Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A cultura do trigo apresenta grande importância econômica no Brasil, sendo que o país produz, anualmente, cerca de 6 milhões de toneladas. Contudo, essa produção é suficiente para atender a aproximadamente 50% da demanda. Essa situação faz com que o Brasil seja um dos maiores importadores deste cereal. O melhoramento genético da cultura tem grande importância na tentativa de aumentar a produção, a produtividade e a qualidade do trigo produzido. Além disso, aumentar a eficiência dos programas de melhoramento é essencial para reduzir os custos e o tempo necessários para o lançamento de novas cultivares. Neste sentido, soluções para a correta avaliação em etapas onde há baixa disponibilidade de sementes ou onde o número de linhagens a serem avaliadas é grande são necessárias. Desta forma, os objetivos deste trabalho foram: 1) avaliar o ganho genético para a cultura do trigo no Brasil, nos últimos 30 anos; 2) utilizar modelos aditivo-dominantes, em gerações F2 e F3, na identificação dos melhores genitores para caracteres de importância agronômica e 3) avaliação de linhagens homozigotas em ensaios multi-ambientes sem o uso de repetições. Para todas estas análises foram utilizados modelos mistos. Para a análise do ganho genético foram utilizados dados de 126 cultivares brasileiras de trigo, lançadas entre 1984 e 2014. Estas cultivares foram avaliadas em 187 ensaios, conduzidos em 25 locais, distribuídos na Região Sul do Brasil, entre os anos de 2002 e 2014. O ambiente foi responsável por mais de 70% da variância e os genótipos apresentaram comportamento similar entre os ambientes avaliados. O ganho genético obtido foi de 33,9 kg ha-1 ano-1,o que representa 1,28% ano-1. Além disso, os dados indicam que não há estagnação no ganho genético para a cultura do trigo no Brasil. A análise, via modelos aditivo-dominantes, de gerações heterozigotas (F2 e F3) indicou cultivares e linhagens que apresentam elevados efeitos aditivos, que são os principais efeitos quando o objetivo é o lançamento de cultivares a partir de linhagens homozigotas. Para o caractere rendimento de grãos, se destacaram as cultivares TBIO Seleto, Mirante, TBIO Mestre, Sinuelo e Ametista, além das linhagens UTFT 0932, UTFT 0908 e UTFT 0944. Na análise de adaptabilidade, estabilidade e produtividade, as linhagens UTFT 1110, UTFT 1608, UTFT 1620, UTFT 1025 e UTFT 1691 se destacaram e seriam selecionadas em cada um dos ambientes avaliados. Contudo, as linhagens UTFT 1634 e UTFT 1405 estiveram entre as linhagens selecionadas no conjunto de locais, mas poderiam ter sido eliminadas caso o ensaio tivesse sido conduzido em um único local, com repetições. / Wheat crop has great economic importance in Brazil, producing annually about 6 million tons. However, this production is only sufficient to meet ~ 50% of demand. This condition makes Brazil one of the largest importers of this cereal worldwide. The genetic improvement of this crop has great importance in the attempt of increasing production, productivity and quality of wheat produced in Brazil. Furthermore, increasing the efficiency of breeding programs is essential to reduce costs and the time required to release new cultivars. In this sense, solutions are necessary for the correct evaluation in steps where limited seeds are available or where the number of lines to be evaluated is very hight. Thus, the objectives of this work were: 1) to evaluate the genetic gain of wheat crop in Brazil in the last 30 years; 2) to use additive-dominant models, in generations F2 and F3, to identify the best parents for agronomic traits, i.e., grain yield, hectoliter mass, thousand grain mass, plant height, among others; and 3) to evaluate homozygous lines in designs without repetitions in multi-environment trials. For all analyses, mixed models were used. Genetic gain was evaluated using 126 Brazilian wheat cultivars released 1984 and 2014. Cultivars were evaluated in 187 trials, conducted in 25 locations, distributed in the Southern Region of Brazil, between 2002 and 2014. Environment effects was responsible for more than 70% of the total variance and genotypes presented similar behavior in the evaluated environments. Genetic gain was of 33.9 kg ha-1 year-1, which represents 1.28% year-1. Moreover, results indicated absence of stagnation in the genetic gain in Brazil. Analysis of F2 and F3 generations with additive-dominant models show cultivars and lines with high additive effects, which are the main effects when the objective is to release homozygous cultivars. For grain yield, cultivars TBIO Seleto, Mirante, TBIO Mestre, Sinuelo and Ametista and lines UTFT 0932, UTFT 0908 and UTFT 0944 presented the highest additive effects. In the analysis of adaptability, stability and productivity, lines UTFT 1110, UTFT 1608, UTFT 1620, UTFT 1025 and UTFT 1691 would be selected in each of the evaluated environments. However, lines UTFT 1634 and UTFT 1405 were among the selected lineages in the set of locations but could have been eliminated if the trial had been conducted in a design with replications in a single location.

