A detailed investigation of the linear model and some of its underlying assumptions

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dc.contributor.advisorTroskie, Casper Gen_ZA
dc.contributor.authorCoutsourides, Dimitrisen_ZA
dc.date.accessioned2016-03-17T07:12:42Z
dc.date.available2016-03-17T07:12:42Z
dc.date.issued1977en_ZA
dc.descriptionBibliography: p. 178-182.en_ZA
dc.description.abstractThe purpose of this thesis is to provide a study of the linear model. The whole work has been split into 6 chapters. In Chapter 1 we define and examine the two linear models, i.e. the regression and the correlation model. More specifically we show that the regression model is the conditional version of the correlation model. In Chapter 2 we deal with the problem of multicollinearity. We investigate the sources of near singularities, we give some methods of detecting the multicollinearity, and we state briefly methods for overcoming this problem. In Chapter 3 we consider the least squares method with restrictions, and we dispose of some tests for testing the linear restrictions. The theory concerning the sign of least squares estimates is discussed, then we deal with the method for augmenting existing data. Chapter 4 is mainly devoted to ridge regression. We state methods for selecting the best estimate for k. Some extensions are given dealing with the shrinkage estimators and the linear transforms of the least squares. In Chapter 5 we deal with the principal components, and we give methods for selecting the best subset of principal components. Much attention was given to a method called fractional rank and latent root regression analysis. In Chapter 6 comparisons were performed between estimators previously mentioned. Finally the conclusions are stated.en_ZA
dc.identifier.apacitationCoutsourides, D. (1977). <i>A detailed investigation of the linear model and some of its underlying assumptions</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Statistical Sciences. Retrieved from http://hdl.handle.net/11427/17882en_ZA
dc.identifier.chicagocitationCoutsourides, Dimitris. <i>"A detailed investigation of the linear model and some of its underlying assumptions."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 1977. http://hdl.handle.net/11427/17882en_ZA
dc.identifier.citationCoutsourides, D. 1977. A detailed investigation of the linear model and some of its underlying assumptions. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Coutsourides, Dimitris AB - The purpose of this thesis is to provide a study of the linear model. The whole work has been split into 6 chapters. In Chapter 1 we define and examine the two linear models, i.e. the regression and the correlation model. More specifically we show that the regression model is the conditional version of the correlation model. In Chapter 2 we deal with the problem of multicollinearity. We investigate the sources of near singularities, we give some methods of detecting the multicollinearity, and we state briefly methods for overcoming this problem. In Chapter 3 we consider the least squares method with restrictions, and we dispose of some tests for testing the linear restrictions. The theory concerning the sign of least squares estimates is discussed, then we deal with the method for augmenting existing data. Chapter 4 is mainly devoted to ridge regression. We state methods for selecting the best estimate for k. Some extensions are given dealing with the shrinkage estimators and the linear transforms of the least squares. In Chapter 5 we deal with the principal components, and we give methods for selecting the best subset of principal components. Much attention was given to a method called fractional rank and latent root regression analysis. In Chapter 6 comparisons were performed between estimators previously mentioned. Finally the conclusions are stated. DA - 1977 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1977 T1 - A detailed investigation of the linear model and some of its underlying assumptions TI - A detailed investigation of the linear model and some of its underlying assumptions UR - http://hdl.handle.net/11427/17882 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/17882
dc.identifier.vancouvercitationCoutsourides D. A detailed investigation of the linear model and some of its underlying assumptions. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Statistical Sciences, 1977 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/17882en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Statistical Sciencesen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherRegression analysisen_ZA
dc.subject.otherMulticollinearityen_ZA
dc.subject.otherCorrelation (Statistics)en_ZA
dc.titleA detailed investigation of the linear model and some of its underlying assumptionsen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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