Search results for: regression hypothesis

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: Esther Mafunda, Simbarashe Muparangi

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The present paper tests the applicability of the Regression Hypothesis on the pathological language dissolution of a Shona male adult with Broca’s aphasia. It particularly assesses the prediction of the Regression Hypothesis, which states that the process according to which language is forgotten will be the reversal of the process according to which it will be acquired. The main aim of the paper is to find out whether mirror symmetries between L1 acquisition and L1 dissolution of tense in Shona and, if so, what might cause these regression patterns. The paper also sought to highlight the practical contributions that Linguistic theory can make to solving language-related problems. Data was collected from a 46-year-old male adult with Broca’s aphasia who was receiving speech therapy at St Giles Rehabilitation Centre in Harare, Zimbabwe. The primary data elicitation method was experimental, using the probe technique. The TART (Test for Assessing Reference Time) Shona version in the form of sequencing pictures was used to access tense by Broca’s aphasic and 3.5-year-old child. Using the SPSS (Statistical Package for Social Studies) and Excel analysis, it was established that the use of the future tense was impaired in Shona Broca’s aphasic whilst the present and past tense was intact. However, though the past tense was intact in the male adult with Broca’s aphasic, a reference to the remote past was made. The use of the future tense was also found to be difficult for the 3,5-year-old speaking child. No difficulties were encountered in using the present and past tenses. This means that mirror symmetries were found between L1 acquisition and L1 dissolution of tense in Shona. On the basis of the results of this research, it can be concluded that the use of tense in a Shona adult with Broca’s aphasia supports the Regression Hypothesis. The findings of this study are important in terms of speech therapy in the context of Zimbabwe. The study also contributes to Bantu linguistics in general and to Shona linguistics in particular. Further studies could also be done focusing on the rest of the Bantu language varieties in terms of aphasia.

Keywords: Broca’s Aphasia, regression hypothesis, Shona, language dissolution

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Authors: Lavinia B. Dulla

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The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Fatima Zehra Allahverdi, Nukhet Bayer

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Objective: Three questions were formulated to examine stressful working units (intensive care units, emergency unit nurses) utilizing the self-perception theory and social support theory. This study provides a distinctive input by inspecting the combination of variables regarding stressful working environments. Method: The descriptive research was conducted with the participation of 400 nurses working at Ankara City Hospital. The study used Multivariate Analysis of Variance (MANOVA), regression analysis, and a mediation model. Hypothesis one used MANOVA followed by a Scheffe post hoc test. Hypothesis two utilized regression analysis using a hierarchical linear regression model. Hypothesis three used a mediation model. Result: The study utilized mediation analyses. Findings supported the hypotheses that intensive care units have significantly high scores in virtual communication and virtual tolerance. The number of years on the job, virtual communication, virtual tolerance, and phubbing significantly predicted 51% of the variance of perception of addiction. Interestingly, the number of years on the job, while significant, was negatively related to perception of addiction. Conclusion: The reasoning behind these findings and the lack of significance in the emergency unit is discussed. Around 7% of the variance of phubbing was accounted for through working in intensive care units. The model accounted for 26.80 % of the differences in the perception of addiction.

Keywords: phubbing, social media, working units, years on the job, stress

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Authors: Songul Cinaroglu

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Machine learning regression methods are recommended as an alternative to classical regression methods in the existence of variables which are difficult to model. Data for health expenditure is typically non-normal and have a heavily skewed distribution. This study aims to compare machine learning regression methods by hyperparameter tuning to predict health expenditure per capita. A multiple regression model was conducted and performance results of Lasso Regression, Random Forest Regression and Support Vector Machine Regression recorded when different hyperparameters are assigned. Lambda (λ) value for Lasso Regression, number of trees for Random Forest Regression, epsilon (ε) value for Support Vector Regression was determined as hyperparameters. Study results performed by using 'k' fold cross validation changed from 5 to 50, indicate the difference between machine learning regression results in terms of R², RMSE and MAE values that are statistically significant (p < 0.001). Study results reveal that Random Forest Regression (R² ˃ 0.7500, RMSE ≤ 0.6000 ve MAE ≤ 0.4000) outperforms other machine learning regression methods. It is highly advisable to use machine learning regression methods for modelling health expenditures.

