 3.10581 4.02470

12 0.69548 1.35622 1.78229 2.17881 2.68100 3.05454 3.92963

13 0.69383 1.35017 1.77093 2.16037 2.65031 3.01228 3.85198

14 0.69242 1.34503 1.76131 2.14479 2.62449 2.97684 3.78739

15 0.69120 1.34061 1.75305 2.13145 2.60248 2.94671 3.73283

16 0.69013 1.33676 1.74588 2.11991 2.58349 2.92078 3.68615

17 0.68920 1.33338 1.73961 2.10982 2.56693 2.89823 3.64577

18 0.68836 1.33039 1.73406 2.10092 2.55238 2.87844 3.61048

19 0.68762 1.32773 1.72913 2.09302 2.53948 2.86093 3.57940

20 0.68695 1.32534 1.72472 2.08596 2.52798 2.84534 3.55181

21 0.68635 1.32319 1.72074 2.07961 2.51765 2.83136 3.52715

22 0.68581 1.32124 1.71714 2.07387 2.50832 2.81876 3.50499

23 0.68531 1.31946 1.71387 2.06866 2.49987 2.80734 3.48496

24 0.68485 1.31784 1.71088 2.06390 2.49216 2.79694 3.46678

25 0.68443 1.31635 1.70814 2.05954 2.48511 2.78744 3.45019

26 0.68404 1.31497 1.70562 2.05553 2.47863 2.77871 3.43500

27 0.68368 1.31370 1.70329 2.05183 2.47266 2.77068 3.42103

28 0.68335 1.31253 1.70113 2.04841 2.46714 2.76326 3.40816

29 0.68304 1.31143 1.69913 2.04523 2.46202 2.75639 3.39624

30 0.68276 1.31042 1.69726 2.04227 2.45726 2.75000 3.38518

31 0.68249 1.30946 1.69552 2.03951 2.45282 2.74404 3.37490

32 0.68223 1.30857 1.69389 2.03693 2.44868 2.73848 3.36531

33 0.68200 1.30774 1.69236 2.03452 2.44479 2.73328 3.35634

34 0.68177 1.30695 1.69092 2.03224 2.44115 2.72839 3.34793

35 0.68156 1.30621 1.68957 2.03011 2.43772 2.72381 3.34005

36 0.68137 1.30551 1.68830 2.02809 2.43449 2.71948 3.33262

37 0.68118 1.30485 1.68709 2.02619 2.43145 2.71541 3.32563

38 0.68100 1.30423 1.68595 2.02439 2.42857 2.71156 3.31903

39 0.68083 1.30364 1.68488 2.02269 2.42584 2.70791 3.31279

40 0.68067 1.30308 1.68385 2.02108 2.42326 2.70446 3.30688

Catatan: Probabilita yang lebih kecil yang ditunjukkan pada judul tiap kolom adalah luas daerah

dalam satu ujung, sedangkan probabilitas yang lebih besar adalah luas daerah dalam

kedua ujung


Documents

REGRE SI LINEA R IN TRIN S IK M AKALA Hrepository.usd.ac.id/478/2/083114005_full.pdf · REGRE SI LINEA R IN TRIN SIK M AKALA H Dia j uk an Untu k Memenu hi Salah Satu Sy arat Mempe