Search results for: orthogonal regression

Authors: Martin Grootveld, Benita Percival, Sarah Moumtaz, Kerry L. Grootveld

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Objectives/Hypotheses: The adverse health effect potential of dietary lipid oxidation products (LOPs) has evoked much clinical interest. Therefore, we employed a ¹H NMR-linked Principal Component Regression (PCR) chemometrics modelling strategy to explore relationships between data matrices comprising (1) aldehydic LOP concentrations generated in culinary oils/fats when exposed to laboratory-simulated shallow frying practices, and (2) the prior saturated (SFA), monounsaturated (MUFA) and polyunsaturated fatty acid (PUFA) contents of such frying media (FM), together with their heating time-points at a standard frying temperature (180 ^oC). Methods: Corn, sunflower, extra virgin olive, rapeseed, linseed, canola, coconut and MUFA-rich algae frying oils, together with butter and lard, were heated according to laboratory-simulated shallow-frying episodes at 180 ^oC, and FM samples were collected at time-points of 0, 5, 10, 20, 30, 60, and 90 min. (n = 6 replicates per sample). Aldehydes were determined by ¹H NMR analysis (Bruker AV 400 MHz spectrometer). The first (dependent output variable) PCR data matrix comprised aldehyde concentration scores vectors (PC1* and PC2*), whilst the second (predictor) one incorporated those from the fatty acid content/heating time variables (PC1-PC4) and their first-order interactions. Results: Structurally complex trans,trans- and cis,trans-alka-2,4-dienals, 4,5-epxy-trans-2-alkenals and 4-hydroxy-/4-hydroperoxy-trans-2-alkenals (group I aldehydes predominantly arising from PUFA peroxidation) strongly and positively loaded on PC1*, whereas n-alkanals and trans-2-alkenals (group II aldehydes derived from both MUFA and PUFA hydroperoxides) strongly and positively loaded on PC2*. PCR analysis of these scores vectors (SVs) demonstrated that PCs 1 (positively-loaded linoleoylglycerols and [linoleoylglycerol]:[SFA] content ratio), 2 (positively-loaded oleoylglycerols and negatively-loaded SFAs), 3 (positively-loaded linolenoylglycerols and [PUFA]:[SFA] content ratios), and 4 (exclusively orthogonal sampling time-points) all powerfully contributed to aldehydic PC1* SVs (p 10^-3 to < 10^-9), as did all PC1-3 x PC4 interaction ones (p 10^-5 to < 10^-9). PC2* was also markedly dependent on all the above PC SVs (PC2 > PC1 and PC3), and the interactions of PC1 and PC2 with PC4 (p < 10^-9 in each case), but not the PC3 x PC4 contribution. Conclusions: NMR-linked PCR analysis is a valuable strategy for (1) modelling the generation of aldehydic LOPs in heated cooking oils and other FM, and (2) tracking their unsaturated fatty acid (UFA) triacylglycerol sources therein.

Keywords: Frying oils, frying episodes, lipid oxidation products, cytotoxic/genotoxic aldehydes, chemometrics, principal component regression, NMR Analysis.

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Authors: Jiaxiang Zhao

Abstract:

We present a novel construction of 16-QAM codewords of length n = 2k . The number of constructed codewords is 162×[4k-1×k-k+1] . When these constructed codewords are utilized as a code in OFDM systems, their peak-to-mean envelope power ratios (PMEPR) are bounded above by 3.6 . The principle of our scheme is illustrated with a four subcarrier example.

Keywords: Extended Rudin-Shapiro construction, orthogonal frequency division multiplexing (OFDM), peak-to-mean envelope power ratio (PMEPR)

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Authors: Alsaidi M. Altaher, Mohd T. Ismail

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In wavelet regression, choosing threshold value is a crucial issue. A too large value cuts too many coefficients resulting in over smoothing. Conversely, a too small threshold value allows many coefficients to be included in reconstruction, giving a wiggly estimate which result in under smoothing. However, the proper choice of threshold can be considered as a careful balance of these principles. This paper gives a very brief introduction to some thresholding selection methods. These methods include: Universal, Sure, Ebays, Two fold cross validation and level dependent cross validation. A simulation study on a variety of sample sizes, test functions, signal-to-noise ratios is conducted to compare their numerical performances using three different noise structures. For Gaussian noise, EBayes outperforms in all cases for all used functions while Two fold cross validation provides the best results in the case of long tail noise. For large values of signal-to-noise ratios, level dependent cross validation works well under correlated noises case. As expected, increasing both sample size and level of signal to noise ratio, increases estimation efficiency.

