identification correlation between economic variables and welfare
TRANSCRIPT
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 $TATI|5|TTCAL TTITNKING FOR
TBCHNOLOGY I'EYELOPMENT''
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MATHEMATIC S DEPARTMENT
INSTI ruT TEKNOLO GI SEP ULUH NOPEMBER SURABAYA, INDONESIA
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I NTERNAT IONAL C Ot l FEREN C E ON lrlATH Ett^ATlCS, STATIST ICS
AND ITS APPLICAT|CI.IS 2012
KIUSA 2012
Editor :
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ORGANIZING COMMITTEE
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STEERING : Dean Faculty of Mathematbs andNahral Scbnces ITS
TNTERNATIONAL SCIENTIFIC COMMITTEE
Prof. Basuki \Mifodo (ITS - kdonesb)Prof. Nur lrhwan(ITS - Indonesb)Prof. Nyoman Budbntara (ITS - Indonesb)Prof. M. Isa Irawan (ITS - Indonesia)
Dr. Muhammad Mashuri(ITS - Indonesb)Dr, Erna Apriliani (ITS - Indonesia)Dr. Subiono (ITS - Indonesb)Subcharu Ph. D (ITS - Indonesia)Prof. Dr. Herrnan Mawengkang (University of Surnatera utaa - Indonesia)Dr. Hizir So$an (Sybh Kuah University - Indonesb)Dr. Saib Suwilo (University of Sumatera Utara - Indonesia)
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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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