Keywords: machine learning, lasso regression, random forest regression, support vector regression, hyperparameter tuning, health expenditure

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Authors: Bohsiu Wu

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Among serious crimes, child homicide is a rather rare event. However, the killing of children stirs up a special type of emotion in society that pales other criminal acts. This study examines the relevancy of three possible community-level explanations for child homicide: social deprivation, female empowerment, and social isolation. The social deprivation hypothesis posits that child homicide results from lack of resources in communities. The female empowerment hypothesis argues that a higher female status translates into a higher level of capability to prevent child homicide. Finally, the social isolation hypothesis regards child homicide as a result of lack of social connectivity. Child homicide data, aggregated by US postal ZIP codes in California from 1990 to 1999, were analyzed with a negative binomial regression. The results of the negative binomial analysis demonstrate that social deprivation is the most salient and consistent predictor among all other factors in explaining child homicide victimization at the ZIP-code level. Both social isolation and female labor force participation are weak predictors of child homicide victimization across communities. Further, results from the negative binomial regression show that it is the communities with a higher, not lower, degree of female labor force participation that are associated with a higher count of child homicide. It is possible that poor communities with a higher level of female employment have a lesser capacity to provide the necessary care and protection for the children. Policies aiming at reducing social deprivation and strengthening female empowerment possess the potential to reduce child homicide in the community.

Keywords: child homicide, deprivation, empowerment, isolation

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Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Auliya Adzillatin Uzhma, M. Adrian Rizky, Puri Diah Santyarini

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Bekasi Industrial Area in Kab. Bekasi and SEZ (Special Economic Zone) Sei Mangkei in Kab. Simalungun are two areas whose have the same main economic activity that are manufacturing industrial. Manufacturing industry in Bekasi Industrial Area contributes more than 70% of Kab. Bekasi’s GDP, while manufacturing industry in SEZ Sei Mangkei contributes less than 20% of Kab. Simalungun’s GDP. The dependent variable in the research is labor productivity, while the independent variable is the amount of labor, the level of labor education, the length of work and salary. This research used linear regression method to find the model for represent actual condition of productivity in two industrial area, then the equalization using dummy variable on labor education level variable. The initial hypothesis (Ho) in this research is that labor productivity in Bekasi Industrial Area will be higher than the productivity of labor in SEZ Sei Mangkei. The variable that supporting the accepted hypothesis are more labor, higher education, longer work and higher salary in Bekasi Industrial Area.

Keywords: labor, industrial city, linear regression, productivity

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Authors: Vaishali Joshi, Pallav Joshi

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The main objective of this study is to examine the fashion consumption behavior of females with respect to their age group. Differences were studied in the pre-purchase, purchase and post-purchase behavior of females belonging to three age cohorts such as Generation X, Generation Y, and Generation Z. Quantitative approach was used to conduct this research. Data was collected through structured questionnaire. The questionnaire consisted of three sections. Section one included a question of the source of information of purchasing fashion apparels which measure the pre-purchase behavior. Section two measures purchase behavior which included two questions: i. motivations for purchasing fashion apparel and ii. important attributes considered for purchasing fashion apparel. The last section included a question regarding disposal of fashion apparel which measures the post-purchase behavior. Hundred females were selected as the respondents for this study through convenience sampling in the fashion streets. They were categorized into three age groups and then the results were analyzed. Four hypotheses were developed after reviewing the existing literature. Regression analysis was conducted for testing the hypothesis. Hypothesis one was accepted which stated that ‘social influence’ as a source of information for purchasing fashion apparels decreases with age. Hypothesis two was accepted which suggested that motivation of ‘Attention seeking’ for purchasing fashion apparel decreases with age. Hypothesis three and four also accepted which suggested that the importance of ‘Quality’ and ‘Price’ increases with age but hypothesis five was rejected which suggested that the importance of ‘Fit’ increases with age and last but not the least hypothesis six was accepted which suggested that the ‘duration’ of using fashion apparel increases with age. Limitation of the study deals with the sample of only female respondents. Implication can be made from this research in the field of Fashion apparel industry with respect to consumer segmentation and better marketing approaches can be implemented by the marketers form this study. Further research can be concluded by including male respondents also.

