Linear Models in StatisticsWiley, 2000 - 578페이지 Linear models made easy with this unique introduction Linear Models in Statistics discusses classical linear models from a matrix algebra perspective, making the subject easily accessible to readers encountering linear models for the first time. It provides a solid foundation from which to explore the literature and interpret correctly the output of computer packages, and brings together a number of approaches to regression and analysis of variance that more experienced practitioners will also benefit from. With an emphasis on broad coverage of essential topics, Linear Models in Statistics carefully develops the basic theory of regression and analysis of variance, illustrating it with examples from a wide range of disciplines. Other features of this remarkable work include: * Easy-to-read proofs and clear explanations of concepts and procedures * Special topics such as multiple regression with random x's and the effect of each variable on R¯2 * Advanced topics such as mixed and generalized linear models as well as logistic and nonlinear regression * The use of real data sets in examples, with all data sets available over the Internet * Numerous theoretical and applied problems, with answers in an appendix * A thorough review of the requisite matrix algebra * Graphs, charts, and tables as well as extensive references |
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analysis of variance B₁ B₁x Chapter coefficients columns contrasts Corollary correlation cov(B cov(y covariance matrix defined degrees of freedom distributed eigenvalues eigenvector elements equal estimable functions example expected mean squares expressed Ɛij Ɛijk F-statistic factor following theorem full model full rank given idempotent illustrate interaction inverse Jn Jn Jn least squares linear combination linearly independent moment-generating function Multiply multivariate normal nonsingular normal equations o²I obtain one-way model orthogonal p-value parameters partitioned positive definite Problem Proof quadratic form random effects model random variables rank(A reduced model regression residuals rows sample Section Show side conditions slope SS(au SS(µ SSEy.x sum of squares symmetric Table Theorem X₁ Xẞ y'Ay y₁ Yijk βι σ²