Search results for: generalized regression

Authors: Sifriyani Sifriyani, I Nyoman Budiantara, Sri Haryatmi, Gunardi Gunardi

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East Java Province has a first rank as a province that has the most counties and cities in Indonesia and has the largest population. In 2015, the population reached 38.847.561 million, this figure showed a very high population growth. High population growth is feared to lead to increase the levels of unemployment. In this study, the researchers mapped and modeled the unemployment rate with 6 variables that were supposed to influence. Modeling was done by nonparametric geographically weighted regression methods with truncated spline approach. This method was chosen because spline method is a flexible method, these models tend to look for its own estimation. In this modeling, there were point knots, the point that showed the changes of data. The selection of the optimum point knots was done by selecting the most minimun value of Generalized Cross Validation (GCV). Based on the research, 6 variables were declared to affect the level of unemployment in eastern Java. They were the percentage of population that is educated above high school, the rate of economic growth, the population density, the investment ratio of total labor force, the regional minimum wage and the ratio of the number of big industry and medium scale industry from the work force. The nonparametric geographically weighted regression models with truncated spline approach had a coefficient of determination 98.95% and the value of MSE equal to 0.0047.

Keywords: East Java, nonparametric geographically weighted regression, spatial, spline approach, unemployed rate

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Authors: Idrissa Kayijuka

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The logistic regression and Cox regression models (proportional hazard model) at present are being employed in the analysis of prospective epidemiologic research looking into risk factors in their application on chronic diseases. However, a theoretical relationship between the two models has been studied. By definition, Cox regression model also called Cox proportional hazard model is a procedure that is used in modeling data regarding time leading up to an event where censored cases exist. Whereas the Logistic regression model is mostly applicable in cases where the independent variables consist of numerical as well as nominal values while the resultant variable is binary (dichotomous). Arguments and findings of many researchers focused on the overview of Cox and Logistic regression models and their different applications in different areas. In this work, the analysis is done on secondary data whose source is SPSS exercise data on BREAST CANCER with a sample size of 1121 women where the main objective is to show the application difference between Cox regression model and logistic regression model based on factors that cause women to die due to breast cancer. Thus we did some analysis manually i.e. on lymph nodes status, and SPSS software helped to analyze the mentioned data. This study found out that there is an application difference between Cox and Logistic regression models which is Cox regression model is used if one wishes to analyze data which also include the follow-up time whereas Logistic regression model analyzes data without follow-up-time. Also, they have measurements of association which is different: hazard ratio and odds ratio for Cox and logistic regression models respectively. A similarity between the two models is that they are both applicable in the prediction of the upshot of a categorical variable i.e. a variable that can accommodate only a restricted number of categories. In conclusion, Cox regression model differs from logistic regression by assessing a rate instead of proportion. The two models can be applied in many other researches since they are suitable methods for analyzing data but the more recommended is the Cox, regression model.

Keywords: logistic regression model, Cox regression model, survival analysis, hazard ratio

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Authors: Weiwen Li, Hao Huang, Chengmao You, Jianji Liao, Lei Wang, Lina An

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Zooplankton are a central issue in the ecology which makes a great contribution to maintaining the balance of an ecosystem. It is critical in promoting the material cycle and energy flow within the ecosystems. A generalized additive model (GAM) was applied to analyze the relationships between the density (individuals per m³) of zooplankton and other variables in West Daya Bay. All data used in this analysis (the survey month, survey station (longitude and latitude), the depth of the water column, the superficial concentration of chlorophyll a, the benthonic concentration of chlorophyll a, the number of zooplankton species and the number of zooplankton species) were collected through monthly scientific surveys during January to December 2016. GLM model (generalized linear model) was used to choose the significant variables’ impact on the density of zooplankton, and the GAM was employed to analyze the relationship between the density of zooplankton and the significant variables. The results showed that the density of zooplankton increased with an increase of the benthonic concentration of chlorophyll a, but decreased with a decrease in the depth of the water column. Both high numbers of zooplankton species and the overall total number of zooplankton individuals led to a higher density of zooplankton.

