In this paper we investigate (d + 1)-point D-optimal designs for d-th degree polynomial regression with weight function w(x) > 0 on the interval [a, b]. Suppose that w'(x)/w(x) is a rational function and the information of whether the optimal support contains the boundary points a and b is available. Then the problem of constructing (d + 1)-point D-optimal designs can be transformed into a differential equation problem leading us to a certain matrix with k auxiliary unknown constants. We characterize the weight functions corresponding to the cases when k= 0 and k= 1. Then, we can solve (d + 1)-point D-optimal designs directly from differential equation (k = 0) or via eigenvalue problems (k = 1). The numerical results show us an interesting relationship between optimal designs and ordered eigenvalues.

The new growth theory establishes, among other things, that government expenditure can manipulate economic growth of a country. This study attempts to explain whether government expenditure increases or decreases economic growth in the context of Sri Lanka. Results obtained applying an analytical framework based on time series and second degree polynomial regressions are generally consistent with previous findings: government expenditure and economic growth are positively correlated; excessive government expenditure is negatively correlated with economic growth; and an open economy promotes growth. In a separate section, the paper examines Armey's (1995) idea of a quadratic curve that explains the level of government expenditure in an economy and the corresponding level of economic growth. The findings confirm the possibility of constructing the Armey curve for Sri Lanka, and it estimates the optimal level of government expenditure to be approximately 27 per cent. This paper adds to the literature indicating that the Armey curve is a reality not only for developed economies, but also for developing economies.(author's abstract) / Series: SRE - Discussion Papers

The purpose of this study was to investigate perceptions of academic and social competence among adolescents with a continuum of inattentive and hyperactive/impulsive symptoms. Past literature suggests that children with Attention-Deficit/Hyperactivity Disorder (ADHD) display self-perceptions that are overly positive compared to external indicators of competence, a phenomenon that is referred to as the positive illusory bias (PIB; Owens, Goldfine, Evangelista, Hoza, & Kaiser, 2007). The PIB is well supported among children with ADHD, and recent research suggests that the PIB persists into adolescence. To date, research on the PIB has relied on difference scores (i.e., an indicator of competence is subtracted from student self-ratings); however, difference scores suffer from numerous methodological limitations (Edwards, 2002). The current study investigated the relationship between self and teacher ratings of academic and social competence and inattentive, hyperactive/impulsive, and overall ADHD symptoms among a diverse sample of 395 students and their teachers. Polynomial regression and response surface methods were used to account for self and teacher ratings separately and decrease reliance on differences scores. These methods have been recommended to answer complex questions related to agreement and disagreement between ratings. The results of this study suggest that some adolescents with ADHD symptoms demonstrate the PIB, while others perceive their impairments and rate themselves as having low competence aligned with teacher ratings. Accurate ratings of low competence were more common within the academic domain than the social domain for students with overall ADHD symptoms as well as specific inattentive and hyperactive/impulsive symptoms. Results within the social domain indicate that all ADHD symptoms increased more sharply as the discrepancy between self and teacher ratings increased. Student overestimation of competence in both the academic and social domains was shown to be more predictive of high inattentive symptoms compared to hyperactive/impulsive symptoms. These findings suggest this new analysis approach allowed for a more nuanced understanding of the complex relationship between student and teacher competence ratings and ADHD symptoms. Gaining a better understanding of the PIB through this improved methodology has the potential to influence assessment and intervention practices among school psychologists, and to contribute to future research in this area. This study contributes to the literature by being the first to (1) examine the PIB in relation to a range of general and specific ADHD symptoms, (2) use polynomial regression/response surface methods to address limitations of difference scores, and (3) explore the PIB among a school-based sample of adolescents.

Das Thema behandelt die Analyse stochastischer technischer Systeme mittels Regressionsrechnung. Ausgehend von einer Modellbildung erfolgt eine Messdatenerfassung der Eingangs- und Ausgangsparameter in einer Messreihe. Die Messdaten werden einer Polynomregression unterworfen. Über die Berechnung des Bestimmtheitsmaßes erfolgt die Beurteilung der Güte der Anpassung der Regressionsfunktion an das Datenmaterial. Der Polynomgrad kann variiert werden um die Güte der Anpassung zu beeinflussen. Der Geltungsbereich der Regressionsfunktion wird festgelegt. Als Beispiel wird die Analyse eines Dampferzeugers vorgenommen. Die ermittelte Regressionsfunktion stellt die Übertragungsfunktion des Dampferzeugers dar, mit der weitere Eigenschaften des Systems (Wirkungsgradverlauf, Verlustleistungsverlauf) abgeleitet und dargestellt werden. Zur mathematischen Bearbeitung wird das Computer-Algebra-System MathCAD verwendet.

