"Very nice features of the book are the many practical hints and discussion on how to do model building, the various rules of thumb, the summaries and exercises. ... I think that the book will turn out helpful in particular for people interested in modeling aspects of linear regression with some mathematical background." (Alexander Lindner, zbMath 1417.62002, 2019)
Introduction.- Multiple Linear Regression.- Building an MLR Model.- WLS and Generalized Least Squares.- One Way Anova.- The K Way Anova Model.- Block Designs.- Orthogonal Designs.- More on Experimental Designs.- Multivariate Models.- Theory for Linear Models.- Multivariate Linear Regression.- GLMs and GAMs.- Stuff for Students.
David Olive is a Professor at Southern Illinois University, Carbondale, IL, USA. His research interests include the development of computationally practical robust multivariate location and dispersion estimators, robust multiple linear regression estimators, and resistant dimension reduction estimators.
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models.
This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics.
