E jurnal Matematika

6-10

Authors: I PUTU EKA IRAWAN, I KOMANG GDE SUKARSA, NI MADE ASIH

Principal Component Regression is a method to overcome multicollinearity techniques by combining principal component analysis with regression analysis. The calculation of classical principal component analysis is based on the regular covariance matrix. The covariance matrix is optimal if the data originated from a multivariate normal distribution, but is very sensitive to the presence of outliers. Alternatives are used to overcome this problem the method of Least Median Square-Minimum Covariance Determinant (LMS-MCD). The purpose of this research is to conduct a comparison between Principal Component Regression (RKU) and Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD) in dealing with outliers. In this study, Method of Least Median Square - Minimum Covariance Determinant (LMS-MCD) has a bias and mean square error (MSE) is smaller than the parameter RKU. Based on the difference of parameter estimators, still have a test that has a difference of parameter estimators method LMS-MCD greater than RKU method. Keywords: Multicollinearity, Outlier, Principal Component Regression, LMS, MCD

17-22

Authors: I MADE ANOM ARIAWAN, I PUTU EKA NILA KENCANA, NI LUH PUTU SUCIPTAWATI

One of functions of multivariate analysis is to group data. Multivariate analysis often used in grouping data are cluster analysis and biplot analysis. In this paper, a comparative analysis will be made between clusters analysis and biplot analysis for grouping the data. Technique used in the cluster analysis is k-mean method and biplot analysis used two-dimensional display. The results ware that biplot analysis produces are better in grouping accuracy than clusters analysis. But in general, biplot analysis can not be said to be better than clusters analysis in grouping the data and vice versa. Keywords: comparative, multivariate analysis , clusters analysis, biplot analysis

33-39

Authors: I KOMANG GEDE ANTARA, I PUTU EKA NILA KENCANA, KETUT JAYANEGARA

Latent variables are variables that can not be measured directly. In analysis of causal relationship involving three latent variables, one latent variable can be a moderator or mediator variables. Goodness of Fit moderation and mediation model of latent variables is affected by the value of the canonical correlation between moderator/mediator latent variables with the independent latent variables and dependent latent variables. If the value of both canonical correlation is well , so the Goodness of Fit models of mediation is getting better, while the opposite Goodness of Fit models will be better moderation. Keywords: Latent Variables, Moderator, Mediator, Canonical Correlation

46-52

Authors: AGUS EKA ARIESTA1, G.K. GANDHIADI, NI KETUT TARI TASTRAWATI, I PUTU EKA NILA KENCANA

Computational geometry is the mathematical science of computation by using the algorithm analysis to solve the problems of geometry. The problems of computational include polygon triangulations, convex hulls, Voronoi diagrams, and motion planning. Convex hull is the set of points that form a convex polygon that covers the entire set of points. The algorithms for determining the convex hull, among others, Graham Scan, Jarvis March, and Divide and Conquer. In the two-dimensional case, Graham Scan algorithm is highly efficient in the use of time complexity. This article discusses the quest convex hull of the data bank debtors, some of the data used to look at the classification accuracy of the convex hull formed. The coordinates of all the data found by using principal component analysis.After the data are analyzed, we get the accuracy of classification by 74%. Keywords: Computational geometry, convex hull, graham scan, principal component analysis

11-16

Authors: LUH PUTU SAFITRI PRATIWI, I GUSTI AYU MADE SRINADI, MADE SUSILAWATI

Poverty still a complex problems for both at national and regional level, so it requires an appropriate and sustainable strategy mitigation. Every household in the different regions has different characteristics and influenced factors, so it requires the identification of the factors that influence poverty by paying attention to the influence of the area using the Spatial Durbin Model (SDM). The purpose of SDM modeling is to determine the spatial dependency relationship which occur not only in the dependent variables, but also on the independent variables. The result shows that the significant lagged dependent variable is indicated by the parameter ρ=5,9804〖>χ〗_(0,05;1)^2=3,841. Lag significant independent variables are independent variables with a significant weighting, but there are no independent variables that are significant with the weighting. Keywords: Poverty, OLS, Spatial Durbin Model

23-28

Authors: LUH KOMANG MARDIANI, I KOMANG GDE SUKARSA, I GUSTI AYU MADE SRINADI

The Poisson regression analysis is one of the regression methods used for count data and has the assumption of equidispersion. However, it is the overdispersion and then underestimate standard errors will be obtained. If the data are overdispersed and more data is zero then ZIP (Zero Inflated Regression) regression is used. ZIP regression model is more appropriate to be used to analyze the amount of Senior High School/Madrasah Aliyah who do not pass the exam with five independent variables, because a lot of data failure is zero. In this paper, data are overdispersed on Poisson regression, so ZIP regression are used. ZIP regression models obtained are only influenced by the proportion of Senior High School/Madrasah Aliyah classroom were damaged (X3), is ln⁡〖(μ)〗=-1,7237+0,0911 X_3 and logit (ω)=-0,4867+0,0465 X_3. Keywords: Poisson Regression, Overdispersion, ZIP Regression, National Examination Test Failure.

