Formulas Useful for Linear Regression Analysis and Related Matrix Theory

Simo Puntanen earned his PhD in statistics from the University of Tampere (Tampere, Finland) in 1987, where he is now a Docent and Lecturer of Statistics. He has published over 110 research papers in matrix methods for statistics with particular emphasis on linear statistical models. He is currently the book review editor of the International Statistical Review. Jarkko Isotalo earned his PhD in statistics from the University of Tampere (Tampere, Finland) in 2007, where he is now a Lecturer of Statistics. His main research interests have been linear statistical models, matrix methods for statistics, and computational statistics. He is currently also doing applied research on statistical genetics. Puntanen, Styan, and Isotalo, knowing just what is expected of authors, would like to agree with P. G. Wodehouse and apologize for childhoods that were as normal as rice-pudding and lives that consisted of little more than sitting in front of the laptop and cursing a bit. George P. H. Styan earned his PhD in mathematical statistics from Columbia University in 1969 and received an Honorary PhD from the University of Tampere in 2000. He is now Professor Emeritus of Mathematics and Statistics at McGill University in Montreal, Canada. He has published over 140 research papers, mostly in matrix methods for statistics, and since 2005, his main interests have focused on magic squares, and mathematical and statistical philately.

• The Model Matrix.- Fitted Values and Residuals.- Regression Coefficients.- Alternative Estimators.- Decompositions of Sums of Squares.- Partial Correlations.- Distributions.- Testing Hypotheses.- Diagnostics.- BLUE: Some Helpful Identities.- Estimability.- Best Linear Unbiased Estimator.- The Watson Efficiency.- Linear Sufficiency and Admissibility.- Best Linear Unbiased Predictor.- Mixed Model.- Multivariate Linear Model.- Inverse of a Partitioned Matrix.- Generalized Inverses.- Projectors.- Eigenvalues.- Discriminant Analysis.- Factor Analysis.- Canonical Correlations.- Matrix Decompositions.- Principal Component Analysis.- Löwner Ordering.- Rank Rules.- Inequalities.- Kronecker Product.- Matrix Derivatives.

"This is a book entirely of formulas with no text. ... the book would be most useful to instructors of applied linear algebra, mathematic statistics, and/or statistical computing or those in need of a formula identity to prove or derive a result." (David E. Booth, Technometrics, Vol. 56 (4), November, 2014) "This book is a handy collection of formulas. It includes a wide range of topics in regression analysis, multivariate statistics and areas involving matrices. Each section covers from its simple definitions to specialised results. ... It is useful, not only for students and researchers in statistics, econometrics and related areas, but also for experts on their particular topics." (Shuangzhe Liu, International Statistical Review, Vol. 82 (1), 2014) "The book contains very useful formulas for linear regression analysis including related matrix theory. ... very useful for those who work in the field of linear regression and need a brief refreshment on formulas and tools." (Nicoleta Breaz, zbMATH, Vol. 1276, 2014)