PNOGEET'TNG

I NTERNAT IONAL C Ot.I FEREN CE ON AAATH EI,IAT ICS, STAT I ST ICS

AND ITS APPLICATIOT{S 2012

]CMSA 2At2

..MI\THEMATIGAI. AIIID $TATI|5|TTCAL TTITNKING FOR

TBCHNOLOGY I'EYELOPMENT''

Publbhed by:

MATHEMATIC S DEPARTMENT

INSTI ruT TEKNOLO GI SEP ULUH NOPEMBER SURABAYA, INDONESIA

PNOGEEI}II{G

I NTERNAT IONAL C Ot l FEREN C E ON lrlATH Ett^ATlCS, STATIST ICS

AND ITS APPLICAT|CI.IS 2012

KIUSA 2012

Editor :

Prof Dr. Basuki Wijodo, M.Sc.

Prof Dr. M. lsa lrawan, MT.Dr. SubbnoSubcharL PttDProf Nur Iriawaq PhDfh.rer.pol Heri Kuswanto

Dr. Muhammad Mashuri

rsBN 97 8-97 9-96152-7-5

Thb Conference is lreH by cooperatbn withStatistic Department ITS

Mathenratbs Department, Udayana

Secretariat :

Mathernatb s Departme nt

Kanpus ITS Sukolilo Stnabaya 60111, Irdonesia

icmsa2O 1 2@its. ac. id. icmsa201 2.org

ORGANIZING COMMITTEE

PATRONS :Rector of ITS

STEERING : Dean Faculty of Mathematbs andNahral Scbnces ITS

TNTERNATIONAL SCIENTIFIC COMMITTEE

Prof. Basuki \Mifodo (ITS - kdonesb)Prof. Nur lrhwan(ITS - Indonesb)Prof. Nyoman Budbntara (ITS - Indonesb)Prof. M. Isa Irawan (ITS - Indonesia)

Dr. Muhammad Mashuri(ITS - Indonesb)Dr, Erna Apriliani (ITS - Indonesia)Dr. Subiono (ITS - Indonesb)Subcharu Ph. D (ITS - Indonesia)Prof. Dr. Herrnan Mawengkang (University of Surnatera utaa - Indonesia)Dr. Hizir So$an (Sybh Kuah University - Indonesb)Dr. Saib Suwilo (University of Sumatera Utara - Indonesia)

Dr. Tarm2iUsman (Syiah Kuala University - Indonesia)Prof. DatoDr. Roshan M. Ali(UniversitiSains Malaysia - Malaysia)

Assoc. Prof. Dr. Anton Abduhasah Kamil (Universiti Sains Mabysh - Mahysh)Assoc. Prof. Adam Bahanrn (Universiti Sains Mahysb - Mahysia)Assoc. Prof. Dr. Pachitjanut Siripanitch (Natbnal Irstitute of DevebprnentAdminbfration - Thailand)Assoc. Prof. Dr. Surapong Auwabnamongfuol (National Institute of Development

Adminbhation - Thaihnd)Assoc. Prof- Putipong Bookkamana (Chhng MaiUniversfty - Thailand)

COMMITEE

Dr. SuhartonoDr. DarrnajiDr. SantiWubn PurnamiSobha, M.SiDr.Irhamah

TechnbalProgramrne :

Dr. KomangDharmawanDrs. Daryono BudiUtomo, M.SiDrs. Lukman Hanafi M.Sc.Subchan, Ph. D

Dr.rar.net. Heri KuswantoDr. SutknoDr. Agnes Tuti Rumiati

Web andPublication :

Dr. Imam MukhbsDr. Brodjol Sutiio S.U.

Transportatbn and Accommodatbn :

Dr, PurhadiDrs.I GustiNgurah Rai, M.SiDrs. Bandung Ary, M.lKom.