Orientador: Mauricio Enrique Zevallos Herencia / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T02:03:22Z (GMT). No. of bitstreams: 1 Reis_SandraSantosdos_M.pdf: 1897835 bytes, checksum: 24e50267c694dbcb380ddcfc9d7bdace (MD5) Previous issue date: 2013 / Resumo: Neste trabalho discutimos a detecção de observações influentes em modelos simétricos lineares e não lineares. Em primeiro lugar é realizado um estudo de simulação para avaliar o desempenho de três métodos de estimação em dados gerados por quatro situações: sem observações influentes, com outliers na variável resposta, com observações influentes de média alavancagem e com observações influentes de alta alavancagem. São analisados dois métodos de máxima verossimilhança e um método robusto. Foram considerados modelos de regressão linear e não linear com erros logísticos tipo II e t-Student. Em segundo lugar é discutida detecção de observações influentes mediante a distância de Cook generalizada, a estatística de Peña e a estatística de Andrews-Pregibon. Em particular é discutida a conveniência de utilizar a metodologia de limiares para caracterizar uma observação como influente ou não influente, assim como o efeito da estimação de parâmetros na construção de limiares. Estas medidas foram aplicadas a conjuntos de dados reais e simulados considerando o ajuste de alguns modelos simétricos com uma adaptação no método de estimação scoring de Fisher / Abstract: We discuss the detection of influential observations in symmetrical linear and nonlinear regression models. First a simulation study is conducted to evaluate the performance of three estimation methods on data generated by four situations: without influential observations with outliers in the response variable, with influential observations average leverage and influential observations with high leverage. Two methods of maximum likelihood and robust method are analyzed. We considered linear and nonlinear regression models with logistic-II and Student-t errors. Secondly detection of influential observations by generalized Cook's distance, the statistic PeÃ?a and Andrews - Pregibon statistic is discussed. In particular the convenience of using the methodology to characterize a threshold observation as influential or not influential, as well as the effect of parameter estimation in the construction of thresholds is discussed. These measures were applied to sets of real and simulated data considering the fit of some symmetrical regression models with an adaptation estimation method of Fisher scoring / Mestrado / Estatistica / Mestra em Estatística

Cette thèse s’inscrit dans le cadre du projet « SCALA » financé par l’ANR à travers le programme ANR-11-SECU-0005. Son objectif consiste à surveiller des systèmes de contrôle et d’acquisition de données (SCADA) contre des attaques cyber-physiques. Il s'agit de résoudre un problème de détection-localisation séquentielle de signaux transitoires dans des systèmes stochastiques et dynamiques en présence d'états inconnus et de bruits aléatoires. La solution proposée s'appuie sur une approche par redondance analytique composée de deux étapes : la génération de résidus, puis leur évaluation. Les résidus sont générés de deux façons distinctes, avec le filtre de Kalman ou par projection sur l’espace de parité. Ils sont ensuite évalués par des méthodes d’analyse séquentielle de rupture selon de nouveaux critères d’optimalité adaptés à la surveillance des systèmes à sécurité critique. Il s'agit donc de minimiser la pire probabilité de détection manquée sous la contrainte de niveaux acceptables pour la pire probabilité de fausse alarme et la pire probabilité de fausse localisation. Pour la tâche de détection, le problème d’optimisation est résolu dans deux cas : les paramètres du signal transitoire sont complètement connus ou seulement partiellement connus. Les propriétés statistiques des tests sous-optimaux obtenus sont analysées. Des résultats préliminaires pour la tâche de localisation sont également proposés. Les algorithmes développés sont appliqués à la détection et à la localisation d'actes malveillants dans un réseau d’eau potable / This PhD thesis is registered in the framework of the project “SCALA” which received financial support through the program ANR-11-SECU-0005. Its ultimate objective involves the on-line monitoring of Supervisory Control And Data Acquisition (SCADA) systems against cyber-physical attacks. The problem is formulated as the sequential detection and isolation of transient signals in stochastic-dynamical systems in the presence of unknown system states and random noises. It is solved by using the analytical redundancy approach consisting of two steps: residual generation and residual evaluation. The residuals are firstly generated by both Kalman filter and parity space approaches. They are then evaluated by using sequential analysis techniques taking into account certain criteria of optimality. However, these classical criteria are not adequate for the surveillance of safety-critical infrastructures. For such applications, it is suggested to minimize the worst-case probability of missed detection subject to acceptable levels on the worst-case probability of false alarm and false isolation. For the detection task, the optimization problem is formulated and solved in both scenarios: exactly and partially known parameters. The sub-optimal tests are obtained and their statistical properties are investigated. Preliminary results for the isolation task are also obtained. The proposed algorithms are applied to the detection and isolation of malicious attacks on a simple SCADA water network

