Search results for: Multi Linear Regression

Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: S. Deswal, M. Pal

Abstract:

The paper aims to compare the performance of vertical and inclined multiple plunging jets and to model and predict their mass transfer capacity by multi-linear regression based approach. The multiple vertical plunging jets have jet impact angle of θ = 90^O; whereas, multiple inclined plunging jets have jet impact angle of θ = 60^O. The results of the study suggests that mass transfer is higher for multiple jets, and inclined multiple plunging jets have up to 1.6 times higher mass transfer than vertical multiple plunging jets under similar conditions. The derived relationship, based on multi-linear regression approach, has successfully predicted the volumetric mass transfer coefficient (K_La) from operational parameters of multiple plunging jets with a correlation coefficient of 0.973, root mean square error of 0.002 and coefficient of determination of 0.946. The results suggests that predicted overall mass transfer coefficient is in good agreement with actual experimental values; thereby, suggesting the utility of derived relationship based on multi-linear regression based approach and can be successfully employed in modeling mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, multi-linear regression.

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

Abstract:

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: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Mohammad Namazi, Mohammad Sadeghzadeh Maharluie

Abstract:

Predicting earnings management is vital for the capital market participants, financial analysts and managers. The aim of this research is attempting to respond to this query: Is there a significant difference between the regression model and neural networks’ models in predicting earnings management, and which one leads to a superior prediction of it? In approaching this question, a Linear Regression (LR) model was compared with two neural networks including Multi-Layer Perceptron (MLP), and Generalized Regression Neural Network (GRNN). The population of this study includes 94 listed companies in Tehran Stock Exchange (TSE) market from 2003 to 2011. After the results of all models were acquired, ANOVA was exerted to test the hypotheses. In general, the summary of statistical results showed that the precision of GRNN did not exhibit a significant difference in comparison with MLP. In addition, the mean square error of the MLP and GRNN showed a significant difference with the multi variable LR model. These findings support the notion of nonlinear behavior of the earnings management. Therefore, it is more appropriate for capital market participants to analyze earnings management based upon neural networks techniques, and not to adopt linear regression models.

Keywords: Earnings management, generalized regression neural networks, linear regression, multi-layer perceptron, Tehran stock exchange.

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Authors: M. Moeinaddini, Z. Asadi-Shekari, M. Zaly Shah, A. Hamzah

Abstract:

Currently, planners try to have more green travel options to decrease economic, social and environmental problems. Therefore, this study tries to find significant urban travel factors to be used to increase the usage of alternative urban travel modes. This paper attempts to identify the relationship between prominent urban mobility indicators and daily trips by public transport in 30 cities from various parts of the world. Different travel modes, infrastructures and cost indicators were evaluated in this research as mobility indicators. The results of multi-linear regression analysis indicate that there is a significant relationship between mobility indicators and the daily usage of public transport.

Keywords: Green travel modes, urban travel indicators, daily trips by public transport, multi-linear regression analysis.

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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 analyzed EU countries is positively correlated with statistically significant variable Gross Domestic Product per capita (GDPpc). Also, analyzed 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: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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Authors: Liu Zhiyuan, Sun Zongdi, Liu Zhiyuan, Sun Zongdi

Abstract:

Qingdao is a seaside city. Taking into account the characteristics of Qingdao, this article established a multiple linear regression model to analyze the impact of macroeconomic factors on housing prices. We used stepwise regression method to make multiple linear regression analysis, and made statistical analysis of F test values and T test values. According to the analysis results, the model is continuously optimized. Finally, this article obtained the multiple linear regression equation and the influencing factors, and the reliability of the model was verified by F test and T test.

Keywords: Housing prices, multiple linear regression model, macroeconomic factors, Qingdao City.

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Authors: Shih-Pin Chen, Shih-Syuan You

Abstract:

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: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Arkady Bolotin

Abstract:

Dichotomization of the outcome by a single cut-off point is an important part of various medical studies. Usually the relationship between the resulted dichotomized dependent variable and explanatory variables is analyzed with linear regression, probit regression or logistic regression. However, in many real-life situations, a certain cut-off point dividing the outcome into two groups is unknown and can be specified only approximately, i.e. surrounded by some (small) uncertainty. It means that in order to have any practical meaning the regression model must be robust to this uncertainty. In this paper, we show that neither the beta in the linear regression model, nor its significance level is robust to the small variations in the dichotomization cut-off point. As an alternative robust approach to the problem of uncertain medical categories, we propose to use the linear regression model with the fuzzy membership function as a dependent variable. This fuzzy membership function denotes to what degree the value of the underlying (continuous) outcome falls below or above the dichotomization cut-off point. In the paper, we demonstrate that the linear regression model of the fuzzy dependent variable can be insensitive against the uncertainty in the cut-off point location. In the paper we present the modeling results from the real study of low hemoglobin levels in infants. We systematically test the robustness of the binomial regression model and the linear regression model with the fuzzy dependent variable by changing the boundary for the category Anemia and show that the behavior of the latter model persists over a quite wide interval.