35-39

Authors: PUTU EKA ARIWIJAYANTHI, I WAYAN SUMARJAYA, TJOKORDA BAGUS OKA

Small area is an area with insufficient sample for direct estimation. Limited survey objects, cause direct estimation can not produce better parameter estimates. Based on this, an indirect estimation method called empirical Bayes is used to obtain a better estimate. This study will compare means squared error by direct estimation method and empirical Bayes method to find a better method on a small area. Jackknife is used to get the means squared error in the empirical Bayes. The results is, empirical Bayes methods give a better parameters based on mean squared errors. Empirical Bayes can produce a smaller mean squared error more than direct estimation in small area. Keywords: Pendugaan Area Kecil, Bayes Empirik, Jackknife

46-52

Authors: SLAMET SAMSUL HIDAYAT, I PUTU EKA NILA KENCANA, KETUT JAYANEGARA

Trans Sarbagita is a public transportation services people at Denpasar, Badung, Gianyar and Tabanan. Trans Sarbagita is aimed to resolve a problems caused by accretion volume of vehicles in Bali. This study conducted to forecast the number of Trans Sarbagita passengers in 2013 using ANFIS. The ANFIS system composed by five layers where each layers has a different function and its divide in two phases, i.e. forward and backward phases. The ANFIS uses a hybrid learning algorithm which is a combination of Least Squares Estimator (LSE) on forwards phases and Error Backpropagation (EBP) on the backward phases. The results show, ANFIS with six inputs with M.F of Pi produces smallest error, compared to seven and eight input and M.F gauss and generalizedbell. Forecast of Trans Sarbagita passenger numbers in 2013 have to fluctuated every day and the average of passenger’s Trans Sarbagita for a day is 1627 passengers with MSE equal to 10210 and MAPE is 4.01%. Keywords: ANFIS, fuzzy inference system, Error backpropagation algorithm

6-10

Authors: PUTU SUSAN PRADAWATI, KOMANG GDE SUKARSA, I GUSTI AYU MADE SRINADI

Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

18-26

Authors: IDA BAGUS KADE PUJA ARIMBAWA K., KETUT JAYANEGARA, I PUTU EKA NILA KENCANA

This study compares the accuracy of forecasting using ANFIS and Fuzzy Time Series the number of Australian tourists to Bali. The data used in this study are data on the number of Australia tourists visit to Bali from the period January 2006 through December 2011. ANFIS consists of two stages of learning and testing phases. Least Squares Estimator is used to study the forward direction and Error Back Propagation learning is used in the reverse direction. Forecasting with Fuzzy Time Series is forecast to capture the pattern of previous data is then used to project the data to come. The results of comparison of both methods showed that the ANFIS method has a higher forecasting accuracy than the method of Fuzzy Time Series. Forecasting by using ANFIS method obtained AFER aqual to 9,26% while the prediction using the method of Fuzzy Time Series obtained AFER aqual to 14,02% Keywords: ANFIS, Fuzzy Time Series, Forecasting, Australian Tourist Forecasting

32-36

Authors: ADE KUSUMA DEWI, I WAYAN SUMARJAYA, I GUSTI AYU MADE SRINADI

The experiments were conducted to determine the relationship between response variable and independent variable and the effect of independent variables to response variable. Multiple comparison tests can be used to find the level that makes optimal response. However, this test has a drawback that it only finds the optimal level tested at the level being considered. Thus test is more suitable for qualitative independent variables. On the other hand, for quantitative independent variables we can use the orthogonal polynomial method and response surface method (RSM).The purpose of this research is to apply RSM to produce optimal response. It can be concluded that RSM is an efficient used to find the level of independent variables to makes optimal response. Keywords: Experiments Design, Response Surface Method.

42-48

Authors: PANDE GDE DONY GUMILAR, LUH PUTU IDA HARINI, KARTIKA SARI

The metric dimension of connected graph G is the cardinality of minimum resolving set in graph G. In this research, we study how to find the metric dimension of lobster graph L_n (q;r). Lobster graph L_n (q;r) is a regular lobster graph with n vertices backbone on the main path, every backbone vertex is connected to q hand vertices and every hand vertex is connected to r finger vertices, with n,q,r ∈N,n≥2. We obtain the metric dimension of lobster graph L_2 (1;1) is 1, the metric dimension of lobster graph L_n (1;1) for n>2 is 2, the metric dimension of lobster graph L_n (q;1) for n≥2 and q≥2 is n(q-1) and the metric dimension of lobster graph L_n (q;r) for n≥2,q≥1 and r≥2 is nq(r-1). Keywords: lobster graph, metric dimension, resolving set.