ChairmanCo-chairmanSecrehry

Finance

ill

CONTENTS

CoverOrganizing CommitteeMessage from Rector of Institut Teknologi Sepuluh Nopember (ITS)

Message from Dean Faculty of Mathematics and Natural Sciences

Message from Chairman of Organizing Committee

ContentsTentative Schedule

Paper of PlenaryMathematics PapersPMl Value Theorems and Holder

PM2 A Study Permutation Theory and Its ApplicationSquare-X (Subiono, Muhammad Syifu'ul Mufid)

PM3 The locating chrornatic nurnber of strong product of two paths

(L A. Purwasih, M' Bu-ca, and E- T' Baskoro)pM4 Generating functions of polynomial sequences ovef integral domains and

quotient fields (fi.rsuf Chebao)

Polydule varieties over finite-dimensional algebra

Muchtadi'AlamsYah, and lrawoti)n: Box Dimension, Hausdorff, Dimension, and Potential

Theoretic Method (Mario Ane stasia)pMZ Some Sufficient Conditions for Corona Graphs to be Product Cordial

Graphs(D.K Syofuon qnd A,N.M. Salman)

lnvertible Matrices over The Synrmetrized Max Plus Algebra

(Gregoria Ariyanti, Ari Suparwanto, and Budi Surodjo)

On almost weakly self'dual normal bases

(Irwansyah, Ahmad Muchlis, Diokn Supriyanto, and Intan Muchtadi)

Pollard Rho Algorithm for Elliptic Curves over Composite Fields

(Int an Muchtadi -A I am syah)

Estimation and Control Design of Mobile Robot Position

(ErnaApritiani, Subchan, Fitri Yunaini, and Santi Hortini)Pedestrian flow characteristics in a least developing country'

(Khatidur Rqhman, Noraida Ahdul Ghani, Anton Abdulbasah Ksmil, Adli

Mustafa)Numerical Solution To Control The Exploitation Of Ground Water

(Suharmadi SanjaYo)

Determination the Error and Delta Error for Braking Control System ofThree Phase Motor(Purwanti, B. S. ,R. , Yusivar, F., and Garniwa, I. M' K)Dynamic Stability Model For A Small Submarine

(Aries Sulisetyorc)

l

llllv

Connection Between Parvate-Gangal Mean

Continuous Function of Order c e (0,1)

(Supriyadi Wib owo, Mus lich)

vviviixii

to Enumeration of Latin

PM8

PM5

PM6

PM9

PMIO

AM1

A}'42

AM3

AM4

AM5

vil

AM6 Optimization Model On Quadratic Programming Problem \[i,th Fuzzy

(Sugiyorto), AM7 Detecting Fouling In Heat Exchanger By Extended Kalman Filter Method

And Etrsemble Kalman Filter(Lukman Hanafi , Erna Aprilioni, qnd Ana Fadlilah)

AM8 Review of Asset Return Disttibution and Ils Application(Sandya N. Kumari and A. Tan)

AM9 Control System Roket Rkx-200 Lapan Using Pid Controller

(Subchan, Putra Setya Bagus J'N' dan Idris E'P')

AMl0 Modified Feige-Fiat-Shamir Signature Scheme with Message Recovery

(Dessi Nursari , Elena Sabarina, and Rizki Yugitamo)

AMl l The effect of the use of the MDS matrices in the T-020 block cipher

algorithm(Sutoro, BetY HaYat Susanti)

AM12 RAN Signature Scheme

(Novita Loveria, Rizfuo Mardyonti, Ayubi Wirara)

AM13 Studies on Simplifred Chaos Hash Algorithm-l (SCHA-I) using Yuval's

BirthdaY Attack(Adrian Admi, BetY HaYat Susanti)

AM14 The Implement of extracting the partial subkey bits from Linear

(Bashir Anohman, Elena Sabarina, and Prilia Trianantia Lestari)

AM15 UDD Assumption for Life Annuity with m-thly Payments

(Faroh Krtsfiani)AM16 Orchestration of semantic web service using OWL-S for variations ofERP

business process

(Anang Kunaefi, Riyanarto Sarno , BandungArry Sanioyo, Imam

Mukhlash, Hanim Maria Astuti)

AM17 Comparing The Distribution ofNon Stationary Processes : A Spatial

Dominance APProach(Irwan Susanto, Respatiwulan and Supriyadi Wibowo)

AM18 The Correlation Between Hydrodynamic Of River And Pollutant

Dispersion In A River.Mixed Geographically Weighted Multivariate Linier Model (Case Study :

The Rainfall and Moqphometry Effects in the Determination of Water

Flow Rate and Sediment in Konto Hulu Watershed) ( Basuki Widodo,

Bambang Agas S., Setiawan)

AMlg Stochastic Divination Reckoning Enactment on Multi class Queueing

SYstem'(K. Sivaselvan and C'Vij ayalakshmi )