Thesis (MComm)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Work Engagement is one construct of many that forms part of the complex nomological network of constructs underlying the behaviour of working man2. Work Engagement is an important construct both from an individual as well as from an organisational perspective. Human resource management interventions aimed at enhancing Work Engagement aspire to contribute to the achievement of the organisation’s primary objective and the well-being of the organisation’s employees. Such interventions will most likely also be valued by individuals within the workplace, as individuals will be able to experience a sense of personal fulfilment through self-expression at work. It is therefore essential to gain a valid understanding of the Work Engagement construct and the psychological mechanism that underpins it, in order to design human resource interventions that will successfully enhance Work Engagement. The current study raises the question why variance in Work Engagement exists amongst different employees working in different organisational contexts. The research objective of the current study is to develop and empirically test an explanatory Work Engagement structural model that will provide a valid answer to this question. In this study, a comprehensive Work Engagement structural model was proposed. An ex post facto correlational design with structural equation modelling (SEM) as the statistical analysis technique was used to test the substantive research hypotheses as represented by the Work Engagement structural model. Furthermore, the current study tested two additional narrow-focus structural models describing the impact of value congruence on Work Engagement by using an ex post facto correlational design with polynomial regression as the statistical analysis technique. A convenience sample of 227 teachers working in public sector schools falling under the jurisdiction of the Western Cape Education Department (WCED) participated in the study. The comprehensive Work Engagement model achieved reasonable close fit. Support was found for all of the hypothesised theoretical relationships in the Work Engagement structural model, except for the influence of the PsyCap*Job Characteristics interaction effect on Meaningfulness and for three of the five latent polynomial regression terms added in the model in an attempt to derive response surface test values. The response surface analyses findings were mixed. Based on the obtained results, meaningful practical recommendations were derived. / AFRIKAANSE OPSOMMING: Werkverbintenis1 is een van ‘n groot verskeidenheid konstrukte wat deel vorm van die komplekse nomologiese netwerk van konstrukte wat die gedrag van die arbeidende mens onderlê. Werkverbintenis word as ‘n belangrike konstruk beskou vanuit ‘n individuele sowel as vanuit ‘n organisatoriese perspektief. Menslike hulpbronbestuurs-intervensies gerig op die bevordering van Werkverbintenis streef daarna om by te dra tot die bereiking van die organisasie se primêre doel sowel as tot die welstand van die organisasie se werknemers. Sodanige intervensies sal waarskynlik ook deur werknemers waardeer word, aangesien sodanige intervensies die kanse verhoog dat individue selfvervulling in hul werk sal ervaar omdat die werk hul die geleentheid bied om hulself in hul werk uit te leef. Dit is gevolglik noodsaaklik om ‘n geldige begrip te ontwikkel van die Werkverbintenis-konstruk en die sielkundige meganisme wat dit onderlê ten einde menslike hulpronbestuurs-intervensies te ontwerp wat suksesvol Werkverbintenis sal bevorder. Die huidige studie stel die vraag aan die orde waarom variansie in Werkverbintenis tussen verskillende werknemers bestaan wat in verskillende organisatoriese kontekste werk. Die navorsingsdoelstelling van die huidige studie is om ‘n verklarende Werkverbintenisstrukturele model te ontwikkel en te toets wat ‘n geldige antwoord op hierdie vraag sal bied. ‘n Omvattende Werkverbintenis strukturele model is in hierdie studie voorgestel. ‘n Ex post facto korrelatiewe ontwerp met strukturele vergelykingsmodellering (SVM) as die statistiese ontledingstegniek is gebruik om die substantiewe navorsingshipotese soos voorgestel deur die Werkverbintenis strukturele model te toets. Die huidige studie het voorts twee addisionele nouer-fokus strukturele modelle getoets wat die impak van waardekongruensie op Werkverbintenis beskryf deur middel van ‘n ex post facto korrelatiewe ontwerp met polinomiese regressie-ontleding as statistiese ontledingstegniek. ‘n Geriefsteekproef van 227 onderwysers wat in openbare skole werksaam is wat onder die beheer van die Wes Kaapse Department van Onderwys val (WKDO) het aan die studie deelgeneem. Die omvattende Werkverbintenis-model het redelik goeie pasgehalte getoon. Steun is gevind vir all die voorgestelde teoretiese verwantskappe in die Werkverbintenis strukturele model, behalwe vir die invloed van die Sielkundige kapitaal*Werk eienskappe-interaksie-effek op Betekenisvolheid en vir drie van die vyf polinomiese latente regressie-terme wat in die model ingesluit is in ‘n poging om responsoppervlakte-waardes af te lei. Gemengde resultate is verkry vir die responsoppervlakte-ontleding. Betekenisvolle praktiese aanbevelings is gemaak op grond van die navorsingsresultate.

