CiNii 図書 - Regression diagnostics : an introduction

Regression diagnostics are methods for determining whether a regression model that has been fit to data adequately represents the structure of the data. For example, if the model assumes a linear (straight-line) relationship between the response and an explanatory variable, is the assumption of linearity warranted? Regression diagnostics not only reveal deficiencies in a regression model that has been fit to data but in many instances may suggest how the model can be improved. The Second Edition of this bestselling volume by John Fox considers two important classes of regression models: the normal linear regression model (LM), in which the response variable is quantitative and assumed to have a normal distribution conditional on the values of the explanatory variables; and generalized linear models (GLMs) in which the conditional distribution of the response variable is a member of an exponential family. R code and data sets for examples within the text can be found on an accompanying website.

Series Editors Introduction About the Author Acknowledgements Chapter 1. Introduction Chapter 2. The Linear Regression Model: Review The Normal Linear Regression Models Least-Squares Estimation Statistical Inference for Regression Coefficients The Linear Regression Model in Matrix Forms Chapter 3. Examining and Transforming Regression Data Univariate Displays Transformations for Symmetry Transformations for Linearity Transforming Nonconstant Variation Interpreting Results When Variables are Transformed Chapter 4. Unusual data Measuring Leverage: Hatvalues Detecting Outliers: Studentized Residuals Measuring Influence: Cook's Distance and Other Case-Deletion Diagnostics Numerical Cutoffs for Noteworthy Case Diagnostics Jointly Influential Cases: Added-Variable Plots Should Unusual Data Be Discarded? Unusual Data: Details Chapter 5. Non-Normality and Nonconstant Error Variance Detecting and Correcting Non-Normality Detecting and Dealing With Nonconstant Error Variance Robust Coefficient Standard Errors Bootstrapping Weighted Least Squares Robust Standard Errors and Weighted Least Squares: Details Chapter 6. Nonlinearity Component-Plus-Residual Plots Marginal Model Plots Testing for Nonlinearity Modeling Nonlinear Relationships with Regression Splines Chapter 7. Collinearity Collinearity and Variance Inflation Visualizing Collinearity Generalized Variance Inflation Dealing With Collinearity *Collinearity: Some Details Chapter 8. Diagnostics for Generalized Linear Models Generalized Linear Models: Review Detecting Unusual Data in GLMs Nonlinearity Diagnostics for GLMs Diagnosing Collinearity in GLMs Quasi-Likelihood Estimation of GLMs *GLMs: Further Background Chapter 9. Concluding Remarks Complementary Reading References Index

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Regression diagnostics : an introduction

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