| Description |
1 online resource (521 pages) |
| Contents |
Generalized Linear Models: With Applications in Engineering and the Sciences; Contents; Preface; 1. Introduction to Generalized Linear Models; 1.1 Linear Models; 1.2 Nonlinear Models; 1.3 The Generalized Linear Model; 2. Linear Regression Models; 2.1 The Linear Regression Model and Its Application; 2.2 Multiple Regression Models; 2.2.1 Parameter Estimation with Ordinary Least Squares; 2.2.2 Properties of the Least Squares Estimator and Estimation of s2; 2.2.3 Hypothesis Testing in Multiple Regression; 2.2.4 Confidence Intervals in Multiple Regression |
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2.2.5 Prediction of New Response Observations2.2.6 Linear Regression Computer Output; 2.3 Parameter Estimation Using Maximum Likelihood; 2.3.1 Parameter Estimation Under the Normal-Theory Assumptions; 2.3.2 Properties of the Maximum Likelihood Estimators; 2.4 Model Adequacy Checking; 2.4.1 Residual Analysis; 2.4.2 Transformation of the Response Variable Using the Box-Cox Method; 2.4.3 Scaling Residuals; 2.4.4 Influence Diagnostics; 2.5 Using R to Perform Linear Regression Analysis; 2.6 Parameter Estimation by Weighted Least Squares; 2.6.1 The Constant Variance Assumption |
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2.6.2 Generalized and Weighted Least Squares2.6.3 Generalized Least Squares and Maximum Likelihood; 2.7 Designs for Regression Models; Exercises; 3. Nonlinear Regression Models; 3.1 Linear and Nonlinear Regression Models; 3.1.1 Linear Regression Models; 3.1.2 Nonlinear Regression Models; 3.1.3 Origins of Nonlinear Models; 3.2 Transforming to a Linear Model; 3.3 Parameter Estimation in a Nonlinear System; 3.3.1 Nonlinear Least Squares; 3.3.2 The Geometry of Linear and Nonlinear Least Squares; 3.3.3 Maximum Likelihood Estimation; 3.3.4 Linearization and the Gauss-Newton Method |
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3.3.5 Using R to Perform Nonlinear Regression Analysis3.3.6 Other Parameter Estimation Methods; 3.3.7 Starting Values; 3.4 Statistical Inference in Nonlinear Regression; 3.5 Weighted Nonlinear Regression; 3.6 Examples of Nonlinear Regression Models; 3.7 Designs for Nonlinear Regression Models; Exercises; 4. Logistic and Poisson Regression Models; 4.1 Regression Models Where the Variance Is a Function of the Mean; 4.2 Logistic Regression Models; 4.2.1 Models with a Binary Response Variable; 4.2.2 Estimating the Parameters in a Logistic Regression Model |
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4.2.3 Interpellation of the Parameters in a Logistic Regression Model4.2.4 Statistical Inference on Model Parameters; 4.2.5 Lack-of-Fit Tests in Logistic Regression; 4.2.6 Diagnostic Checking in Logistic Regression; 4.2.7 Classification and the Receiver Operating Characteristic Curve; 4.2.8 A Biological Example of Logistic Regression; 4.2.9 Other Models for Binary Response Data; 4.2.10 More than Two Categorical Outcomes; 4.3 Poisson Regression; 4.4 Overdispersion in Logistic and Poisson Regression; Exercises; 5. The Generalized Linear Model; 5.1 The Exponential Family of Distributions |
| Summary |
Praise for the First Edition"The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities."--TechnometricsGeneralized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Main |
| Notes |
5.2 Formal Structure for the Class of Generalized Linear Models |
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Print version record |
| Subject |
Linear models (Statistics)
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MATHEMATICS -- Probability & Statistics -- Multivariate Analysis.
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Linear models (Statistics)
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| Form |
Electronic book
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| Author |
Montgomery, Douglas C.
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Vining, G. Geoffrey, 1954-
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Robinson, Timothy J
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| ISBN |
9780470556979 |
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0470556978 |
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9780470556986 |
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0470556986 |
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