Keywords: density, generalized linear model, generalized additive model, the West Daya Bay, zooplankton

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Authors: Masahiro Ohmura, Koh Kakusho, Takeshi Okadome

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This paper presents a regression model with autocorrelated errors in which the inputs are social moods obtained by analyzing the adjectives in Twitter posts using a document topic model. The regression model predicts Dow Jones Industrial Average (DJIA) more precisely than autoregressive moving-average models.

Keywords: stock market prediction, social moods, regression model, DJIA

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Authors: Shiwei Deng, Yang Bao

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In this paper, we present a model-based regression test suite reducing approach that uses EFSM model dependence analysis and probability-driven greedy algorithm to reduce software regression test suites. The approach automatically identifies the difference between the original model and the modified model as a set of elementary model modifications. The EFSM dependence analysis is performed for each elementary modification to reduce the regression test suite, and then the probability-driven greedy algorithm is adopted to select the minimum set of test cases from the reduced regression test suite that cover all interaction patterns. Our initial experience shows that the approach may significantly reduce the size of regression test suites.

Keywords: dependence analysis, EFSM model, greedy algorithm, regression test

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Authors: Suparman

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Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

Keywords: piecewise regression, bayesian, reversible jump MCMC, segmentation

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Yohei Saika

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On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, multiple interferograms, statistical mechanics

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

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In this paper, quantitative structure-retention relationships (QSRR) analysis was applied in order to correlate in silico biological and lipophilicity molecular descriptors with retention values for the set of selected s-triazine herbicides. In silico generated biological and lipophilicity descriptors were discriminated using generalized pair correlation method (GPCM). According to this method, the significant difference between independent variables can be noticed regardless almost equal correlation with dependent variable. Using established multiple linear regression (MLR) models some biological characteristics could be predicted. Established MLR models were evaluated statistically and the most suitable models were selected and ranked using sum of ranking differences (SRD) method. In this method, as reference values, average experimentally obtained values are used. Additionally, using SRD method, similarities among investigated s-triazine herbicides can be noticed. These analysis were conducted in order to characterize selected s-triazine herbicides for future investigations regarding their biodegradability. This study is financially supported by COST action TD1305.

Keywords: descriptors, generalized pair correlation method, pesticides, sum of ranking differences

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Authors: Shiva Abdoli, Daniel T.Semere

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Several researches have been conducted to study consumption of energy in cutting process. Most of these researches are focusing to measure the consumption and propose consumption reduction methods. In this work, the relation between the cutting parameters and the consumption is investigated in order to establish a generalized energy consumption model that can be used for process and production planning in real production lines. Using the generalized model, the process planning will be carried out by taking into account the energy as a function of the selected process parameters. Similarly, the generalized model can be used in production planning to select the right operational parameters like batch sizes, routing, buffer size, etc. in a production line. The description and derivation of the model as well as a case study are given in this paper to illustrate the applicability and validity of the model.

Keywords: process parameters, cutting process, energy efficiency, Material Removal Rate (MRR)

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Imaneh Abbasi, Ladan Fata, Majid Sadeghi, Sara Banihashemi, Abolfazl Mohammadee

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Background: Dimensional and transdiagnostic approaches as a result of high comorbidity among mental disorders have captured researchers and clinicians interests for exploring the latent factors of development and maintenance of some psychological disorders. The goal of present study is to compare some of these common factors between generalized anxiety disorder and unipolar mood disorder. Methods: 27 patients with generalized anxiety disorder, 29 patients with depression disorder were recruited using SCID-I and 69 non-clinical population were selected using GHQ cut off point. MANCOVA was used for analyzing data. Results: The results show that worry, rumination, intolerance of uncertainty, maladaptive metacognitive beliefs, and experiential avoidance were all significantly different between GAD and unipolar mood disorder groups. However, there were not any significant differences in difficulties in emotion regulation and neuroticism between GAD and unipolar mood disorder groups. Discussion: Results indicate that although there are some transdiagnostic and common factors in GAD and unipolar mood disorder, there may be some specific vulnerability factors for each disorder. Further study is needed for answering these questions.