54-58

Authors: PUTU NOPITA PURNAMA NINGSIH, KETUT JAYANEGARA, I PUTU EKA NILA KENCANA

The aim of this research is to determine the relationship between environmental, behavioral, health services, education, and economic variables to health status in the Province of Bali. These variables are constructs (latents ) that can not be measured directly by observation. If there was a relationship between latent and its indicators, it is recomended to use Structural Equation Modeling (SEM). In this research we used variance-based SEM i.e. Generalized Structured Component Analysis (GSCA). This method not based on many assumptions such as the data does not have a multivariate normal distribution, the sample size does is not necessary large. Moreover, GSCA provides by overall goodness-fit of the model. The result of this research indicates that the environmental, behavioral, economic and educational variable influenced health status, but health service does not significantly affect the health status; economic does not significantly affect the environment; and education does not significantly affect the behavior. The result of the FIT value 0.450 and the AFIT value 0.429 showed that overall model in this research is not good enough because of both of these values are under 0.50. Keywords: Latent Variable, Structural Equation Modeling (SEM), Generalized Structured Component Analysis(GSCA), Derajat Kesehatan

6-13

Authors: IDA AYU PRASETYA UTHAMI, I KOMANG GDE SUKARSA, I PUTU EKA NILA KENCANA

In regression analysis, the method used to estimate the parameters is Ordinary Least Squares (OLS). The principle of OLS is to minimize the sum of squares error. If any of the assumptions were not met, the results of the OLS estimates are no longer best, linear, and unbiased estimator (BLUE). One of the assumptions that must be met is the assumption about homoscedasticity, a condition in which the variance of the error is constant (same). Violation of the assumptions about homoscedasticity is referred to heteroscedasticity. When there exists heteroscedas¬ticity, other regression techniques are needed, such as median quantile regression which is done by defining the median as a solution to minimize sum of absolute error. This study intended to estimate the regression parameters of the data were known to have heteroscedasticity. The secondary data were taken from the book Basic Econometrics (Gujarati, 2004) and analyzing method were performed by EViews 6. Parameter estimation of the median quantile regression were done by estimating the regression parameters at each quantile τth, then an estimator was chosen on the median quantile as regression coefficients estimator. The result showed heteroscedasticity problem has been solved with median quantile regression although error still does not follow normal distribution properties with a value of R2 about 71 percent. Therefore it can be concluded that median quantile regression can overcome heteroscedasticity but the data still abnormalities. Keywords: Heteroscedasticity, Median Quantile Regression, EViews

19-23

Authors: FEMY AYU ASTITI, NI MADE ASIH, I NYOMAN WIDANA

Optimization problems can be solved by various methods, such as Lagrange Method. This method can be used to find the solution. Using Lagrange method, the extreme value can be obtained, so that the optimal solution can be found. In this research, the maximum revenue of UD. Sari Madu is a limited by several constraints. After the objective function and constraint function being model, than maximum revenue is found. From first until fourth quarterly, the maximum revenue is found Rp. 9.701.333, Rp. 10.064.148, 9.793.272 and Rp. 9.397.730 respectively. Keywords: Lagrange Method, Ekstrem Value, Optimization

33-36

Authors: KADEK FRISCA AYU DEVI, KOMANG DHARMAWAN, NI MADE ASIH

Utility function can use to give risk preference for investors who want to get the benefits gained meets investment targets. Quadratic utility functions on optimal portfolio is strongly influenced by the expected return and standard deviation. The establishment of optimal portfolios using a quadratic utility function optimization problems. Under the settlement portfolio optimization, the necessary data is expected return, variance, and variance covariance matrix. The optimal portfolio is affected by some factors Risky less Rate, risk aversion index, and Borrow Rate. The results of settlement portfolio optimization is obtaining the utility value while the relatively large changes influencing by risk averse index. Keywords: Portofolio optimal, Historical data, utility function

42-48

Authors: KADEK RISNA WITARI, I.G.K. GANDHIADI, I PUTU EKA NILA KENCANA

The closeness of the relationship between dogs and human makes the dog can be trained, played together, lived together with human and are invited to socialize with human and other dogs. But, despite its this relationship, the dogs can also have a contagious disease that may be harmful to human. Diagnostic expert system for infectious disease in dogs for as web-based system with the media android used as a tool for diagnosing infectious diseases in dogs based on physical characteristics or symptoms that can be seen or felt without through examination of the specifics. The diagnostics final results are expected to be a reference for further examination and handling of dogs that contract the disease is detected to prevent the disease for humans. This expert system uses a forward chaining inference method and Certainty Factor to infer. Keywords: expert systems, forward chaining, certainty factor

54-59

Authors: NI KETUT TRI UTAMI, I KOMANG GDE SUKARSA,I PUTU EKA NILA KENCANA

Ordinary least square is parameter estimation method for linier regression analysis by minimizing residual sum of square. In the presence of multicollinearity, estimators which are unbiased and have a minimum variance can not be generated. Multicollinearity refers to a situation where regressor variables are highly correlated. Generalized Ridge Regression is an alternative method to deal with multicollinearity problem. In Generalized Ridge Regression, different biasing parameters for each regressor variables were added to the least square equation after transform the data to the space of orthogonal regressors. The analysis showed that Generalized Ridge Regression was satisfactory to overcome multicollinearity. Keywords: Linear regression, parameter estimation, multicollinearity, Generalized Ridge Regression