Keywords: Categorization, Uncertain medical categories, Binomial regression model, Fuzzy dependent variable, Robustness.

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Authors: Anastasiia Yu. Timofeeva

Abstract:

Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: Grade point average, orthogonal regression, penalized regression spline, locally weighted regression.

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Authors: S. Deswal, M. Pal

Abstract:

Presently various computational techniques are used in modeling and analyzing environmental engineering data. In the present study, an intra-comparison of polynomial and radial basis kernel functions based on Support Vector Regression and, in turn, an inter-comparison with Multi Linear Regression has been attempted in modeling mass transfer capacity of vertical (θ = 90O) and inclined (θ multiple plunging jets (varying from 1 to 16 numbers). The data set used in this study consists of four input parameters with a total of eighty eight cases, forty four each for vertical and inclined multiple plunging jets. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 along with corresponding root mean square error values of 0.0025 and 0.0020 were achieved by using polynomial and radial basis kernel functions based Support Vector Regression respectively. An intra-comparison suggests improved performance by radial basis function in comparison to polynomial kernel based Support Vector Regression. Further, an inter-comparison with Multi Linear Regression (correlation coefficient = 0.973 and root mean square error = 0.0024) reveals that radial basis kernel functions based Support Vector Regression performs better in modeling and estimating mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, polynomial and radial basis kernel functions, Support Vector Regression.

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Authors: G. Lavanya Devi, Allam Appa Rao, A. Damodaram, GR Sridhar, G. Jaya Suma

Abstract:

Cluster analysis divides data into groups that are meaningful, useful, or both. Analysis of biological data is creating a new generation of epidemiologic, prognostic, diagnostic and treatment modalities. Clustering of protein sequences is one of the current research topics in the field of computer science. Linear relation is valuable in rule discovery for a given data, such as if value X goes up 1, value Y will go down 3", etc. The classical linear regression models the linear relation of two sequences perfectly. However, if we need to cluster a large repository of protein sequences into groups where sequences have strong linear relationship with each other, it is prohibitively expensive to compare sequences one by one. In this paper, we propose a new technique named General Regression Model Technique Clustering Algorithm (GRMTCA) to benignly handle the problem of linear sequences clustering. GRMT gives a measure, GR*, to tell the degree of linearity of multiple sequences without having to compare each pair of them.

Keywords: Clustering, General Regression Model, Protein Sequences, Similarity Measure.

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Authors: Aly Farag, Ayman El-Baz, Refaat Mohamed

Abstract:

In this paper we present a novel approach for density estimation. The proposed approach is based on using the logistic regression model to get initial density estimation for the given empirical density. The empirical data does not exactly follow the logistic regression model, so, there will be a deviation between the empirical density and the density estimated using logistic regression model. This deviation may be positive and/or negative. In this paper we use a linear combination of Gaussian (LCG) with positive and negative components as a model for this deviation. Also, we will use the expectation maximization (EM) algorithm to estimate the parameters of LCG. Experiments on real images demonstrate the accuracy of our approach.

Keywords: Logistic regression model, Expectationmaximization, Segmentation.

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Authors: Yakin Hajlaoui, Richard Labib, Jean-Franc¸ois Plante, Michel Gamache

Abstract:

This study presents the Multi-Layer Inverse Distance Weighting Model (ML-IDW), inspired by the mathematical formulation of both multi-layer neural networks (ML-NNs) and Inverse Distance Weighting model (IDW). ML-IDW leverages ML-NNs’ processing capabilities, characterized by compositions of learnable non-linear functions applied to input features, and incorporates IDW’s ability to learn anisotropic spatial dependencies, presenting a promising solution for nonlinear spatial interpolation and learning from complex spatial data. We employ gradient descent and backpropagation to train ML-IDW. The performance of the proposed model is compared against conventional spatial interpolation models such as Kriging and standard IDW on regression and classification tasks using simulated spatial datasets of varying complexity. Our results highlight the efficacy of ML-IDW, particularly in handling complex spatial dataset, exhibiting lower mean square error in regression and higher F1 score in classification.

Keywords: Deep Learning, Multi-Layer Neural Networks, Gradient Descent, Spatial Interpolation, Inverse Distance Weighting.

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Authors: Chie Obayashi, Hidekazu Tanaka, Yoshiji Takagi

Abstract:

In multi-parameter family of distributions, conditions for a modified maximum likelihood estimator to be second order admissible are given. Applying these results to the multi-parameter logistic regression model, it is shown that the maximum likelihood estimator is always second order inadmissible. Also, conditions for the Berkson estimator to be second order admissible are given.