Keywords: fashion, consumption behavior, age cohorts, motivation

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Authors: Saima Shafiq, Najma Iqbal Malik

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This study was aimed to explore the relationship of perceived stigma, perception of burden and psychological distress among parents of intellectually disabled children. The study also aimed to explore the moderating role of perceived social support on all the variables of the study. The sample of the study comprised of (N = 250) parents of intellectually disabled children. The present study utilized the co-relational research design. It consists of two phases. Phase-I consisted of two steps which contained the translation of two scales that were used in the present study and tried out on the sample of parents (N = 70). The Affiliated Stigma Scale and Care Giver Burden Inventory were translated into Urdu for the present study. Phase-1 revealed that translated scaled entailed satisfactory psychometric properties. Phase -II of the study was carried out in order to test the hypothesis. Correlation, linear regression analysis, and t-test were computed for hypothesis testing. Hierarchical regression analysis was applied to study the moderating effect of perceived social support. Findings revealed that there was a positive relationship between perceived stigma and psychological distress, perception of burden and psychological distress. Linear regression analysis showed that perceived stigma and perception of burden were positive predictors of psychological distress. The study did not show the moderating role of perceived social support among variables of the present study. The major limitation of the study is the sample size and the major implication is awareness regarding problems of parents of intellectually disabled children.

Keywords: perceived stigma, perception of burden, psychological distress, perceived social support

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Authors: Phan Thi Song Thuong

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This paper uses data from a survey on the green consumption behavior of Hanoi residents in October 2022. Data was gathered from a survey conducted in ten districts in the center of Hanoi, with 393 respondents. The hypothesis focuses on understanding the factors that may affect green consumption behavior, such as demographic characteristics, concerns about the environment and health, people living around, self-efficiency, and mass media. A number of methods, such as the T-test, exploratory factor analysis, and a linear regression model, are used to prove the hypotheses. Accordingly, the results show that gender, age, and education level have separate effects on the green consumption behavior of respondents.

Keywords: green consumption, urban residents, environment, sustainable, linear regression

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Authors: Anastasiia Yu. Timofeeva

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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: Eva Kotlánová

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After recession that began in 2007 in the United States and subsequently spilled over the Europe we could expect recovery of economic growth. According to the last estimation of economic progress of European countries, this recovery is not strong enough. Among others, it will depend on economic policy, where and in which way, the economic indicators will proceed. Economic theories postulate that the economic subjects prefer stably, continual economic policy without repeated and strong fluctuations. This policy is perceived as support of economic growth. Mostly in crises period, when the government must cope with consequences of recession, the economic policy becomes unpredictable for many subjects and economic policy uncertainty grows, which have negative influence on economic growth. The aim of this paper is to use panel regression to prove or disprove this hypothesis on the example of five largest European economies in the period 2008–2012.

Keywords: economic crises in Europe, economic policy, uncertainty, panel analysis regression

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Authors: Yi-Cheng Tian, Miin-Shen Yang

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The mixture likelihood approach to clustering is a popular clustering method where the expectation and maximization (EM) algorithm is the most used mixture likelihood method. In the literature, the EM algorithm had been used for mixture regression models. However, these EM mixture regression algorithms are sensitive to initial values with a priori number of clusters. In this paper, to resolve these drawbacks, we construct a learning-based schema for the EM mixture regression algorithm such that it is free of initializations and can automatically obtain an approximately optimal number of clusters. Some numerical examples and comparisons demonstrate the superiority and usefulness of the proposed learning-based EM mixture regression algorithm.

Keywords: clustering, EM algorithm, Gaussian mixture model, mixture regression model

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Authors: Elizabeth Malebogo Mosepele