AM20 Using SVAR with B-Q Restristion to examine post-tsunami inflation in

Aceh(Soiful Mahdi)

AM2l Mathematical Modeling of Circular Cylinder Drag Coefficient with I-Type as a Passive Control(chairul Imron, Suhariningsih, Bqsuki widodo, and Triyogi Ytmono)

A\/122 Analyzing portfolio performance of Bangladesh stock market

vill

(Md. Zabaer llosan, AntonAbdalbqsoh Kamil, Adli lufustafa and Md-

Azizul Baten)

Implernentation Of The Algorithm Kalman Filter On Reduction Model(Didih Khusnul Arif, Wdodo, Salmah, Erna Apriliani)

, AMA3

Statistics PapersSA1

SA2

SA3

SA4

SA5

SA6

sA7

SA8

SA9

SAIO

SAIl

SA12

SAI3

SA14

SAI5

Dimension reductilon with sliced i,nverse regresSion as pra-proCessing in

(Ni Wa-yan Dewinta Ayuni and S*ilon)Application of Structural Equation Modelling (sEM) to Analysed the

Behaviour of Consumers forthe Products of Embroidery and Pariaman

Needlework(Liso Nesti, Irna EkawatfiComparison of stability long-horizon R-forecasting and V-forecasting

SSA(Awit M. Sakinah, ToniToharudin, Gumgum Darmawan)

The weibull prior distribution on the information-based approach

asset pricing model by brody hughston macrina

(Muti|ah)Hypothesis Testing In Regression Model Bivariate Weibull

(Andi Quraisy and Purhadi)Identification Correlation Between Economic Variables and Welfare

Variables With Canonical Correlation Analysis

(Asep RuEtana, audhatul Jannah)

Spatial Bayesian Poisson Lognormal Analysis of Dengue Relative Risk

Incidence in Surabaya on 2010

(Mukhsar, Iriawan, N , (Jlama, B. S. E Sutifuto, Kuswanto, H)

Survival Analysis With Cox Regression Model (Case Study : Dengue

Hemorrhagic Fever (DHF) Patients in The Haji Hospital at Surabaya).

(Ni Putu Lisa Ernqwatiningsihand Purhadi)

Smoothing Spline Estimators in Semipa,rametric Multivariable Regression

Model(Rita Diana, I. Nyoman Budiantara, Purhadi dan Satyviho Darmesto)

Multivariate adaptive regression splines (MARS) approach for poverty

data in East Java Province (Memi Nor Hayati and Purhadi)

A Copula Approach to Construct Vulnerability Rice Puso Maps in East

Java With El-Nino Southern Oscillation (ENSO) Indicator

(Protnya Paramitha Oktaviana, Sutifuto, and Heri Kuswanto)

Model Based Clustering Versus Traditional Clustering Methods: AComparison Based On Intemal and External Validation Measure

(I Gede Nyoman Mindra Jaya, Henk Folmet, Budi Nurani Ruchiana)

The Identification of the relationship between the area of the rice harvest

and rainfall using Copula Approach.

(Iis Dewi Ratih, Sutilmo, dan Setiawan)

Simulation of The Stationary Spatio-Temporal Disaggregation using

Bayesian State-space with Adjusting Procedure

(Suci Astutik, Nur lriswan, Suhsrtono, and Sutikzn)

Optimal Smoothing Parameter for Spline Partial Estimator in

tx

Multire sponse Sent iparametri c Regress ion(Walryu Wibowo, Sri Haryatmi, I Nyoman Budiantara)

, 5,4.16 Bayesian Model Comparison : BIC for Nonlinear SEM

(Margaretha Ari Anggorowati, Nur lriawun Suhqrtono and Hasyim

Gautama)SA17 Modeling of Gross Regional Domestic Product Manufacturing Industries

Sector in East Java: a Spatial Durbin Model Approach

(Setiawan)

SAlS Multi Input Intervention Model for Evaluating the Impact of the Asian

Crisis and Terrorist Attacks on Tourist Arrivals in Bali

(Sri Rezeki, Suhsrtono, SuYadi)

SAlg Parameters Estimation of the Additive Outlier of the VectorAutoregression(Agus Suharsono, Suryo Guritno, Subanar)

SA20 Breeder Genetic Algorithm for bi-objective Multiple VRP with Stochastic

Demands(Irhamah and ZuhaimTt Ismail)

