LEADER 00987nam a2200217 i 4500 001 991003659429707536 008 080529s2004 it ||| | ita 020 $a8871402677 035 $ab13730976-39ule_inst 040 $aDip.to Filologia Class. e Scienze Filosofiche$bita 245 00$aSupplementa italica. Nuova serie.$n22,$pForum Iulii Iriensium. Supplementorum Supplementa. Italia, Sicilia, Sardinia Epigraphicae /$c[a cura dell'] Unione Accademica Nazionale 246 30$aForum Iulii Iriensium. Supplementorum Supplementa. 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Rencher and G. Bruce Schaalje 205 $a2nd ed. 210 $aHoboken, N.J. $cWiley-Interscience$dc2008 215 $a1 online resource (690 p.) 300 $aDescription based upon print version of record. 311 08$a9780471754985 311 08$a0471754986 320 $aIncludes bibliographical references (p. 653-661) and index. 327 $aLINEAR MODELS IN STATISTICS; CONTENTS; Preface; 1 Introduction; 1.1 Simple Linear Regression Model; 1.2 Multiple Linear Regression Model; 1.3 Analysis-of-Variance Models; 2 Matrix Algebra; 2.1 Matrix and Vector Notation; 2.1.1 Matrices, Vectors, and Scalars; 2.1.2 Matrix Equality; 2.1.3 Transpose; 2.1.4 Matrices of Special Form; 2.2 Operations; 2.2.1 Sum of Two Matrices or Two Vectors; 2.2.2 Product of a Scalar and a Matrix; 2.2.3 Product of Two Matrices or Two Vectors; 2.2.4 Hadamard Product of Two Matrices or Two Vectors; 2.3 Partitioned Matrices; 2.4 Rank; 2.5 Inverse 327 $a2.6 Positive Definite Matrices2.7 Systems of Equations; 2.8 Generalized Inverse; 2.8.1 Definition and Properties; 2.8.2 Generalized Inverses and Systems of Equations; 2.9 Determinants; 2.10 Orthogonal Vectors and Matrices; 2.11 Trace; 2.12 Eigenvalues and Eigenvectors; 2.12.1 Definition; 2.12.2 Functions of a Matrix; 2.12.3 Products; 2.12.4 Symmetric Matrices; 2.12.5 Positive Definite and Semidefinite Matrices; 2.13 Idempotent Matrices; 2.14 Vector and Matrix Calculus; 2.14.1 Derivatives of Functions of Vectors and Matrices; 2.14.2 Derivatives Involving Inverse Matrices and Determinants 327 $a2.14.3 Maximization or Minimization of a Function of a Vector3 Random Vectors and Matrices; 3.1 Introduction; 3.2 Means, Variances, Covariances, and Correlations; 3.3 Mean Vectors and Covariance Matrices for Random Vectors; 3.3.1 Mean Vectors; 3.3.2 Covariance Matrix; 3.3.3 Generalized Variance; 3.3.4 Standardized Distance; 3.4 Correlation Matrices; 3.5 Mean Vectors and Covariance Matrices for Partitioned Random Vectors; 3.6 Linear Functions of Random Vectors; 3.6.1 Means; 3.6.2 Variances and Covariances; 4 Multivariate Normal Distribution; 4.1 Univariate Normal Density Function 327 $a4.2 Multivariate Normal Density Function4.3 Moment Generating Functions; 4.4 Properties of the Multivariate Normal Distribution; 4.5 Partial Correlation; 5 Distribution of Quadratic Forms in y; 5.1 Sums of Squares; 5.2 Mean and Variance of Quadratic Forms; 5.3 Noncentral Chi-Square Distribution; 5.4 Noncentral F and t Distributions; 5.4.1 Noncentral F Distribution; 5.4.2 Noncentral t Distribution; 5.5 Distribution of Quadratic Forms; 5.6 Independence of Linear Forms and Quadratic Forms; 6 Simple Linear Regression; 6.1 The Model; 6.2 Estimation of ?(0), ?(1), and ?(2) 327 $a6.3 Hypothesis Test and Confidence Interval for ?(1)6.4 Coefficient of Determination; 7 Multiple Regression: Estimation; 7.1 Introduction; 7.2 The Model; 7.3 Estimation of ? and ?(2); 7.3.1 Least-Squares Estimator for ?; 7.3.2 Properties of the Least-Squares Estimator ?; 7.3.3 An Estimator for ?(2); 7.4 Geometry of Least-Squares; 7.4.1 Parameter Space, Data Space, and Prediction Space; 7.4.2 Geometric Interpretation of the Multiple Linear Regression Model; 7.5 The Model in Centered Form; 7.6 Normal Model; 7.6.1 Assumptions; 7.6.2 Maximum Likelihood Estimators for ? and ?(2) 327 $a7.6.3 Properties of ? and ?(2) 330 $aThe essential introduction to the theory and application of linear models-now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of vari 606 $aLinear models (Statistics) 615 0$aLinear models (Statistics) 676 $a519.5/35 700 $aRencher$b Alvin C.$f1934-$0116940 701 $aSchaalje$b G. Bruce$0315945 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019467103321 996 $aLinear models in statistics$9719875 997 $aUNINA