Keywords: wavelet regression, simulation, Threshold.

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Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining.

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Authors: Surinder Deswal, Mahesh Pal

Abstract:

An Artificial Neural Network based modeling technique has been used to study the influence of different combinations of meteorological parameters on evaporation from a reservoir. The data set used is taken from an earlier reported study. Several input combination were tried so as to find out the importance of different input parameters in predicting the evaporation. The prediction accuracy of Artificial Neural Network has also been compared with the accuracy of linear regression for predicting evaporation. The comparison demonstrated superior performance of Artificial Neural Network over linear regression approach. The findings of the study also revealed the requirement of all input parameters considered together, instead of individual parameters taken one at a time as reported in earlier studies, in predicting the evaporation. The highest correlation coefficient (0.960) along with lowest root mean square error (0.865) was obtained with the input combination of air temperature, wind speed, sunshine hours and mean relative humidity. A graph between the actual and predicted values of evaporation suggests that most of the values lie within a scatter of ±15% with all input parameters. The findings of this study suggest the usefulness of ANN technique in predicting the evaporation losses from reservoirs.

Keywords: Artificial neural network, evaporation losses, multiple linear regression, modeling.

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Authors: Chang, Chun-Lang, Liu, Chun-Kai

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This study, for its research subjects, uses patients who had undergone total knee replacement surgery from the database of the National Health Insurance Administration. Through the review of literatures and the interviews with physicians, important factors are selected after careful screening. Then using Cross Entropy Method, Genetic Algorithm Logistic Regression, and Particle Swarm Optimization, the weight of each factor is calculated and obtained. In the meantime, Excel VBA and Case Based Reasoning are combined and adopted to evaluate the system. Results show no significant difference found through Genetic Algorithm Logistic Regression and Particle Swarm Optimization with over 97% accuracy in both methods. Both ROC areas are above 0.87. This study can provide critical reference to medical personnel as clinical assessment to effectively enhance medical care quality and efficiency, prevent unnecessary waste, and provide practical advantages to resource allocation to medical institutes.

Keywords: Total knee replacement, Case Based Reasoning, Cross Entropy Method, Genetic Algorithm Logistic Regression, Particle Swarm Optimization.

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Authors: Xingping Sheng

Abstract:

Let T and S be a subspace of Cn and Cm, respectively. Then for A ∈ Cm×n satisfied AT ⊕ S = Cm, the generalized inverse A(2) T,S is given by A(2) T,S = (PS⊥APT )†. In this paper, a finite formulae is presented to compute generalized inverse A(2) T,S under the concept of restricted inner product, which defined as < A,B >T,S=< PS⊥APT,B > for the A,B ∈ Cm×n. By this iterative method, when taken the initial matrix X0 = PTA∗PS⊥, the generalized inverse A(2) T,S can be obtained within at most mn iteration steps in absence of roundoff errors. Finally given numerical example is shown that the iterative formulae is quite efficient.

Keywords: Generalized inverse A(2) T, S, Restricted inner product, Iterative method, Orthogonal projection.

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Authors: Kefaya Qaddoum

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The aim of this study is to predict breast cancer and to construct a supportive model that will stimulate a more reliable prediction as a factor that is fundamental for public health. In this study, we utilize general regression neural networks (GRNN) to replace the normal predictions with prediction periods to achieve a reasonable percentage of confidence. The mechanism employed here utilises a machine learning system called conformal prediction (CP), in order to assign consistent confidence measures to predictions, which are combined with GRNN. We apply the resulting algorithm to the problem of breast cancer diagnosis. The results show that the prediction constructed by this method is reasonable and could be useful in practice.

Keywords: Neural network, conformal prediction, cancer classification, regression.