SA2l Forecasting Fruit Sales At Moena Fresh Bali Using Calendar Variation

Model(Dwiatmorn Agus lVidodo, Ni Made Dwi Ermayanthi, and

Suhartono)

SBI Credit Scoring for Cooperative of Financial Services Using LogisticRegression Estimated by Genetic Algorithm(Sulanol, Asep Sholahuddin2, Krishna Prafidya Romontica)

SB2 ANOVA estimation in longitudinal linked data

(Klairung Samart, RoY Chombers)

SB3 Multivariate Adaptive Regression Splines (Mars) Approach For Analysis

Of Poverty Data InEast Java Province(Erma Ohania Permatasari and Bambortg Widianarkn Otok)

SB4 Exploration of factor analysis using R and SPSS to identiff the Potential

Factors on Indonesia Community Health Development Index (IPKM).

Qurnila Marli Ke s ums, Viras akdi Chongswiv atw ong)

SB5 Optimization In Process Production Of Envelopes By MultiresponTaguchi Method And FuzzY Logic.(kny Sunaryo, Albertus Lourcnsh$ Setyabudhi)

586 Breast Cancer Diagnosis Using Smooth Support Vector Machine and

Multivariate Adaptive Regression Splines

(Shofi Andari, Santi W' Purnami, BambangW'O)

SB7 ModelingLong Memory Time SeriesBy Singular Spectrum Analysis (

Case Study : HandYmax Price Data)

(Gurngum Darmawan)

sBs Multivarite Poisson control chart and its Applications

(Wibawati, and Muhammad Mashuri)

SB9 Adaptive Nouro-Fuzzy Inference System for Short Term Load Forecasting

In Indonesia.(ndah Puspitasari, Suhartono, M. Siahid Akbar)

SBlO

SBII

SB12

SB13

SBI4

SB15

SBI6

SBIT

SB18

SB19

S82O

SB2T

Forecasting Inflation in Indonesia using Ensemble Method .

(Mega Silfiani and Suhartono)

Weighted Fwy Rule Base To Modeling Time Series Data And Its

Application In Prediction Of Stock Prices'

(Nurhoyadi, Subanar, Abduralilman, Agus Maman Abadi)

Modeling The Effects of Modern Market Existence of Traders Traditional

Market Income by Using Support Vector Regression (SVR)

(Dwi E. Kusrini, Isnaini P. Dewi, and lrhamah)

Nonparametric Classification Method Of Walfare Households In The

Province Of East Java

(Bambang Widianarko Otok & Suhartono)

Optimization in Process Production of Envelopes by Multi-response

Taguchi Method andFuzzY Logic(Brodjol S.S. Uamo and Mohmuddin, A)Air Temperature Modeling By Using Artificial Neural Networks

Approach(Edyfradinata, ST, MT)

Smooth Support Vector Regression for Floating Breakwater Performance

(Yoyok Setyo Hadiwidodo and Santi Wulan Purnami)

Daily rainfall prediction using time delay neural networks

(Fithriasari, K; Iriqwan, N; (Jlama, B' S; Sutihrto; Kuswanlo, H)

The Classification Of Breast Cancer Malignancy Using Ordinal Logistic

Regression And Support Vector Machine (SVIv[).

(Farizi Rachmanl and Santi Wulan Purnami)

Optimization of Steel Cutting Process Using Bootstrapping Response

Surface(Wiwieksetya Wnahiu )Estimating costs for oil spills with Simultan Equation Modelling

(Mukhtasor, Dwi Endah Kusrini, Mauludiyah)

Optimization of Design of Experiment forhybrid fuel-system of Premium

Benzene and LPG in motorcycling vehicles

(Hendro Nurhodi)

X1

P roceed in c tntern ationa I Conference on Mathematics,Statistics ainU its Applications 201 2 (lCl\lls A 2012)

rsBN 978-979-961 52-7-s

Identification Correlation Between EconomicVariables and Welfare Variables

With Canonical Correlation Analysis

Asep Rusyanal, Nurhasanah2, Raudhatul Jannah

r,2 Department of Mathematics, Faculty of Mathematics and Natural Sciences,

Syiah Kualo UniversitYasep . rusyanaG fur-ipa . unsyiah . ac - id'

Ab*tract. The re frctors that

affecting the we 2009' The

method that was PurPoses ofresearch are to ideotiry correlation between economic variables and the welfare variables,

and also to detemrine the variahles that are most intluent economic and welfare in Acehprovince in 2009. The dBta used in ths reseach was secondary data from the Central

