Theses and Dissertations (Mathematical Sciences)
http://hdl.handle.net/10500/3017
Fri, 27 Nov 2015 15:49:04 GMT2015-11-27T15:49:04ZStatistical modelling of return on capital employed of individual units
http://hdl.handle.net/10500/19627
Statistical modelling of return on capital employed of individual units
Burombo, Emmanuel Chamunorwa
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.
Wed, 01 Oct 2014 00:00:00 GMThttp://hdl.handle.net/10500/196272014-10-01T00:00:00ZGrade 11 mathematics learner's concept images and mathematical reasoning on transformations of functions
http://hdl.handle.net/10500/19569
Grade 11 mathematics learner's concept images and mathematical reasoning on transformations of functions
Mukono, Shadrick
The study constituted an investigation for concept images and mathematical reasoning of
Grade 11 learners on the concepts of reflection, translation and stretch of functions. The
aim was to gain awareness of any conceptions that learners have about these
transformations. The researcher’s experience in high school and university mathematics
teaching had laid a basis to establish the research problem.
The subjects of the study were 96 Grade 11 mathematics learners from three conveniently
sampled South African high schools. The non-return of consent forms by some learners
and absenteeism during the days of writing by other learners, resulted in the subsequent
reduction of the amount of respondents below the anticipated 100. The preliminary
investigation, which had 30 learners, was successful in validating instruments and
projecting how the main results would be like. A mixed method exploratory design was
employed for the study, for it was to give in-depth results after combining two data
collection methods; a written diagnostic test and recorded follow-up interviews. All the 96
participants wrote the test and 14 of them were interviewed.
It was found that learners’ reasoning was more based on their concept images than on
formal definitions. The most interesting were verbal concept images, some of which were
very accurate, others incomplete and yet others exhibited misconceptions. There were a lot of inconsistencies in the students’ constructed definitions and incompetency in using
graphical and symbolical representations of reflection, translation and stretch of functions.
For example, some learners were misled by negative sign on a horizontal translation to the right to think that it was a horizontal translation to the left. Others mistook stretch for
enlargement both verbally and contextually.
The research recommends that teachers should use more than one method when teaching
transformations of functions, e.g., practically-oriented and process-oriented instructions,
with practical examples, to improve the images of the concepts that learners develop.
Within their methodologies, teachers should make concerted effort to be aware of the
diversity of ways in which their learners think of the actions and processes of reflecting,
translating and stretching, the terms they use to describe them, and how they compare the
original objects to images after transformations. They should build upon incomplete
definitions, misconceptions and other inconsistencies to facilitate development of accurate
conceptions more schematically connected to the empirical world. There is also a need for
accurate assessments of successes and shortcomings that learners display in the quest to
define and master mathematical concepts but taking cognisance of their limitations of
language proficiency in English, which is not their first language. Teachers need to draw a
clear line between the properties of stretch and enlargement, and emphasize the need to
include the invariant line in the definition of stretch. To remove confusion around the effect
of “–” sign, more practice and spiral testing of this knowledge could be done to constantly
remind learners of that property. Lastly, teachers should find out how to use smartphones,
i-phones, i-pods, tablets and other technological devices for teaching and learning, and
utilize them fully to their own and the learners’ advantage in learning these and other
concepts and skills
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10500/195692015-02-01T00:00:00ZTriple generations of the Lyons sporadic simple group
http://hdl.handle.net/10500/19568
Triple generations of the Lyons sporadic simple group
Motalane, Malebogo John
The Lyons group denoted by Ly is a Sporadic Simple Group of order
51765179004000000 = 28 37 56 7 11 31 37 67. It(Ly) has a trivial Schur Multiplier
and a trivial Outer Automorphism Group. Its maximal subgroups are G2(5) of order
5859000000 and index 8835156, 3 McL:2 of order 5388768000 and index 9606125,
53 L3(5) of order 46500000 and index 1113229656, 2 A11 of order 29916800 and index
1296826875, 51+4
+ :4S6 of order 9000000 and index 5751686556, 35:(2 M11) of order
3849120 and index 13448575000, 32+4:2 A5 D8 of order 699840 and index 73967162500,
67:22 of order 1474 and index 35118846000000 and 37:18 of order 666 and index
77725494000000.
Its existence was suggested by Richard Lyons. Lyons characterized its order as
the unique possible order of any nite simple group where the centralizer of some
involution is isomorphic to the nontrivial central extension of the alternating group
of degree 11 by the cyclic group of order 2. Sims proved the existence of this group
and its uniqueness using permutations and machine calculations.
In this dissertation, we compute the (p; q; t)-generations of the Lyons group for dis-
tinct primes p, q and t which divide the order of Ly such that p < q < t. For
computations, we made use of the Computer Algebra System GAP
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10500/195682015-03-01T00:00:00ZThe use of effect sizes in credit rating models
http://hdl.handle.net/10500/18790
The use of effect sizes in credit rating models
Steyn, Hendrik Stefanus
The aim of this thesis was to investigate the use of effect sizes to report the results of
statistical credit rating models in a more practical way. Rating systems in the form of
statistical probability models like logistic regression models are used to forecast the
behaviour of clients and guide business in rating clients as “high” or “low” risk borrowers.
Therefore, model results were reported in terms of statistical significance as well as business
language (practical significance), which business experts can understand and interpret. In this
thesis, statistical results were expressed as effect sizes like Cohen‟s d that puts the results into
standardised and measurable units, which can be reported practically. These effect sizes
indicated strength of correlations between variables, contribution of variables to the odds of
defaulting, the overall goodness-of-fit of the models and the models‟ discriminating ability
between high and low risk customers.
Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/10500/187902014-12-01T00:00:00Z