Orientador: Víctor Hugo Lachos Dávila / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-26T19:55:07Z (GMT). No. of bitstreams: 1 Massuia_MoniqueBettio_M.pdf: 2926597 bytes, checksum: 2a1154c0a61b13f369e8390159fc4c3e (MD5) Previous issue date: 2015 / Resumo: Este trabalho tem como objetivo principal apresentar os modelos de regressão lineares com respostas censuradas sob a classe de distribuições de mistura de escala skew-normal (SMSN), visando generalizar o clássico modelo Tobit ao oferecer alternativas mais robustas à distribuição Normal. Um estudo de inferência clássico é desenvolvido para os modelos em questão sob dois casos especiais desta família de distribuições, a Normal e a t de Student, utilizando o algoritmo EM para obter as estimativas de máxima verossimilhança dos parâmetros dos modelos e desenvolvendo métodos de diagnóstico de influência global e local com base na metodologia proposta por Cook (1986) e Poom & Poon (1999). Sob o enfoque Bayesiano, o modelo de regressão para respostas censuradas é estudado sob alguns casos especiais da classe SMSN, como a Normal, a t de Student, a skew-Normal, a skew-t e a skew-Slash. Neste caso, o amostrador de Gibbs é a principal ferramenta utilizada para a inferência sobre os parâmetros do modelo. Apresentamos também alguns estudos de simulação para avaliar a metodologia desenvolvida que, por fim, é aplicada em dois conjuntos de dados reais. Os pacotes SMNCensReg, CensRegMod e BayesCR para o software R dão suporte computacional aos desenvolvimentos deste trabalho / Abstract: This work aims to present the linear regression model with censored response variable under the class of scale mixture of skew-normal distributions (SMSN), generalizing the well known Tobit model as providing a more robust alternative to the normal distribution. A study based on classic inference is developed to investigate these censored models under two special cases of this family of distributions, Normal and t-Student, using the EM algorithm for obtaining maximum likelihood estimates and developing methods of diagnostic based on global and local influence as suggested by Cook (1986) and Poom & Poon (1999). Under a Bayesian approach, the censored regression model was studied under some special cases of SMSN class, such as Normal, t-Student, skew-Normal, skew-t and skew-Slash. In these cases, the Gibbs sampler was the main tool used to make inference about the model parameters. We also present some simulation studies for evaluating the developed methodologies that, finally, are applied on two real data sets. The packages SMNCensReg, CensRegMod and BayesCR implemented for the software R give computational support to this work / Mestrado / Estatistica / Mestra em Estatística

Orientador: Víctor Hugo Lachos Dávila / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-27T06:40:31Z (GMT). No. of bitstreams: 1 GalarzaMorales_ChristianEduardo_M.pdf: 5076076 bytes, checksum: 0967f08c9ad75f9e7f5df339563ef75a (MD5) Previous issue date: 2015 / Resumo: Os dados longitudinais são frequentemente analisados usando modelos de efeitos mistos normais. Além disso, os métodos de estimação tradicionais baseiam-se em regressão na média da distribuição considerada, o que leva a estimação de parâmetros não robusta quando a distribuição do erro não é normal. Em comparação com a abordagem de regressão na média convencional, a regressão quantílica (RQ) pode caracterizar toda a distribuição condicional da variável de resposta e é mais robusta na presença de outliers e especificações erradas da distribuição do erro. Esta tese desenvolve uma abordagem baseada em verossimilhança para analisar modelos de RQ para dados longitudinais contínuos correlacionados através da distribuição Laplace assimétrica (DLA). Explorando a conveniente representação hierárquica da DLA, a nossa abordagem clássica segue a aproximação estocástica do algoritmo EM (SAEM) para derivar estimativas de máxima verossimilhança (MV) exatas dos efeitos fixos e componentes de variância em modelos lineares e não lineares de efeitos mistos. Nós avaliamos o desempenho do algoritmo em amostras finitas e as propriedades assintóticas das estimativas de MV através de experimentos empíricos e aplicações para quatro conjuntos de dados reais. Os algoritmos SAEMs propostos são implementados nos pacotes do R qrLMM() e qrNLMM() respectivamente / Abstract: Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation for non-normal error distributions. Compared to the conventional mean regression approach, quantile regression (QR) can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. This thesis develops a likelihood-based approach to analyzing QR models for correlated continuous longitudinal data via the asymmetric Laplace distribution (ALD). Exploiting the nice hierarchical representation of the ALD, our classical approach follows the stochastic Approximation of the EM (SAEM) algorithm for deriving exact maximum likelihood (ML) estimates of the fixed-effects and variance components in linear and nonlinear mixed effects models. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to four real life datasets. The proposed SAEMs algorithms are implemented in the R packages qrLMM() and qrNLMM() respectively / Mestrado / Estatistica / Mestre em Estatística