Bgreau of Statistics Aceh. The result of canonical correlation analysis indicales there are

correlation between economic and welfarc with correlation value is 0.9?481. Caronical

Ioading shows the economic variables that have correlated with the first canonical

variable are economic growth, percentage ofpoor population and GDP at 2000 constant

market prices. The warfare variables tbat have correlated with the first canonicel variable

are nean years of schooling, number of working people and percentage of households

with decant clean water as sources ofdrinking water"

Kelrvords : Canonical correlation analysis, economic' welfare'

I Introduction

Development is activities which must be planned by a government for

making good lociety welfare with participation from all society elements'

Society *elfut" has many aspects and they are not easy to be measured'

Several the aspects are ele;tricity, housing, education' etc. The development ofan area must be felt by all society levels, but sometimes it is not done because

of culture, area position, and resourge in specific area.

Central bureau of statistics has determined society welfare and

economy aspects. The economy aspects must influence welfare aspects so that

government can increase economy aspects to repair welfare aspects.

purposes of the research are to identiff correlation between society

welfare aspects and economy aspects in 2009, and to know elements which

influent significantly in society welfare and economy indicators.

sA5

2 Literature Study

2. 1. Canonical Correlation Analysis

Canonical correlation analysis is one of multivariate analysis to identifycorrelation between two variable set. Initially, the technic is developed by

Hoteltring (Hiirdle dan Simar, 2007).Supranto (2004) tells that canonical correlation analysis can correlate

simultalrtly several dependent variables Y with several independent variables

X. Canonical correiation analysis makes correlation between linear

combination of dependent variables and linear combination of indeperrdent

variables. Principat idea of, this analysis looks for pair of linear combination

which have the highest corelation (Diah,2009).

2.2 Assume of Canonical Correlation Analysis

Linearity

Linearity is very important for canonical correlation analysis because

linearity assume influences two aspects of this analysis results. The first,correlation coeficient between two variables is based on linear pattern. The

second, canonical correlation is based on linear pattern ztmong variates (Hair, et

al, 1998).

Normality

Canonical correlation analysis can use each maffix without strictnormality assume. Multivariate normality is needed to test statistical inference

about importance of each canonical function. Multivariate normal software

which can analyze multivariate normal has not provided. There is guidance thatmultivariate normal distribution means eaoh of vmiables must have distributionof univariate normal.

3 Materials and Methods

3.1Data

Data used in the research are secondary data. They are society welfare

variables and economical variables for 23 regencies or cities in Aceh Province.

Source of the data is Central Bureau of Statistics, and the data period is in2009.

There are 17 variables which will be arralized. They include 9 society

welfare variables and 8 econornical variables. The variables are:

l. Society welfare variables are population growth rate (Yl)' population in

productive age (Y2), count of population which has job (Y3), lifeexpectation rate (Y4),literate rate (Y5), average of formal education

(Y6), average of expenditure per person (Y7), household with drinking

water from a company (Vg), and household with floor < l0m2 (Y9).

The variables are called dependent variables.

2. Economical variables are economical growth (Xl), PDRB which isbased on price now (X2), PDnB which is based on constant price (X3),

unemployment rate (X4), poor rate (X5), contribution of agriculture toqDRE (X6), contribution of industry to PDRB (X7), and income ofAceh (X8), they are called indeperrdent variables.

3.2 Research Steps

There are 5 (five) steps of this research, they are :

o Testing of canonical eorrelation assurnes'

There are two assumes in canorrical correlation analysis, they are normal and

linear. It means variables must have multivariate normal distribution, and

relation between each independent variable and depandent variable are linear.

. Making and estimation of canonical function.

Here there are 9 dependent variables and 8 independent variable, so that 8

function will be got. Then function which have signifieant influence will be

looked for so that we will have only one, two, or three fUnction which are

representative of E functions.r Statistic testStatistics test is held twice, simultant test and individual test. Simultant test is

used for testing all function. If H0 is accepted, it means that all function can

not be used for explain correlation between independent variables and

dependent variables, in the other word independent variables do not have

correlation with dependent variables. Then individual variables is to test each

of functions. If H0 is accepted for testing of a function, it means the function

can explain correlation between independent and dependent variables.

r Interpretation of canonical function. It explains conelation economy

variables (X) and independent variables (D with the function and then willbe detected variable individually in X which have significant influence to

X, and variable individually in Y which have significant influence to Y.