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Authors: Patricia B. Cruz, Catrina Jean G. Valenzuela, Analyn N. Yumang

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Nearly a hundred per million of the Filipino population is diagnosed with Chronic Kidney Disease (CKD). The early stage of CKD has no symptoms and can only be discovered once the patient undergoes urinalysis. Over the years, different methods were discovered and used for the quantification of the urinary albumin such as the immunochemical assays where most of these methods require large machinery that has a high cost in maintenance and resources, and a dipstick test which is yet to be proven and is still debated as a reliable method in detecting early stages of microalbuminuria. This research study involves the use of the liquid chromatography concept in microfluidic instruments with biosensor as a means of separation and detection respectively, and linear regression to quantify human urinary albumin. The researchers’ main objective was to create a miniature system that quantifies and detect patients’ urinary albumin while reducing the amount of volume used per five test samples. For this study, 30 urine samples of unknown albumin concentrations were tested using VITROS Analyzer and the microfluidic system for comparison. Based on the data shared by both methods, the actual vs. predicted regression were able to create a positive linear relationship with an R² of 0.9995 and a linear equation of y = 1.09x + 0.07, indicating that the predicted values and actual values are approximately equal. Furthermore, the microfluidic instrument uses 75% less in total volume – sample and reagents combined, compared to the VITROS Analyzer per five test samples.

Keywords: Chronic kidney disease, microfluidics, linear regression, VITROS analyzer, urinary albumin.

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Authors: Entisar A. Elgmati

Abstract:

Martingale model diagnostic for assessing the fit of logistic regression model to recurrent events data are studied. One way of assessing the fit is by plotting the empirical standard deviation of the standardized martingale residual processes. Here we used another diagnostic plot based on martingale residual covariance. We investigated the plot performance under several types of model misspecification. Clearly the method has correctly picked up the wrong model. Also we present a test statistic that supplement the inspection of the two diagnostic. The test statistic power agrees with what we have seen in the plots of the estimated martingale covariance.

Keywords: Covariance, logistic model, misspecification, recurrent events.

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Authors: Tsuyoshi Okita, Tatsuya Niwa

Abstract:

For a given specific problem an efficient algorithm has been the matter of study. However, an alternative approach orthogonal to this approach comes out, which is called a reduction. In general for a given specific problem this reduction approach studies how to convert an original problem into subproblems. This paper proposes a formal modeling language to support this reduction approach. We show three examples from the wide area of learning problems. The benefit is a fast prototyping of algorithms for a given new problem.

Keywords: Formal language, statistical inference problem, reduction.

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Authors: Ing-Jr Ding

Abstract:

This paper presents a technical speaker adaptation method called WMLLR, which is based on maximum likelihood linear regression (MLLR). In MLLR, a linear regression-based transform which adapted the HMM mean vectors was calculated to maximize the likelihood of adaptation data. In this paper, the prior knowledge of the initial model is adequately incorporated into the adaptation. A series of speaker adaptation experiments are carried out at a 30 famous city names database to investigate the efficiency of the proposed method. Experimental results show that the WMLLR method outperforms the conventional MLLR method, especially when only few utterances from a new speaker are available for adaptation.

Keywords: hidden Markov model, maximum likelihood linearregression, speech recognition, speaker adaptation.

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Authors: V. V. Reddy, N. V. S. N. Sarma

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A circularly polarized fractal boundary microstrip antenna is presented. The sides of a square patch along x- axis, yaxis are replaced with Minkowski and Koch curves correspondingly. By using the fractal curves as edges, asymmetry in the structure is created to excite two orthogonal modes for circular polarization (CP) operation. The indentation factors of the fractal curves are optimized for pure CP. The simulated results of the novel polyfractal antenna are demonstrated.

Keywords: Circular polarization, Fractal, Koch, Minkowski.

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Authors: P. V. Pramila, V. Mahesh