A estimação e previsão da volatilidade de ativos são de suma importância para os mercados financeiros. Temas como risco e incerteza na teoria econômica moderna incentivaram a procura por métodos capazes de modelar uma variância condicional que evolui ao longo do tempo. O objetivo principal desta dissertação é comparar alguns métodos de regressão global e local quanto à extração da volatilidade dos índices Ibovespa e Standard and Poor´s 500. Para isto, são realizadas estimações e previsões com os modelos GARCH paramétricos e com os modelos aditivos semi-paramétricos. Os primeiros, tradicionalmente utilizados na estimação de segundos momentos condicionais, têm sua capacidade sugerida em diversos artigos. Os segundos provêm alta flexibilidade e descrições visualmente informativas das relações entre as variáveis, tais como assimetrias e não linearidades. Sendo assim, testar o desempenho dos últimos frente às estruturas paramétricas consagradas apresenta-se como uma investigação apropriada. A realização das comparações ocorre em períodos selecionados de alta volatilidade no mercado financeiro internacional (crises), sendo a performance dos modelos medida dentro e fora da amostra. Os resultados encontrados sugerem a capacidade dos modelos semi-paramétricos em estimar e prever a volatilidade dos retornos dos índices nos momentos analisados. / Volatility estimation and forecasting are very important matters for the financial markets. Themes like risk and uncertainty in modern economic theory have encouraged the search for methods that allow for the modeling of time varying variances. The main objective of this dissertation is to compare global and local regressions in terms of their capacity to extract the volatility of Ibovespa and Standard and Poor 500 indexes. To achieve this aim, parametric GARCH and semiparametric additive models estimation and forecasting are performed. The first ones, traditionally applied in the estimation of conditional second moments, have their capacity suggested in many papers. The second ones provide high flexibility and visually informative descriptions of the relationships between the variables, like asymmetries and nonlinearities. Therefore, testing the last ones´ performance against the acknowledged parametric structures is an appropriate investigation. Comparisons are made in selected periods of high volatility in the international financial market (crisis), measuring the models´ performance inside and outside sample. The results that were found suggest the capacity of semiparametric models to estimate and forecast the Indexes returns´ volatility at the analyzed moments.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The objective of this study was to evaluate the optimum addition level of arginine and the relationship of antagonism between amino acids arginine and lysine in diets for juvenile south brazilin catfish (Rhamdia quelen) for variables that were studied live performance, composition and nutrient retention, biochemical parameters , liver and digestive. The first trial lasted 45 days, was conducted in the fish farming Laboratory of Federal University of Santa Maria, in water recirculation system, using 24 280 l tanks, each equipped with two experimental units (cages with useful volume of 15 l), each unit was populated with 12 fish (initial weight of 2.00 ± 0.04 g). The experimental design was completely randomized in a factorial arrangement of two for six, and to 4.5% and 5.1% lysine were used following arginine levels: 2.5, 3.0, 3.6, 4, 3, 5.0 and 5.6%, totaling 12 treatments with 4 replicates. The second experiment lasted 49 days, following the same methodology as the first varying levels of inclusions arginine, lysine content keeping fixed at 6.65% of the protein fraction, testing six increasing levels of arginine: 4.20, 4.65, 5.0, 5.35, 5.65 and 6.00% each with four replications. Each unit was populated with 15 fish (mean weight 0.3 ± 3.00 g). In the first study based on the results obtained by polynomial regression equations, we conclude that the combination of 5.1% to 4.6% lysine with arginine provided better performance associated with greater carcass yield and lower body fat deposition. The second study that remained fixed in 6.65% lysine (protein), found better response to the inclusion of 5.8% arginine in the protein fraction of the diet. / O objetivo deste trabalho foi avaliar o nível ótimo de inclusão de arginina e a relação de antagonismo entre os aminoácidos lisina e arginina em dietas para juvenis de jundiá (Rhamdia quelen), e para isso foram estudadas variáveis de desempenho zootécnico, composição e retenção de nutrientes, parâmetros bioquímicos, hepáticos e digestivos. O primeiro experimento teve duração de 45 dias, foi conduzido no Laboratório de Piscicultura da Universidade Federal de Santa Maria, em sistema de recirculação de água, utilizando-se 24 tanques de 280 L, cada qual equipado com duas unidades experimentais (tanques-rede com volume útil de 15 L), cada unidade foi povoada com 12 peixes (peso inicial de 2,00 ± 0,04 g). O delineamento experimental foi inteiramente casualizado, em arranjo fatorial dois por seis, sendo que para 4,5% e 5,1% de lisina foram utilizados os seguintes níveis de arginina: 2,5, 3,0, 3,6, 4,3, 5,0 e 5,6% (da fração proteica), totalizando 12 tratamentos com 4 repetições. O segundo experimento teve duração de 49 dias, seguindo a mesma metodologia do primeiro variando os níveis de inclusões de arginina e mantendo o teor de lisina fixo em 6,65% da fração proteica, testando seis níveis crescentes de arginina: 4,20, 4,65, 5,0, 5,35, 5,65 e 6,00% cada um com 4 repetições. Cada unidade foi povoada com 15 peixes (peso médio 3,00±0,3 g). No primeiro estudo com base nos resultados obtidos pelas equações de regressão polinomial, concluímos que a combinação de 5,1% de lisina com 4,6% de arginina proporcionou melhor desempenho associado a maior rendimento de carcaça e menor deposição de gordura corporal. Já o segundo estudo que manteve lisina fixa em 6,65% (proteína), encontrou-se melhor resposta à inclusão de arginina em 5,8% da fração proteica das dietas.