Keywords: transdiagnostic, depression, generalized anxiety disorder, emotion regulation

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Authors: Nada Farhani, Naim Terbeh, Mounir Zrigui

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The recognition of the objects contained in images has always presented a challenge in the field of research because of several difficulties that the researcher can envisage because of the variability of shape, position, contrast of objects, etc. In this paper, we will be interested in the recognition of objects. The classical Hough Transform (HT) presented a tool for detecting straight line segments in images. The technique of HT has been generalized (GHT) for the detection of arbitrary forms. With GHT, the forms sought are not necessarily defined analytically but rather by a particular silhouette. For more precision, we proposed to combine the results from the GHT with the results from a calculation of similarity between the histograms and the spatiograms of the images. The main purpose of our work is to use the concepts from recognition to generate sentences in Arabic that summarize the content of the image.

Keywords: recognition of shape, generalized hough transformation, histogram, spatiogram, learning

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Authors: Hadush Kidane Meresa

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The hydrological extremes frequency analysis is the foundation for the hydraulic engineering design, flood protection, drought management and water resources management and planning to utilize the available water resource to meet the desired objectives of different organizations and sectors in a country. This spatial variation of the statistical characteristics of the extreme flood and drought events are key practice for regional flood and drought analysis and mitigation management. For different hydro-climate of the regions, where the data set is short, scarcity, poor quality and insufficient, the regionalization methods are applied to transfer at-site data to a region. This study aims in regional high and low flow frequency analysis for Poland River Basins. Due to high frequent occurring of hydrological extremes in the region and rapid water resources development in this basin have caused serious concerns over the flood and drought magnitude and frequencies of the river in Poland. The magnitude and frequency result of high and low flows in the basin is needed for flood and drought planning, management and protection at present and future. Hydrological homogeneous high and low flow regions are formed by the cluster analysis of site characteristics, using the hierarchical and C- mean clustering and PCA method. Statistical tests for regional homogeneity are utilized, by Discordancy and Heterogeneity measure tests. In compliance with results of the tests, the region river basin has been divided into ten homogeneous regions. In this study, frequency analysis of high and low flows using AM for high flow and 7-day minimum low flow series is conducted using six statistical distributions. The use of L-moment and LL-moment method showed a homogeneous region over entire province with Generalized logistic (GLOG), Generalized extreme value (GEV), Pearson type III (P-III), Generalized Pareto (GPAR), Weibull (WEI) and Power (PR) distributions as the regional drought and flood frequency distributions. The 95% percentile and Flow duration curves of 1, 7, 10, 30 days have been plotted for 10 stations. However, the cluster analysis performed two regions in west and east of the province where L-moment and LL-moment method demonstrated the homogeneity of the regions and GLOG and Pearson Type III (PIII) distributions as regional frequency distributions for each region, respectively. The spatial variation and regional frequency distribution of flood and drought characteristics for 10 best catchment from the whole region was selected and beside the main variable (streamflow: high and low) we used variables which are more related to physiographic and drainage characteristics for identify and delineate homogeneous pools and to derive best regression models for ungauged sites. Those are mean annual rainfall, seasonal flow, average slope, NDVI, aspect, flow length, flow direction, maximum soil moisture, elevation, and drainage order. The regional high-flow or low-flow relationship among one streamflow characteristics with (AM or 7-day mean annual low flows) some basin characteristics is developed using Generalized Linear Mixed Model (GLMM) and Generalized Least Square (GLS) regression model, providing a simple and effective method for estimation of flood and drought of desired return periods for ungauged catchments.

Keywords: flood , drought, frequency, magnitude, regionalization, stochastic, ungauged, Poland

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Authors: M. A. Ansari, A. Hussain, A. Uddin

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A side weir is a flow diversion structure provided in the side wall of a channel to divert water from the main channel to a branch channel. The trapezoidal labyrinth weir is a special type of weir in which crest length of the weir is increased to pass higher discharge. Experimental and numerical studies related to the coefficient of discharge of trapezoidal labyrinth weir in an open channel have been presented in the present study. Group Method of Data Handling (GMDH) with the transfer function of quadratic polynomial has been used to predict the coefficient of discharge for the side trapezoidal labyrinth weir. A new model is developed for coefficient of discharge of labyrinth weir by regression method. Generalized models for predicting the coefficient of discharge for labyrinth weir using Group Method of Data Handling (GMDH) network have also been developed. The prediction based on GMDH model is more satisfactory than those given by traditional regression equations.