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Pulmonary Function Tests are important non-invasive diagnostic tests to assess respiratory impairments and provides quantifiable measures of lung function. Spirometry is the most frequently used measure of lung function and plays an essential role in the diagnosis and management of pulmonary diseases. However, the test requires considerable patient effort and cooperation, markedly related to the age of patients resulting in incomplete data sets. This paper presents, a nonlinear model built using Multivariate adaptive regression splines and Random forest regression model to predict the missing spirometric features. Random forest based feature selection is used to enhance both the generalization capability and the model interpretability. In the present study, flow-volume data are recorded for N= 198 subjects. The ranked order of feature importance index calculated by the random forests model shows that the spirometric features FVC, FEF25, PEF, FEF25-75, FEF50 and the demographic parameter height are the important descriptors. A comparison of performance assessment of both models prove that, the prediction ability of MARS with the `top two ranked features namely the FVC and FEF25 is higher, yielding a model fit of R2= 0.96 and R2= 0.99 for normal and abnormal subjects. The Root Mean Square Error analysis of the RF model and the MARS model also shows that the latter is capable of predicting the missing values of FEV1 with a notably lower error value of 0.0191 (normal subjects) and 0.0106 (abnormal subjects) with the aforementioned input features. It is concluded that combining feature selection with a prediction model provides a minimum subset of predominant features to train the model, as well as yielding better prediction performance. This analysis can assist clinicians with a intelligence support system in the medical diagnosis and improvement of clinical care.

Keywords: FEV1, Multivariate Adaptive Regression Splines Pulmonary Function Test, Random Forest.

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Authors: Yuzhi Cai

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In this paper, we discuss a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. Together with a combining forecasts technique, we then predict USD to GBP currency exchange rates. Combined forecasts contain all the information captured by the fitted QAR models at different quantile levels and are therefore better than those obtained from individual models. Our results show that an unequally weighted combining method performs better than other forecasting methodology. We found that a median AR model can perform well in point forecasting when the predictive density functions are symmetric. However, in practice, using the median AR model alone may involve the loss of information about the data captured by other QAR models. We recommend that combined forecasts should be used whenever possible.

Keywords: Exchange rate, quantile regression, combining forecasts.

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Authors: Ben-Edigbe J, RahmanR

Abstract:

Since primary school trips usually start from home, attention by many scholars have been focused on the home end for data gathering. Thereafter category analysis has often been relied upon when predicting school travel demands. In this paper, school end was relied on for data gathering and multivariate regression for future travel demand prediction. 9859 pupils were surveyed by way of questionnaires at 21 primary schools. The town was divided into 5 zones. The study was carried out in Skudai Town, Malaysia. Based on the hypothesis that the number of primary school trip ends are expected to be the same because school trips are fixed, the choice of trip end would have inconsequential effect on the outcome. The study compared empirical data for home and school trip end productions and attractions. Variance from both data results was insignificant, although some claims from home based family survey were found to be grossly exaggerated. Data from the school trip ends was relied on for travel demand prediction because of its completeness. Accessibility, trip attraction and trip production were then related to school trip rates under daylight and dry weather conditions. The paper concluded that, accessibility is an important parameter when predicting demand for future school trip rates.

Keywords: Trip generation, regression analysis, multiple linearregressions

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Authors: Sunita Verma , Divya Tiwari, Ajay Verma

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Water samples were collected from river Pandu at six stations where human and animal activities were high. Composite samples were analyzed for dissolved oxygen (DO), biochemical oxygen demand (BOD), chemical oxygen demand (COD) , pH values during dry and wet seasons as well as the harmattan period. The total data points were used to establish relationships between the parameters and data were also subjected to statistical analysis and expressed as mean ± standard error of mean (SEM) at a level of significance of p<0.05. Regression analysis was carried out to establish relationships if any between studied parameters and relationships in form of scatter plots were obtained between DO/BOD, COD/DO, BOD/COD, COD/pH, BOD/pH and DO/pH. The high to moderate correlation coefficient observed, R2 ranged from 0.68 to 0.15 between these parameters.

Keywords: BOD, DO, COD, pH, Regression analysis.

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Authors: O. Poleshchuk, E. Komarov

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The paper presents the method developed to assess rating points of objects with qualitative indexes. The novelty of the method lies in the fact that the authors use linguistic scales that allow to formalize the values of the indexes with the help of fuzzy sets. As a result it is possible to operate correctly with dissimilar indexes on the unified basis and to get stable final results. The obtained rating points are used in decision making based on fuzzy expert opinions.

Keywords: complete orthogonal semantic space, qualitativecharacteristic, rating points.