. Make conclusion.

4 Rcsults and Discussions

4.l Normality Test

Multivariate normal distribution is one assumme of the canonical

correlation analysis. Here each variable is tested to identifr whether the

variables are normal or not. The test is appropriate of multivariate normal test.

It is hyphotesis testing with null hyphotesis : distribution is normal and

alternative hyphotesis : distribution is not normal. Table I shows thatX4,X5,X6, Yl, Y2,Y6,and Y9 have normal distrubution.

TaHe l. Result of normality test with Kolmogorov-Smirnov Test'

Variables sig Decision Variables Sig Decision

X4

X5

X6

0,200

0,200

0,200

Accept He

Accept tI6

AcceptFI6

Y1

Y2

Y6

Y9

0,147

0,200

0,200

0.200

Accept Hs

Accept 116

Accept I{n

Accent H"

Table 2 explains that several variables do not have normal distribution

so that they must be transformed before they are tested. They have normal

distribution because of cosinus, ln, and sin transformation. It means that all

variables can have normal distribution and the assume can be fulled.

Table2.Normality test for original and transformed data with Kolmogorov-Smirnov Test.

VariablesBefore transformation Kind of

Transformation

After transformation

sig Decision sig Decision

XIx2

X3

x7

X8

Y3

Y4

Y5

Y7

Y8

0,000

0,004

0,005

0,000

0,000

0,040

0,018

0,050

0,001

0.003

RejectH0

Reject H0

Reject H0

Reject H0

Reject H0

Reject H0

Reject H0

Reject H0

Reject H0

Reiect H0

Cos

Ln

Ln

Sin

Cos

Sin

Sin

Cos

Ln

Ln

0,091

0,200

o,200

0,057

0,200

0200

0,159

0,200

0,200

0.093

Accept 116

Accept FIi

Aocept FIs

Accept IIn

Accept ilo

Accept lln

Accept Ho

Accept IIa

Accept tI6

Acceot H^

4.2 Linearity Test

Hyphotesis test is used for linearity test. Null hypotesis (H0) : the

model is linear versus alternative hyphotesis (H1) : the model is not linear.

Decision creteria for the test is accept H0 in significant level 0,1 if Sig is great

than 0,1, but reject H0 in significant level 0,1 if Sig is less than 0,1' Therefore,

independent variables X with dependent variables Y are linear because all Sig

values are great than 0,1 (see Table 3). In the other word, linearity assume can

be satisfied.

Table 3. Linearity Test

4.3 Canonical Correlation Co€ficient

In the research, there are 8 independent variables (economy indicator)

and 9 dependent variables (society welfare indicator) so that function ofcanonical corelation are 8 (see Table 4).

There are three filnctions which have relatively high scores. They are

the first function 0,97, the second 0,93, and the third function 0,E8. The others

are relatively low scores. The first function can explain total variance 61-52

percent, anAine other functions have variance scores less than 30%- According

lndependenlVariables

Sie(Dependentvariable:

Y,)

Sig(Dependentvariable:

Yr)

Sig

@ependentvariable:

Y")

sig(Dependentvariable :

Y,)

Sig

@ependentvariable =

Y.)

XrX2x3x4X5Xr,

x7X"

0,9250,2020,6450,2030,5930,M80,0530.966

0,7800,2310,5270,145a,4920,0160,0290.319

0,9470,224a,6430,3950,3410,4500,1390.868

0,0630,1000,0050,0510,5320,4960,9890.045

0,0330,5850,9840,2E90,7780,8850,6660.874

lndependentVariables

Sig (Dependentvariablo = Y^)

Sig (Dependentvariable : Yt)

Sig (Dependentvariable = Y*)

Sig (Dependentvariable: Yo)

xrx2xl)Lx5X6X7x"

0,3580,7410,0410,5900,6480,8790,9770.445

0,98I0,4000,1250,0670,0800,7s70,1030.015

0,9680,5960,7650,2920,8330,0170,0400.181

0,5050,7870,4740,6730,0690,8830,0530.821

to Diah (2009), if score has achiwed SAYa, it is good so that this function is

taken to explain correlation between X and Y. And it can also be seen from

statistic test.Positif sign in the first function correlation value shows that if economy

condition in Aceh Province increases, welfare condition will increase and

contrasly.

