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Record Nr. |
UNINA9910452282203321 |
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Autore |
Hocking R. R (Ronald R.), <1932-> |
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Titolo |
Methods and applications of linear models : regression and the analysis of variance / / Ronald R. Hocking, PenHock Statistical Consultants |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : John Wiley & Sons, , 2013 |
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ISBN |
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1-118-59302-2 |
1-118-64019-5 |
1-118-59304-9 |
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Edizione |
[3rd ed.] |
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Descrizione fisica |
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1 online resource (717 p.) |
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Collana |
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Wiley Series in Probability and Statistics |
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Classificazione |
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Disciplina |
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Soggetti |
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Regression analysis |
Analysis of variance |
Linear models (Statistics) |
MATHEMATICS / Probability & Statistics / General |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Methods and Applications of Linear Models; Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; PART I REGRESSION; 1 Introduction to Linear Models; 1.1 Background Information; 1.2 Mathematical and Statistical Models; 1.3 Definition of the Linear Model; 1.4 Examples of Regression Models; 1.4.1 Single-Variable, Regression Model; 1.4.2 Regression Models with Several Inputs; 1.4.3 Discrete Response Variables; 1.4.4 Multivariate Linear Models; 1.5 Concluding Comments; Exercises; 2 Regression on Functions of One Variable |
2.1 The Simple Linear Regression Model2.2 Parameter Estimation; 2.2.1 Least Squares Estimation; 2.2.2 Maximum Likelihood Estimation; 2.2.3 Coded Data: Centering and Scaling; 2.2.4 The Analysis of Variance Table; 2.3 Properties of the Estimators and Test Statistics; 2.3.1 Moments of Linear Functions of Random Variables; 2.3.2 Moments of Least Squares Estimators; 2.3.3 Distribution of the Least Squares Estimators; 2.3.4 The Distribution of Test Statistics; 2.4 The Analysis of Simple Linear Regression Models; 2.4.1 Two Numerical Examples; 2.4.2 |
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A Test for Lack-of-Fit |
2.4.3 Inference on the Parameters of the Model2.4.4 Prediction and Prediction Intervals; 2.5 Examining the Data and the Model; 2.5.1 Residuals; 2.5.2 Outliers, Extreme Points, and Influence; 2.5.3 Normality, Independence, and Variance Homogeneity; 2.6 Polynomial Regression Models; 2.6.1 The Quadratic Model; 2.6.2 Higher Ordered Polynomial Models; 2.6.3 Orthogonal Polynomials; 2.6.4 Regression through the Origin; Exercises; 3 Transforming the Data; 3.1 The Need for Transformations; 3.2 Weighted Least Squares; 3.3 Variance Stabilizing Transformations |
3.4 Transformations to Achieve a Linear Model3.4.1 Transforming the Dependent Variable; 3.4.2 Transforming the Predictors; 3.5 Analysis of the Transformed Model; 3.5.1 Transformations with Forbes Data; Exercises; 4 Regression on Functions of Several Variables; 4.1 The Multiple Linear Regression Model; 4.2 Preliminary Data Analysis; 4.3 Analysis of the Multiple Linear Regression Model; 4.3.1 Fitting the Model in Centered Form; 4.3.2 Estimation and Analysis of the Original Data; 4.3.3 Model Assessment and Residual Analysis; 4.3.4 Prediction; 4.3.5 Transforming the Response |
4.4 Partial Correlation and Added-Variable Plots4.4.1 Partial Correlation; 4.4.2 Added-Variable Plots; 4.4.3 Simple Versus Partial Correlation; 4.5 Variable Selection; 4.5.1 The Case of Orthogonal Predictors; 4.5.2 Criteria for Deletion of Variables; 4.5.3 Nonorthogonal Predictors; 4.5.4 Computational Considerations; 4.5.5 Selection Strategies; 4.6 Model Specification; 4.6.1 Application to Subset Selection; 4.6.2 Improved Mean Squared Error; 4.6.3 Development of the Cp Statistic; Exercises; 5 Collinearity in Multiple Linear Regression; 5.1 The Collinearity Problem; 5.1.1 Introduction |
5.1.2 A Simple Example |
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Sommario/riassunto |
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"The new edition of this "essential desktop reference book. [that] should definitely be on your bookshelf" (Technometrics) features a newly reorganized approach to linear regression that promotes the understanding of theory and models concurrently, featuring newly-developed topics in the field and the use of software applications. It includes numerous exercises; graphics and computations developed using JMP software; a new chapter on recent developments with the distribution of linear and quadratic forms; and new topical coverage of least squares, the cell means model, and more"-- |
"The objective of this book is to present a discussion and a formal definition of a general class of linear models"-- |
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