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Authors: Ishapathik Das

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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: Martin Popescu D. Dana Maria

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The aims of this research are to broaden the study on the relationship between emotional intelligence and counterproductive work behavior (CWB). The study sample consisted in 441 Romanian employees from companies all over the country. Data has been collected through web surveys and processed with SPSS. The results indicated an average correlation between the two constructs and their sub variables, employees with a high level of emotional intelligence tend to be less aggressive. In addition, labeling was considered an individual difference which has the power to influence the level of employee aggression. A regression model was used to underline the importance of emotional intelligence together with labeling as predictors of CWB. Results have shown that this regression model enforces the assumption that labeling and emotional intelligence, taken together, predict CWB. Employees, who label themselves as victims and have a low degree of emotional intelligence, have a higher level of CWB.

Keywords: Aggression, CWB, emotional intelligence, labeling.

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Authors: S. Kotsiantis, A. Kostoulas, S. Lykoudis, A. Argiriou, K. Menagias

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Estimates of temperature values at a specific time of day, from daytime and daily profiles, are needed for a number of environmental, ecological, agricultural and technical applications, ranging from natural hazards assessments, crop growth forecasting to design of solar energy systems. The scope of this research is to investigate the efficiency of data mining techniques in estimating minimum, maximum and mean temperature values. For this reason, a number of experiments have been conducted with well-known regression algorithms using temperature data from the city of Patras in Greece. The performance of these algorithms has been evaluated using standard statistical indicators, such as Correlation Coefficient, Root Mean Squared Error, etc.

Keywords: regression algorithms, supervised machine learning.

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Authors: Mahdi Masoumi, Mehrdad Ardebilipoor, Seyed Aidin Bassam

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This paper proposes a novel frequency offset (FO) estimator for orthogonal frequency division multiplexing. Simplicity is most significant feature of this algorithm and can be repeated to achieve acceptable accuracy. Also fractional and integer part of FO is estimated jointly with use of the same algorithm. To do so, instead of using conventional algorithms that usually use correlation function, we use DFT of received signal. Therefore, complexity will be reduced and we can do synchronization procedure by the same hardware that is used to demodulate OFDM symbol. Finally, computer simulation shows that the accuracy of this method is better than other conventional methods.

Keywords: DFT, Estimator, Frequency Offset, IEEE802.11a, OFDM.

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Authors: Bharatendra Rai

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Cutting tools are widely used in manufacturing processes and drilling is the most commonly used machining process. Although drill-bits used in drilling may not be expensive, their breakage can cause damage to expensive work piece being drilled and at the same time has major impact on productivity. Predicting drill-bit breakage, therefore, is important in reducing cost and improving productivity. This study uses twenty features extracted from two degradation signals viz., thrust force and torque. The methodology used involves developing and comparing decision tree, random forest, and multinomial logistic regression models for classifying and predicting drill-bit breakage using degradation signals.

Keywords: Degradation signal, drill-bit breakage, random forest, multinomial logistic regression.

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Authors: Farhad Kolahan, Mohammad Bironro

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This paper addresses modeling and optimization of process parameters in powder mixed electrical discharge machining (PMEDM). The process output characteristics include metal removal rate (MRR) and electrode wear rate (EWR). Grain size of Aluminum powder (S), concentration of the powder (C), discharge current (I) pulse on time (T) are chosen as control variables to study the process performance. The experimental results are used to develop the regression models based on second order polynomial equations for the different process characteristics. Then, a genetic algorithm (GA) has been employed to determine optimal process parameters for any desired output values of machining characteristics.

Keywords: Regression modeling, PMEDM, GeneticAlgorithm, Optimization.

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Authors: F. Apaydın

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In this empirical research, how marketing managers evaluate their firms- performances and decide to make innovation is examined. They use some standards which are past performance of the firm, target performance of the firm, competitor performance, and average performance of the industry to compare and evaluate the firms- performances. It is hypothesized that marketing managers and owners of the firm compare the firms- current performance with these four standards at the same time to decide when to make innovation relating to any aspects of the firm, either management style or products. Relationship between the comparison of the firm-s performance with these standards and innovation are searched in the same regression model. The results of the regression analysis are discussed and some recommendations are made for future studies and applicants.

Keywords: Innovation, performance evaluation standards

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Authors: V.Sivaraman, S. Sankaran, L. Vijayaraghavan

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Machining through turning was carried out in a lathe to study the chip formation of Multiphase Ferrite (F-B-M) microalloyed steel. Taguchi orthogonal array was employed to perform the machining. Continuous and discontinuous chips were formed for different cutting parameters like speed, feed and depth of cut. Optical and scanning electron microscope was employed to identify the chip morphology.

