Understanding Regression Analysis

<p><em>Understanding Regression Analysis</em> unifies diverse regression applications including the classical model ANOVA models generalized models including Poisson Negative binomial logistic and survival neural networks and decision trees under a common umbrella -- namely the conditional distribution model. It explains why the conditional distribution model is the <i>correct </i>model and it also explains (proves) why the assumptions of the classical regression model are <i>wrong</i>. Unlike other regression books this one from the outset takes a realistic approach that all models are just approximations. Hence the emphasis is to model Nature’s processes realistically rather than to assume (incorrectly) that Nature works in particular constrained ways.</p><p><strong>Key features</strong> of the book include:</p><ul> <p> </p> <li>Numerous worked examples using the R software</li> <p> </p> <li>Key points and self-study questions displayed just-in-time within chapters</li> <p> </p> <li>Simple mathematical explanations (baby proofs) of key concepts</li> <p> </p> <li>Clear explanations and applications of statistical significance (<i>p</i>-values) incorporating the American Statistical Association guidelines</li> <p> </p> <li>Use of data-generating process terminology rather than population</li> <i> </i><p> </p> <li>Random-<i>X</i> framework is assumed throughout (the fixed-<i>X</i> case is presented as a special case of the random-<i>X</i> case)</li> <p> </p> <li>Clear explanations of probabilistic modelling including likelihood-based methods</li> <p> </p> <li>Use of simulations throughout to explain concepts and to perform data analyses</li> </ul><p>This book has a strong orientation towards science in general as well as chapter-review and self-study questions so it can be used as a textbook for research-oriented students in the social biological and medical and physical and engineering sciences. As well its mathematical emphasis makes it ideal for a text in mathematics and statistics courses. With its numerous worked examples it is also ideally suited to be a reference book for all scientists.</p>