Teble 4. Canonical Correlation Coeficient

Function Canonioal Correlation

Coeficient ( P )

Variance

I)3

45

67

8

0,974E10,935120,877360,658760,589220,447490,261690.1 I 570

6l,52Vo22,436/o

10,7660/o

2,469/ol,7l3oh0,806%o,2360/o

0.043o/o

4.4 Statistic Test

Simultan Testing

Canonical correlation test uses Wilks' test:

Hyphotesis:Ha: p, - pz = Pt = ..-= Ps = 0 (There is not correlation significantly)

Hr : at least p, + 00 : 1,2,3,4,..,,8)

,' : fb -t)- )(* + p* r)] r" n

z' = ](zt-t)- i6 * I + r)]rn o'ooo3e

r' = -122-vl-l.weze,, = (-t2ft7 .84%6)

Z2 =702'Ml7According to table chi-square is gotten )f @'- il --

'z1oos'ut1:90,53 '

And 102.0417 > 90-53 so that reject FIo. It can be talked that there are at least

one function can explain correlation between independent variables (X) and

dependent variables (Y).

Individual Testing

Individual testing uses hlphotesis test. Null hyphotesis (H0) : function

can not explain correlation between X and Y, and altemative hyphotesis (Hl) :

funotion can explain correlation between X and Y. Decision oriteria is reject

H0 if P value is less than 0,05, and receive H0 if P-value is great than 0,05. P-

value of the frrst funetion is less than 0,05 so that HO is rejected- The others

show receive H0 (see Table 5). It means that the first function can explain

correlation between variables X and variables Y.

Toble 5. Testing value for canonical function individually

FunctionScore of Lambda

Will$'P Value

I2J

45

6

7

8

0,000390,007850,062530,271600,479830,735010,919050.98661

0,045*0,3510,780o,9770,9770,984a,98:2

0.916Note: * is significanl at a = 0,05

4.5 Canonical Weight Vector

Canonical weight at the first canonical variables for economy variables

can be seen in Table 6 and for we}frre variables can be seen in Table 7.

Econorny variables from the highest to the lowest are X1, )Q' X5, X:, Xa, )k,Xz, and &.

Teble 6. Weight of Independent Variable Canonic

Independent CanonicVariables

The First Function

xrx2&>LX5

&XtX"

0,674050,065E80,407590,42588-0,42316-0,111634,034280.34959

Welfare contributionYz, Ys, Yz, Yg, and Yc.

from the highest to thp lowest &r€ Y6' Y3, Y3, Y1'

Tnble 7. Weight of dependent variabtre canonic

Dependent CanonicVariables

The First Function

YrY2

Y3YqY5

Y6Y7

YsYo

0,19289-0,177340,446860,049000,134341,39402

-0,1 5088-0,48935-0^07235

4.6 Canonical LoadingVectors

Canonical loading vector explains correlation between original

variables and canonical variables. In the other word, the highest original

variable have highest correlation with scores which are got from the first

function. Table & shows that the highest correlation with the first function is

Xr, and the lourcst correlation is )k.

Table L Conelation independent and the first canonical variables function

IndependentCanonical Variables

Correlation

xlXzx3&)Gx6x?Xo

0,671800,20690a,60646-0,21982-0,634430,07545-0,066960.34962

Table 9 shows that the highest correlation with the first function is Y6,

and the lowest correlation is Yq.

Table 9. Corrslation dependent and the first canoniqal variables function

Dependent CanonicalVariables

Correlation

YrY2Y3Y,YsY6Y7

Y8Yq

-0,228140,390360,573220,32502-0,208270,832720,433440,52544-0.10246

5 Conclusions

Conclusions from the research are:

l. Canonical correlation analysis abut association between economy and

society welfare in Aceh Province 2009 shows that there is correlation

with score 0.97481,2. The first function can explain correlation between economy and welfare

variables.3. Canonical loading shows that three original independent variables

which have high correlation with the first canonical variable are

economy growth (X1), poor rate (X5), and PDRB based on constant

price (X3). And three original dependent variables which have high

iorrelation with the first canonical variable are average of school age

(Y6), count of population (Y3) which has job, and household which has

drinking water from a company (Ys).

6 Acknowledgement

The writers thank to Syiah Kuala university which has provided source of the

publish funding partly.

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