Keywords: discharge coefficient, group method of data handling, open channel, side labyrinth weir

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Authors: Zhou Jianhong

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Model averaging is a desirable approach to deal with model uncertainty, which, however, has rarely been explored for Poisson regression. In this paper, we propose a model averaging procedure based on an unbiased estimator of the expected Kullback-Leibler distance for the Poisson regression. Simulation study shows that the proposed model average estimator outperforms some other commonly used model selection and model average estimators in some situations. Our proposed methods are further applied to a real data example and the advantage of this method is demonstrated again.

Keywords: model averaging, poission regression, Kullback-Leibler distance, statistics

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: M. Guemmadi, A. Ouibrahim

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This numerical investigation aims to evaluate how a viscoelastic lubricant described by a generalized Maxwell model, affects the pressure distribution, the load capacity and thermal effect in a journal bearing lubrication. We use for the purpose the CFD package software completed by adapted user define functions (UDFs) to solve the coupled equations of momentum, of energy and of the viscoelastic model (generalized Maxwell model). Two parameters, viscosity and relaxation time are involved to show how viscoelasticity substantially affect the pressure distribution, the load capacity and the thermal transfer by comparison to Newtonian lubricant. These results were also compared with the available published results.

Keywords: journal bearing, lubrication, Maxwell model, viscoelastic fluids, computational modelling, load capacity

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Authors: Jude Opara, Esemokumo Perewarebo Akpos

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This paper is on non-parametric linear regression over its parametric counterparts with large sample size. Data set on anthropometric measurement of primary school pupils was taken for the analysis. The study used 50 randomly selected pupils for the study. The set of data was subjected to normality test, and it was discovered that the residuals are not normally distributed (i.e. they do not follow a Gaussian distribution) for the commonly used least squares regression method for fitting an equation into a set of (x,y)-data points using the Anderson-Darling technique. The algorithms for the nonparametric Theil’s regression are stated in this paper as well as its parametric OLS counterpart. The use of a programming language software known as “R Development” was used in this paper. From the analysis, the result showed that there exists a significant relationship between the response and the explanatory variable for both the parametric and non-parametric regression. To know the efficiency of one method over the other, the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) are used, and it is discovered that the nonparametric regression performs better than its parametric regression counterparts due to their lower values in both the AIC and BIC. The study however recommends that future researchers should study a similar work by examining the presence of outliers in the data set, and probably expunge it if detected and re-analyze to compare results.

Keywords: Theil’s regression, Bayesian information criterion, Akaike information criterion, OLS

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Authors: O. Anan, D. Böhning, A. Maruotti

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The purpose of the study is to estimate the elusive target population size under a truncated count model that accounts for heterogeneity. The purposed estimator is based on the generalized Poisson distribution (GPD), which extends the Poisson distribution by adding a dispersion parameter. Thus, it becomes an useful model for capture-recapture data where concurrent events are not homogeneous. In addition, it can account for over-dispersion and under-dispersion. The ratios of neighboring frequency counts are used as a tool for investigating the validity of whether generalized Poisson or Poisson distribution. Since capture-recapture approaches do not provide the zero counts, the estimated parameters can be achieved by modifying the EM-algorithm technique for the zero-truncated generalized Poisson distribution. The properties and the comparative performance of proposed estimator were investigated through simulation studies. Furthermore, some empirical examples are represented insights on the behavior of the estimators.

Keywords: capture, recapture methods, ratio plot, heterogeneous population, zero-truncated count

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Authors: Kailash C. Madan

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We study the steady state behaviour of a batch arrival single server queue in which the first service with general service times is compulsory and the second service with general service times is optional. We term such a two phase service as generalized Coxian-2 service. Just after completion of a service the server must take a vacation of random length of time with general vacation times. We obtain steady state probability generating functions for the queue size as well as the steady state mean queue size at a random epoch of time in explicit and closed forms. Some particular cases of interest including some known results have been derived.