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Road transport has become increasingly common in the world; people rely on road networks for transportation purpose on a daily basis. However, environmental impact of roads on surrounding landscapes extends their potential effects even further. This study investigates the impact of road network on natural vegetation. The study will provide baseline knowledge regarding roadside vegetation and would be helpful in future for conservation of biodiversity along the road verges and improvements of road verges. The general hypothesis of this study is that the amount and condition of road side vegetation could be explained by road network conditions. Remote sensing techniques were used to analyze vegetation conditions. Landsat 8 OLI image was used to assess vegetation cover condition. NDVI image was generated and used as a base from which land cover classes were extracted, comprising four categories viz. healthy vegetation, degraded vegetation, bare surface, and water. The classification of the image was achieved using the supervised classification technique. Road networks were digitized from Google Earth. For observed data, transect based quadrats of 50*50 m were conducted next to road segments for vegetation assessment. Vegetation condition was related to road network, with the multinomial logistic regression confirming a significant relationship between vegetation condition and road network. The null hypothesis formulated was that 'there is no variation in vegetation condition as we move away from the road.' Analysis of vegetation condition revealed degraded vegetation within close proximity of a road segment and healthy vegetation as the distance increase away from the road. The Chi Squared value was compared with critical value of 3.84, at the significance level of 0.05 to determine the significance of relationship. Given that the Chi squared value was 395, 5004, the null hypothesis was therefore rejected; there is significant variation in vegetation the distance increases away from the road. The conclusion is that the road network plays an important role in the condition of vegetation.

Keywords: Chi squared, geographic information system, multinomial logistic regression, remote sensing, road side vegetation

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Authors: Sakul Jariyachansit

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The purposes of this research were to investigate and to compare the factors affecting the decision for Tourism in Thailand by ASEAN Tourists and among ASEAN community tourists. Samples in this research were 400 ASEAN Community Tourists who travel in Thailand at Suvarnabhumi Airport during November 2016 - February 2016. The researchers determined the sample size by using the formula Taro Yamane at 95% confidence level tolerances 0.05. The English questionnaire, research instrument, was distributed by convenience sampling, for gathering data. Descriptive statistics was applied to analyze percentages, mean and standard deviation and used for hypothesis testing. The statistical analysis by multiple regression analysis (Multiple Regression) was employed to prove the relationship hypotheses at the significant level of 0.01. The results showed that majority of the respondents indicated the factors affecting the decision for Tourism in Thailand by ASEAN Tourists, in general there were a moderate effects and the mean of each side is moderate. Transportation was the most influential factor for tourism in Thailand. Therefore, the mode of transport, information, infrastructure and personnel are very important to factor affecting decision making for tourism in Thailand by ASEAN tourists. From the hypothesis testing, it can be predicted that the decision for choosing Tourism in Thailand is at R2 = 0.449. The predictive equation is decision for choosing Tourism in Thailand = 1.195 (constant value) + 0.425 (tourist attraction) +0.217 (information received) and transportation factors, tourist attraction, information, human resource and infrastructure at the significant level of 0.01.

Keywords: factor, decision making, ASEAN tourists, tourism in Thailand

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Authors: Kisan Sarda, Bhavika Shingote

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This paper aims to evaluate regression modelling for prediction of Energy storage of solar photovoltaic (PV) system using Semi parametric regression techniques because there are some parameters which are known while there are some unknown parameters like humidity, dust etc. Here irradiation of solar energy is different for different places on the basis of Latitudes, so by finding out areas which give more storage we can implement PV systems at those places and our need of energy will be fulfilled. This regression modelling is done for daily, monthly and seasonal prediction of solar energy storage. In this, we have used R modules for designing the algorithm. This algorithm will give the best comparative results than other regression models for the solar PV cell energy storage.

Keywords: semi parametric regression, photovoltaic (PV) system, regression modelling, irradiation

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Authors: Mary Okonkwo Ekwy

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The problem of the growing disillusionment of College of Education teachers with academic life vis-à-vis their job satisfaction and commitment was investigated in this study with a view to finding out if both their job satisfaction and commitment have suffered, and to find out if there was a relationship between job satisfaction and commitment among these College of Education teachers. Due consideration was also given in the study to the possible effects of demographic variables on attitudes to their job. To carry out a study of job satisfaction and commitment among the College of Education teachers and to explore the relationship between them, research instruments were used for measuring the levels of job satisfaction and commitment among them. A sample of 200 Colleges of Education teachers, comprising 15 Professors, 9 Principal Lecturers, 70 Senior Lecturer and 106 Lecturers was used for the study. Five major hypothesis were tested with regard to the relationship between job satisfaction and commitment among the teachers. The Pearson correlation, the F-ratio, and regression analysis were used for data analysis and hypothesis testing. The result of this investigation suggests that, perhaps the best way to secure the commitment of teachers is to ensure their job satisfaction. Future investigations will further enrich our knowledge about these very important themes.

