Regression

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. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential.

Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions.

The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments.

Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh's Probability Models, and T. S. Blyth & E.F. Robertsons' Basic Linear Algebra and Further Linear Algebra.

A self-contained, mathematical introduction to the development and theory of linear models aimed primarily at undergraduate students of mathematics. The clear and concise exposition is supported by a wealth of worked examples and exercises - with full solutions - making it ideal for self-study. A number of special topics, such as non-parametric regression and mixed models, time series, spatial processes and design of experiments are introduced providing avenues for further exploration. Includes supplementary material: sn.pub/extras

Inhalt
Linear Regression.- The Analysis of Variance (ANOVA).- Multiple Regression.- Further Multilinear Regression.- Adding additional covariates and the Analysis of Covariance.- Linear Hypotheses.- Model Checking and Transformation of Data.- Generalised Linear Models.- Other topics.