Keywords: Berkson estimator, modified maximum likelihood estimator, Multi-parameter logistic regression model, second order admissibility.

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Authors: Wint Thida Zaw, Thinn Thu Naing

Abstract:

One of the essential sectors of Myanmar economy is agriculture which is sensitive to climate variation. The most important climatic element which impacts on agriculture sector is rainfall. Thus rainfall prediction becomes an important issue in agriculture country. Multi variables polynomial regression (MPR) provides an effective way to describe complex nonlinear input output relationships so that an outcome variable can be predicted from the other or others. In this paper, the modeling of monthly rainfall prediction over Myanmar is described in detail by applying the polynomial regression equation. The proposed model results are compared to the results produced by multiple linear regression model (MLR). Experiments indicate that the prediction model based on MPR has higher accuracy than using MLR.

Keywords: Polynomial Regression, Rainfall Forecasting, Statistical forecasting.

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Authors: Michal Cerny

Abstract:

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

Keywords: Linear regression, interval-censored data, computational complexity.

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: Fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem.

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Authors: A. K. Al-Othman, H. A. Al-Mekhaizim

Abstract:

Multilevel inverters supplied from equal and constant dc sources almost don-t exist in practical applications. The variation of the dc sources affects the values of the switching angles required for each specific harmonic profile, as well as increases the difficulty of the harmonic elimination-s equations. This paper presents an extremely fast optimal solution of harmonic elimination of multilevel inverters with non-equal dc sources using Tanaka's fuzzy linear regression formulation. A set of mathematical equations describing the general output waveform of the multilevel inverter with nonequal dc sources is formulated. Fuzzy linear regression is then employed to compute the optimal solution set of switching angles.

Keywords: Multilevel converters, harmonics, pulse widthmodulation (PWM), optimal control.

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Authors: Ishapathik Das

Abstract:

The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: Model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs.

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Authors: Ehab Mourtaga, Ahmad Sharieh, Mousa Abdallah

Abstract:

An automatic speech recognition system for the formal Arabic language is needed. The Quran is the most formal spoken book in Arabic, it is spoken all over the world. In this research, an automatic speech recognizer for Quranic based speakerindependent was developed and tested. The system was developed based on the tri-phone Hidden Markov Model and Maximum Likelihood Linear Regression (MLLR). The MLLR computes a set of transformations which reduces the mismatch between an initial model set and the adaptation data. It uses the regression class tree, as well as, estimates a set of linear transformations for the mean and variance parameters of a Gaussian mixture HMM system. The 30th Chapter of the Quran, with five of the most famous readers of the Quran, was used for the training and testing of the data. The chapter includes about 2000 distinct words. The advantages of using the Quranic verses as the database in this developed recognizer are the uniqueness of the words and the high level of orderliness between verses. The level of accuracy from the tested data ranged 68 to 85%.

Keywords: Hidden Markov Model (HMM), MaximumLikelihood Linear Regression (MLLR), Quran, Regression ClassTree, Speech Recognition, Speaker-independent.

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: S. H. Lee, M. J. Park, O. M. Kwon

Abstract:

In this paper, reliable consensus of multi-agent systems with sampled-data is investigated. By using a suitable Lyapunov-Krasovskii functional and some techniques such as Wirtinger Inequality, Schur Complement and Kronecker Product, the results of such system are obtained by solving a set of Linear Matrix Inequalities (LMIs). One numerical example is included to show the effectiveness of the proposed criteria.

Keywords: Multi-agent, Linear Matrix Inequalities (LMIs), Kronecker Product, Sampled-Data, Lyapunov method.

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Authors: Arun Goel

Abstract:

Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly & Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly & Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicate the improvement in the performance of SVM (Poly & Rbf) in comparison to dimensional form of scour.

Keywords: Modeling, pier scour, regression, prediction, SVM (Poly & Rbf kernels).

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Authors: H. N. Suresh, Dr. V. Udaya Shankara

Abstract:

A technique proposed for the automatic detection of spikes in electroencephalograms (EEG). A multi-resolution approach and a non-linear energy operator are exploited. The signal on each EEG channel is decomposed into three sub bands using a non-decimated wavelet transform (WT). The WT is a powerful tool for multi-resolution analysis of non-stationary signal as well as for signal compression, recognition and restoration. Each sub band is analyzed by using a non-linear energy operator, in order to detect spikes. A decision rule detects the presence of spikes in the EEG, relying upon the energy of the three sub-bands. The effectiveness of the proposed technique was confirmed by analyzing both test signals and EEG layouts.

Keywords: EEG, Spike, SNEO, Wavelet Transform

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