Keywords: job satisfaction, commitment, academic staff, college of education

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Authors: Frantisek Mosna

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E-learning has become an efficient and widespread means in process of education at all branches of human activities. Statistics is not an exception. Unfortunately the main focus in the statistics teaching is usually paid to the substitution to formulas. Suitable web-sites can simplify and automate calculation and provide more attention and time to the basic principles of statistics, mathematization of real-life situations and following interpretation of results. We introduce our own web-sites for hypothesis testing. Their didactic aspects, technical possibilities of individual tools for their creating, experience and advantages or disadvantages of them are discussed in this paper. These web-sites do not substitute common statistical software but significantly improve the teaching of the statistics at universities.

Keywords: e-learning, hypothesis testing, PHP, web-sites

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Authors: Mustafa Kirisci

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Arms embargoes have not been adequately examined in terms of their effects on conflict duration. Prior research on arms embargoes has generally investigated the effect of arms embargoes on arms import/export practices and violations in arms embargoes, but it says little about the effect on conflict duration. This paper attempts to fill this gap and aims to investigate the effect of arms embargoes on conflict duration throughout the world. More precisely, the purpose of the paper is to understand how arms embargoes affect the duration of both internal and interstate conflicts. Given the theoretical framework, the main hypothesis of the paper is arms embargoes will have no reduction effect on conflict duration when arms transfer and region are controlled. This hypothesis is tested by using OLS regression. Results indicate that arms embargoes have no effect on both internal and interstate conflict duration. Another crucial result is that both small and major arms transfers made by the embargoed countries during the internal conflict increase the duration of the conflict, but no effect on interstate conflict duration. The final part concludes and provide explanations on what these results imply for finishing the conflict and bringing the peace.

Keywords: arms embargo, arms transfer, internal conflict, international conflict

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Authors: Suparman

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Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

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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: 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: Igor Kuzminov

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Till now, the nature of lightning is not established. A hypothesis of the origin of lightning is proposed. The lightning charge is formed by electromagnetic induction. The role of the conductor is performed by the air mass of the cloud. This conductor moves in the Earth's magnetic field. The upper and lower edges of the cloud are the plates of the capacitor. Lightning is a special case of electromagnetic processes in an atmosphere. The category of lightning occurs in the process of accumulation of a charge. The process of accumulation goes constantly, but the charge is not fixed. Naturally, the hypothesis demands the carrying out of additional experiments and official acknowledgement. As the proof of a hypothesis can serve that the maximal lighting activity in an equatorial zone where cosφ it is close to 1. An experiment conducted privately showed that there is a potential difference in the atmosphere at different levels. The probability of applied value development of power installation is great.

Keywords: electromagnetic induction, Earth's magnetic field, plates of the capacitors, charge accumulation

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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: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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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: 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: Martin Plener

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Developmental and democratization research has a long tradition of focusing on the relationship between democratization and economic development. However, recent studies have shown that economic development is not adequate to measure the actual living conditions of civilian people. In consequence, it is unclear if a democratization process helps to improve people’s quality of life. This work addresses this issue by investigating the influence of democratization on the Human Development Index (HDI) created by the United Nations. The main objective is to study the relationship between democracy and human development and whether democratization positively impacts the living conditions of the population over time. The main mechanism which supports a positive impact is that democratic structures promote participation and political involvement of people from all social classes resulting in a better articulation of interests and thus accountability to the government. To study this issue, a panel regression with Fixed-Effects is conducted. By that, it is examined if democracy has a positive impact on the HDI (Hypothesis 1) and secondly if the same effect weakens in more developed democracies compared to less developed democracies (Hypothesis 2). The results do not reveal a direct positive relationship between the democratization of a country and its development of the HDI, not supporting H1 which denies the first hypothesis. In contrast to the assumption of H2, the effect of democratization on human development seems to be negatively correlated in countries in which democracy is barely developed. Therefore, both hypotheses must be discarded. The results indicate rather a positive correlation between economic development on human development. Therefore, the impact of democracy on the well-being of countries’ citizens needs to be reinvestigated in order to create a better understanding of how improved human development can be achieved.

Keywords: democracy, human development, modernization theory, HDI, TSCS

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