A estimação e previsão da volatilidade de ativos são de suma importância para os mercados financeiros. Temas como risco e incerteza na teoria econômica moderna incentivaram a procura por métodos capazes de modelar uma variância condicional que evolui ao longo do tempo. O objetivo principal desta dissertação é comparar alguns métodos de regressão global e local quanto à extração da volatilidade dos índices Ibovespa e Standard and Poor´s 500. Para isto, são realizadas estimações e previsões com os modelos GARCH paramétricos e com os modelos aditivos semi-paramétricos. Os primeiros, tradicionalmente utilizados na estimação de segundos momentos condicionais, têm sua capacidade sugerida em diversos artigos. Os segundos provêm alta flexibilidade e descrições visualmente informativas das relações entre as variáveis, tais como assimetrias e não linearidades. Sendo assim, testar o desempenho dos últimos frente às estruturas paramétricas consagradas apresenta-se como uma investigação apropriada. A realização das comparações ocorre em períodos selecionados de alta volatilidade no mercado financeiro internacional (crises), sendo a performance dos modelos medida dentro e fora da amostra. Os resultados encontrados sugerem a capacidade dos modelos semi-paramétricos em estimar e prever a volatilidade dos retornos dos índices nos momentos analisados. / Volatility estimation and forecasting are very important matters for the financial markets. Themes like risk and uncertainty in modern economic theory have encouraged the search for methods that allow for the modeling of time varying variances. The main objective of this dissertation is to compare global and local regressions in terms of their capacity to extract the volatility of Ibovespa and Standard and Poor 500 indexes. To achieve this aim, parametric GARCH and semiparametric additive models estimation and forecasting are performed. The first ones, traditionally applied in the estimation of conditional second moments, have their capacity suggested in many papers. The second ones provide high flexibility and visually informative descriptions of the relationships between the variables, like asymmetries and nonlinearities. Therefore, testing the last ones´ performance against the acknowledged parametric structures is an appropriate investigation. Comparisons are made in selected periods of high volatility in the international financial market (crisis), measuring the models´ performance inside and outside sample. The results that were found suggest the capacity of semiparametric models to estimate and forecast the Indexes returns´ volatility at the analyzed moments.

The aim of this work is to get the best detailed knowledge about hardness distribution in first 60 mm below the surface of backing roll. To this end, a method for obtaining multi-dimensional polynomial regression was developed and then a computer program for its processing was written.Way of finding suitable regression surfaces and their subsequent interpretation, is a pivotal part of this work.

Das Thema behandelt die Analyse stochastischer technischer Systeme mittels Regressionsrechnung. Ausgehend von einer Modellbildung erfolgt eine Messdatenerfassung der Eingangs- und Ausgangsparameter in einer Messreihe. Die Messdaten werden einer Polynomregression unterworfen. Über die Berechnung des Bestimmtheitsmaßes erfolgt die Beurteilung der Güte der Anpassung der Regressionsfunktion an das Datenmaterial. Der Polynomgrad kann variiert werden um die Güte der Anpassung zu beeinflussen. Der Geltungsbereich der Regressionsfunktion wird festgelegt. Als Beispiel wird die Analyse eines Dampferzeugers vorgenommen. Die ermittelte Regressionsfunktion stellt die Übertragungsfunktion des Dampferzeugers dar, mit der weitere Eigenschaften des Systems (Wirkungsgradverlauf, Verlustleistungsverlauf) abgeleitet und dargestellt werden. Zur mathematischen Bearbeitung wird das Computer-Algebra-System MathCAD verwendet.