Violation of assumptions in linear regression model: Regressions as remedial measure

The topic of the thesis is violation of assumptions in a multivariate linear regression model and implementation of various regressions as remedies. Chapter 1 is an introductory chapter. It discusses the basics of the multivariate linear regression model and its assumptions. The subsequent chapters deal with the assumptions being violated in some form.;Chapter 2 deals with presence of outlying influential observations in a dataset. Different methods for detecting the influential observations are discussed. Several types of the remedial robust regression are studied.;Chapter 3 focuses on the violation of the assumption of constant variance of the error terms. The resulting case of heteroscedasticity is defined, and several statistical tests for its confirmation are given. The remedial weighted least-squares regression model is given a full treatment.;The regression considered in Chapter 4 deviates from the linear regression in a sense that no known relation between the response variable and the predictor variables is assumed. A number of possibilities in implementing a nonparametric regression are discussed.;Finally, Chapter 5 is devoted to the instance of multicollinearity of the predictor variables. The ridge regression is introduced and discussed at length.