Keywords: batch arrivals, compound Poisson process, generalized Coxian-2 service, steady state

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Authors: Jeeban Amgain

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This paper investigates the impact of the size and composition of government expenditure and tax on GDP per capita growth in 36 Asian economies over the period of 1991-2012. The research employs the technique of panel regression; Fixed Effects and Generalized Method of Moments (GMM) as well as other statistical and descriptive approaches. The finding concludes that the size of government expenditure and tax revenue are generally low in this region. GDP per capita growth is strongly negative in response to Government expenditure, however, no significant relationship can be measured in case of size of taxation although it is positively correlated with economic growth. Panel regression of decomposed fiscal components also shows that the pattern of allocation of expenditure and taxation really matters on growth. Taxes on international trade and property have a significant positive impact on growth. In contrast, a major portion of expenditure, i.e. expenditure on general public services, health and education are found to have significant negative impact on growth, implying that government expenditures are not being productive in the Asian region for some reasons. Comparatively smaller and efficient government size would enhance the growth.

Keywords: government expenditure, tax, GDP per capita growth, composition

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Denys Osipenko, Jonathan Crook

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Because of the variety of the card holders’ behaviour types and income sources each consumer account can be transferred to a variety of states. Each consumer account can be inactive, transactor, revolver, delinquent, defaulted and requires an individual model for the income prediction. The estimation of transition probabilities between statuses at the account level helps to avoid the memorylessness of the Markov Chains approach. This paper investigates the transition probabilities estimation approaches to credit cards income prediction at the account level. The key question of empirical research is which approach gives more accurate results: multinomial logistic regression or multistage conditional logistic regression with binary target. Both models have shown moderate predictive power. Prediction accuracy for conditional logistic regression depends on the order of stages for the conditional binary logistic regression. On the other hand, multinomial logistic regression is easier for usage and gives integrate estimations for all states without priorities. Thus further investigations can be concentrated on alternative modeling approaches such as discrete choice models.

Keywords: multinomial regression, conditional logistic regression, credit account state, transition probability

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Authors: Ksenija Dumičić, Anita Čeh Časni, Irena Palić

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This paper examines economic and Information and Communication Technology (ICT) development influence on recently increasing Internet purchases by individuals for European Union member states. After a growing trend for Internet purchases in EU27 was noticed, all possible regression analysis was applied using nine independent variables in 2011. Finally, two linear regression models were studied in detail. Conducted simple linear regression analysis confirmed the research hypothesis that the Internet purchases in analysed EU countries is positively correlated with statistically significant variable Gross Domestic Product per capita (GDPpc). Also, analysed multiple linear regression model with four regressors, showing ICT development level, indicates that ICT development is crucial for explaining the Internet purchases by individuals, confirming the research hypothesis.

Keywords: European union, Internet purchases, multiple linear regression model, outlier

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Authors: Muhammad Sameer Ahmed, Piotr Remlein, Tansal Gucluoglu

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The technique called as Generalized frequency division multiplexing (GFDM) used in the free space optical channel can be a good option for implementation free space optical communication systems. This technique has several strengths e.g. good spectral efficiency, low peak-to-average power ratio (PAPR), adaptability and low co-channel interference. In this paper, the impact of weather conditions such as haze, rain and fog on GFDM over the gamma-gamma channel model is discussed. A Trade off between link distance and system performance under intense weather conditions is also analysed. The symbol error probability (SEP) of GFDM over the gamma-gamma turbulence channel is derived and verified with the computer simulations.

Keywords: free space optics, generalized frequency division multiplexing, weather conditions, gamma gamma distribution

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: Arindam Chaudhuri

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The research presents epsilon- hierarchical fuzzy twin support vector regression (epsilon-HFTSVR) based on epsilon-fuzzy twin support vector regression (epsilon-FTSVR) and epsilon-twin support vector regression (epsilon-TSVR). Epsilon-FTSVR is achieved by incorporating trapezoidal fuzzy numbers to epsilon-TSVR which takes care of uncertainty existing in forecasting problems. Epsilon-FTSVR determines a pair of epsilon-insensitive proximal functions by solving two related quadratic programming problems. The structural risk minimization principle is implemented by introducing regularization term in primal problems of epsilon-FTSVR. This yields dual stable positive definite problems which improves regression performance. Epsilon-FTSVR is then reformulated as epsilon-HFTSVR consisting of a set of hierarchical layers each containing epsilon-FTSVR. Experimental results on both synthetic and real datasets reveal that epsilon-HFTSVR has remarkable generalization performance with minimum training time.

Keywords: regression, epsilon-TSVR, epsilon-FTSVR, epsilon-HFTSVR

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