Thesis (M.Sc. (Statistics)) -- University of Limpopo, 2020 / Background: Death and economic losses due to road traffic accidents (RTA) are huge global public health and developmental problems and need urgent attention. Each year nearly 1.24 million people die and millions suffer various forms of disability as a result of road accidents. This puts road traffic injuries (RTIs) as the eighth leading cause of death globally and RTIs are set to become the fifth leading cause of death worldwide by the year 2030 unless urgent actions are taken. Aim: In this paper, we investigate factors that contribute to road traffic deaths (RTDs) in the Limpopo province of South Africa using models such as the generalized linear models (GLM) and zero inflated models. Methods: The study was based on retrospective data that comprised of reports of 18,029 road traffic accidents and 4,944 road traffic deaths over the years 2009 – 2015. Generalized linear modelling and zero-inflated models were used to identify factors and determine their relationships to RTDs. Results: The data was split into two categories: deaths that occurred during holidays and those that occurred during non-holiday periods. It was found that the following variables, namely, Monday, human actions, vehicle conditions and vehicle makes, were significant predictors of RTDs during holidays. On the other hand, during non-holiday periods, weekend, Tuesday, Wednesday, national road, provincial road, sedan, LDV, combi and bus were found to be significant predictors of road traffic deaths. Conclusion: GLM techniques, such as the standard Poisson regression model and the negative binomial (NB) model, did little to explain the zero excess, therefore, zero-inflated models, such as zero-inflated negative binomial (ZINB), were found to be useful in explaining excess zeros. Recommendation: The study recommends that the government should make more human power available during the festive seasons, such as the December holidays, and over weekends.

Outcomes Based Education (OBE), has been, since its inception, fraught with problems. OBE in its very nature is complex. To fully embrace this method and ensure its success, schools must be able to make the necessary paradigm shift. This can only be achieved when schools receive relevant and empowering training, support and development. In other words, organisational development must be the key words. The aim of this study is to explore the impact of organisational development interventions on the implementation of OBE. The case study method was employed where it was realised that schools that received organisational development interventions, together with Outcomes Based Education, were able to implement this method with greater understanding, skill, and confidence. The investigation recommends an organisational development design that could be used instead of the cascade model, and provides suggestions on what can be done to ensure a more successful implementation process. / Educational Studies / M. Ed (Education Management)

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)

A recent development in the design of control system for a jet engine is to use a suitable, fast and accurate model running on board. Development of linear models is particularly important as most engine control designs are based on linear control theory. Engine control performance can be significantly improved by increasing the accuracy of the developed model. Current state-of-the-art is to use piecewise linear models at selected equilibrium conditions for the development of set point controllers, followed by scheduling of resulting controller gains as a function of one or more of the system states. However, arriving at an effective gain scheduler that can accommodate fast transients covering a wide range of operating points can become quite complex and involved, thus resulting in a sacrifice on controller performance for its simplicity. This thesis presents a methodology for developing a control oriented analytical linear model of a jet engine at both equilibrium and off-equilibrium conditions. This scheme requires a nonlinear engine model to run onboard in real time. The off-equilibrium analytical linear model provides improved accuracy and flexibility over the commonly used piecewise linear models developed using numerical perturbations. Linear coefficients are obtained by evaluating, at current conditions, analytical expressions which result from differentiation of simplified nonlinear expressions. Residualization of the fast dynamics states are utilized since the fast dynamics are typically outside of the primary control bandwidth. Analytical expressions based on the physics of the aerothermodynamic processes of a gas turbine engine facilitate a systematic approach to the analysis and synthesis of model based controllers. In addition, the use of analytical expressions reduces the computational effort, enabling linearization in real time at both equilibrium and off-equilibrium conditions for a more accurate capture of system dynamics during aggressive transient maneuvers. The methodology is formulated and applied to a separate flow twin-spool turbofan engine model in the Numerical Propulsion System Simulation (NPSS) platform. The fidelity of linear model is examined by validating against a detailed nonlinear engine model using time domain response, the normalized additive uncertainty and the nu-gap metric. The effects of each simplifying assumptions, which are crucial to the linear model development, on the fidelity of the linear model are analyzed in detail. A case study is performed to investigate the case when the current state (including both slow and fast states) of the system is not readily available from the nonlinear simulation model. Also, a simple model based control is used to illustrate benefits of using the proposed modeling approach.

Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done. The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with. To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with. Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE. / Mathematical Sciences / M. Sc. (Statistics)