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Regression
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Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables together with a random error. Because the subject is inherently two- or higher- dimensional, and one should first meet Statistics in one dimension, this book presupposes some prior knowledge of Statistics. But these prerequisites are minimal: the contents of any first course in Statistics will suffice.§In addition to a first course in (one-dimensional) Statistics, important pre-requisites are a first course in Probability and some knowledge of standard Linear Algebra. Here the book s needs are well served within the SUMS series, by John Haigh s Probability Models and by the two volumes Basic Linear Algebra and Further Linear Algebra by T. S. Blyth and E. F. Robertson.§The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA). It goes on to multiple linear regression (several predictor variables), analysis of covariance (ANCOVA), tests of linear hypotheses, departures from standard test conditions, and generalised linear models (GLMs). It concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. There are many worked examples and exercises with full solutions.
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