Linear regression analysis / / George A.F. Seber, Alan J. Lee

• Record Nr.: UNINA9910141318203321
• Autore: Seber G. A. F (George Arthur Frederick), <1938->
• Pubbl/distr/stampa: Hoboken, N.J., : Wiley-Interscience, c2003
• ISBN: 9786613618993; 9781280589164; 1280589167; 9780471431633; 047143163X; 9780471722199; 0471722197; 9781118274422; 1118274423
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (584 p.)
• Collana: Wiley series in probability and statistics
• Altri autori (Persone): LeeA. J. <1946->
• Disciplina: 519.5/36
• Soggetti: Regression analysis; Multivariate analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Linear Regression Analysis; Contents; Preface; 1 Vectors of Random Variables; 1.1 Notation; 1.2 Statistical Models; 1.3 Linear Regression Models; 1.4 Expectation and Covariance Operators; Exercises 1a; 1.5 Mean and Variance of Quadratic Forms; Exercises 1b; 1.6 Moment Generating Functions and Independence; Exercises 1c; Miscellaneous Exercises 1; 2 Multivariate Normal Distribution; 2.1 Density Function; Exercises 2a; 2.2 Moment Generating Functions; Exercises 2b; 2.3 Statistical Independence; Exercises 2c; 2.4 Distribution of Quadratic Forms; Exercises 2d; Miscellaneous Exercises 2; 3 Linear Regression: Estimation and Distribution Theory3.1 Least Squares Estimation; Exercises 3a; 3.2 Properties of Least Squares Estimates; Exercises 3b; 3.3 Unbiased Estimation of σ2; Exercises 3c; 3.4 Distribution Theory; Exercises 3d; 3.5 Maximum Likelihood Estimation; 3.6 Orthogonal Columns in the Regression Matrix; ; Exercises 3e; 3.7 Introducing Further Explanatory Variables; 3.7.1 General Theory; 3.7.2 One Extra Variable; Exercises 3f; 3.8 Estimation with Linear Restrictions; 3.8.1 Method of Lagrange Multipliers; 3.8.2 Method of Orthogonal Projections; Exercises 3g; 3.9 Design Matrix of Less Than Full Rank3.9.1 Least Squares Estimation; Exercises 3h; 3.9.2 Estimable Functions; Exercises 3i; 3.9.3 Introducing Further Explanatory Variables; 3.9.4 Introducing Linear Restrictions; Exercises 3j; 3.10 Generalized Least Squares; Exercises 3k; 3.11 Centering and Scaling the Explanatory Variables; 3.11.1 Centering; 3.11.2 Scaling; Exercises 3l; 3.12 Bayesian Estimation; Exercises 3m; 3.13 Robust Regression; 3.13.1 M-Estimates; 3.13.2 Estimates Based on Robust Location and Scale Measures; 3.13.3 Measuring Robustness; 3.13.4 Other Robust Estimates; Exercises 3n; Miscellaneous Exercises 34 Hypothesis Testing; 4.1 Introduction; 4.2 Likelihood Ratio Test; 4.3 F-Test; 4.3.1 Motivation; 4.3.2 Derivation; Exercises 4a; 4.3.3 Some Examples; 4.3.4 The Straight Line; Exercises 4b; 4.4 Multiple Correlation Coefficient; Exercises 4c; 4.5 Canonical Form for H; Exercises 4d; 4.6 Goodness-of-Fit Test; 4.7 F-Test and Projection Matrices; Miscellaneous Exercises 4; 5 Confidence Intervals and Regions; 5.1 Simultaneous Interval Estimation; 5.1.1 Simultaneous Inferences; 5.1.2 Comparison of Methods; 5.1.3 Confidence Regions; 5.1.4 Hypothesis Testing and Confidence Intervals5.2 Confidence Bands for the Regression Surface; 5.2.1 Confidence Intervals; 5.2.2 Confidence Bands; 5.3 Prediction Intervals and Bands for the Response; 5.3.1 Prediction Intervals; 5.3.2 Simultaneous Prediction Bands; 5.4 Enlarging the Regression Matrix; Miscellaneous Exercises 5; 6 Straight-Line Regression; 6.1 The Straight Line; 6.1.1 Confidence Intervals for the Slope and Intercept; 6.1.2 Confidence Interval for the x-Intercept; 6.1.3 Prediction Intervals and Bands; 6.1.4 Prediction Intervals for the Response; 6.1.5 Inverse Prediction (Calibration)
• Sommario/riassunto: Concise, mathematically clear, and comprehensive treatment of the subject.* Expanded coverage of diagnostics and methods of model fitting.* Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models.* More than 200 problems throughout the book plus outline solutions for the exercises.* This revision has been extensively class-tested.