Keywords: Multiphase microalloyed steel, chip formation, Taguchi technique, turning, cutting parameters

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Authors: Salwa Aftab, Sehrish Riaz

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The objective of this study was to check the impact of grade sensitivity on learning motivation and academic performance of students and to remove the degree of difference that exists among students regarding the cause of their learning motivation and also to gain knowledge about this matter since it has not been adequately researched. Data collection was primarily done through the academic sector of Pakistan and was depended upon the responses given by students solely. A sample size of 208 university students was selected. Both paper and online surveys were used to collect data from respondents. The results of the study revealed that grade sensitivity has a positive relationship with the learning motivation of students and their academic performance. These findings were carried out through systematic correlation and regression analysis.

Keywords: Academic performance, correlation, grade sensitivity, learning motivation, regression.

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Authors: Hassnen M. Jafer, Khalid S. Hashim, W. Atherton, Ali W. Alattabi

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This study investigates the effect of two important parameters (length of curing period and percentage of the added binder) on the strength of soil treated with OPC. An intermediate plasticity silty clayey soil with medium organic content was used in this study. This soft soil was treated with different percentages of a commercially available cement type 32.5-N. laboratory experiments were carried out on the soil treated with 0, 1.5, 3, 6, 9, and 12% OPC by the dry weight to determine the effect of OPC on the compaction parameters, consistency limits, and the compressive strength. Unconfined compressive strength (UCS) test was carried out on cement-treated specimens after exposing them to different curing periods (1, 3, 7, 14, 28, and 90 days). The results of UCS test were used to develop a non-linear multi-regression model to find the relationship between the predicted and the measured maximum compressive strength of the treated soil (qu). The results indicated that there was a significant improvement in the index of plasticity (IP) by treating with OPC; IP was decreased from 20.2 to 14.1 by using 12% of OPC; this percentage was enough to increase the UCS of the treated soil up to 1362 kPa after 90 days of curing. With respect to the statistical model of the predicted qu, the results showed that the regression coefficients (R2) was equal to 0.8534 which indicates a good reproducibility for the constructed model.

Keywords: Cement admixtures, soft soil stabilisation, geotechnical parameters, unconfined compressive strength, multi-regression model.

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Authors: Mohammad Shams Esfand Abadi, Nader Hadizadeh Kashani, Vahid Mehrdad

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In this paper we present a general formalism for the establishment of the family of selective regressor affine projection algorithms (SR-APA). The SR-APA, the SR regularized APA (SR-RAPA), the SR partial rank algorithm (SR-PRA), the SR binormalized data reusing least mean squares (SR-BNDR-LMS), and the SR normalized LMS with orthogonal correction factors (SR-NLMS-OCF) algorithms are established by this general formalism. We demonstrate the performance of the presented algorithms through simulations in acoustic echo cancellation scenario.

Keywords: Adaptive filter, affine projection, selective regressor.

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Authors: Nazrina Aziz, Dong Q. Wang

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There have been various methods created based on the regression ideas to resolve the problem of data set containing censored observations, i.e. the Buckley-James method, Miller-s method, Cox method, and Koul-Susarla-Van Ryzin estimators. Even though comparison studies show the Buckley-James method performs better than some other methods, it is still rarely used by researchers mainly because of the limited diagnostics analysis developed for the Buckley-James method thus far. Therefore, a diagnostic tool for the Buckley-James method is proposed in this paper. It is called the renovated Cook-s Distance, (RD* i ) and has been developed based on the Cook-s idea. The renovated Cook-s Distance (RD* i ) has advantages (depending on the analyst demand) over (i) the change in the fitted value for a single case, DFIT* i as it measures the influence of case i on all n fitted values Yˆ∗ (not just the fitted value for case i as DFIT* i) (ii) the change in the estimate of the coefficient when the ith case is deleted, DBETA* i since DBETA* i corresponds to the number of variables p so it is usually easier to look at a diagnostic measure such as RD* i since information from p variables can be considered simultaneously. Finally, an example using Stanford Heart Transplant data is provided to illustrate the proposed diagnostic tool.

Keywords: Buckley-James estimators, censored regression, censored data, diagnostic analysis, product-limit estimator, renovated Cook's Distance.

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