Oftentimes, application of regression models to analyse cereals data is limited to estimating and predicting crop production or yield. The general approach has been to fit the model without much consideration of the problems that accompany application of regression models to real life data, such as collinearity, models not fitting the data correctly and violation of assumptions. These problems may interfere with applicability and usefulness of the models, and compromise validity of results if they are not corrected when fitting the model. We applied regression models and diagnostics on national and household data to model availability of main cereals in Lesotho, namely, maize, sorghum and wheat. The application includes the linear regression model, regression and collinear diagnostics, Box-Cox transformation, ridge regression, quantile regression, logistic regression and its extensions with multiple nominal and ordinal responses. The Linear model with first-order autoregressive process AR(1) was used to determine factors that affected availability of cereals at the national level. Case deletion diagnostics were used to identify extreme observations with influence on different quantities of the fitted regression model, such as estimated parameters, predicted values, and covariance matrix of the estimates. Collinearity diagnostics detected the presence of more than one collinear relationship coexisting in the data set. They also determined variables involved in each relationship, and assessed potential negative impact of collinearity on estimated parameters. Ridge regression remedied collinearity problems by controlling inflation and instability of estimates. The Box-Cox transformation corrected non-constant variance, longer and heavier tails of the distribution of data. These increased applicability and usefulness of the linear models in modeling availability of cereals. Quantile regression, as a robust regression, was applied to the household data as an alternative to classical regression. Classical regression estimates from ordinary least squares method are sensitive to distributions with longer and heavier tails than the normal distribution, as well as to outliers. Quantile regression estimates appear to be more efficient than least squares estimates for a wide range of error term distribution. We studied availability of cereals further by categorizing households according to availability of different cereals, and applied the logistic regression model and its extensions. Logistic regression was applied to model availability and non-availability of cereals. Multinomial logistic regression was applied to model availability with nominal multiple categories. Ordinal logistic regression was applied to model availability with ordinal categories and this made full use of available information. The three variants of logistic regression model gave results that are in agreement, which are also in agreement with the results from the linear regression model and quantile regression model. / Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.

ABSTRACT INVESTIGATION OF STUDENTS&rsquo / PROBABILISTIC MISCONCEPTIONS MUT, Ali ihsan M.S. in Secondary Science and Mathematics Education Supervisor: Assoc. Prof. Dr. Safure BULUT December 2003, 86 pages The purpose of the study was to investigate the students&rsquo / probabilistic misconceptions with respect to grade level, previous instruction on probability and gender. The sample of the study was 885 students from different types of the schools (general high schools, private collages, Anatolian high school, vocational high schools, and elementary schools) and from grade levels (5, 6, 7, 8, 9 and 10). The sample represented a range of students with respect to socio-economic level and cultural background. To collect data for the study Probabilistic Misconception Test (PMT) and a questionnaire were administered. The test consisted of 14 problems from 8 probabilistic misconception types. Its content validity was tested. The data of the study were analyzed by means of SPSS. Each misconception type is investigated with respect to all variables. The results of the study revealed that: (a) The frequencies of all misconception types varied across grade levels. (b) The percentages of students who received instruction on probability in the school were higher than those who did not received instruction in terms of misconceptions on Effect of Sample Size and Time Axis Fallacy. In addition, the other misconception types were more frequent among the students who did not receive a certain instruction on probability than the students who received a certain instruction probability before the study / (c) The frequencies of all misconception types varied across gender.

Bibliography: leaves 397-406 / 406 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Philosophy, 1986

This thesis is concerned with boundary crossing probabilities and first crossing time densities for stochastic processes. This is a classical problem in probability that goes back to the famous ballot problem (first studied by W. A. Whitworth (1878) and J. Bertrand (1887)) and has numerous applications in diverse areas including mathematical statistics and financial mathematics. Our main objective is the study of approximation methods and control of the resulting approximation error for boundary crossing probabilities where a closed-form solution is unavailable. This leads to the study of bounds for the density of the first crossing time of the boundary, which in turn leads to the derivation of some analytic properties of the densities. This thesis presents a whole suite of closely related new results obtained when working on the outlined research program. (For complete abstract open document).

Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2008. / Includes bibliographical references (leaves 95-101). Also available in electronic version.

Thesis (M.Sc. Earth Sciences)--University of Waikato, 2008. / Title from PDF cover (viewed February 23, 2009) Includes bibliographical references (p. 72-75)

Thesis (Ph. D.)--Carleton University, 2002. / Includes bibliographical references (p. 192-195). Also available in electronic format on the Internet.

Thesis (M.Sc.)--York University, 2006. Graduate Programme in Computer Science. / Typescript. Includes bibliographical references (leaves 117-130). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR29613

Thesis (Ph. D.)--University of Washington, 1998. / Vita. Includes bibliographical references (p. [69]-72).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 106-112). Also available on the Internet.