Regression diagnostics : an introduction
Regression analysis
SAGE Publications, Inc.
2020
Second edition.
EISBN 1071878654
Cover.
About the Author.
Series Editor's Introduction.
Acknowledgments.
1 Introduction.
2 The Linear Regression Model: Review.
The Normal Linear Regression Model.
Least-Squares Estimation.
Statistical Inference for Regression Coefficients.
*The Linear Regression Model in Matrix Form.
3 Examining and Transforming Regression Data.
Univariate Displays.
Transformations for Symmetry.
Transformations for Linearity.
Transforming Nonconstant Variation.
Interpreting Results When Variables Are Transformed.
4 Unusual Data: Outliers, Leverage, and Influence.
Measuring Leverage: Hat Values.
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.
5 Nonnormality and Nonconstant Error Variance.
Detecting and Correcting Nonnormality.
Detecting and Dealing With Nonconstant Error Variance.
Robust Coefficient Standard Errors.
Bootstrapping.
Weighted Least Squares.
*Robust Standard Errors and Weighted Least Squares: Details.
6 Nonlinearity.
Component-Plus-Residual Plots.
Marginal Model Plots.
Testing for Nonlinearity.
Modeling Nonlinear Relationships With Regression Splines.
*Transforming Explanatory Variables Analytically.
7 Collinearity.
Collinearity and Variance Inflation.
Visualizing Collinearity.
Generalized Variance Inflation.
Dealing With Collinearity.
*Collinearity: Some Details.
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.
9 Concluding Remarks.
Complementary Reading.
References.
Index.
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 at https://tinyurl.com/RegDiag.
About the Author.
Series Editor's Introduction.
Acknowledgments.
1 Introduction.
2 The Linear Regression Model: Review.
The Normal Linear Regression Model.
Least-Squares Estimation.
Statistical Inference for Regression Coefficients.
*The Linear Regression Model in Matrix Form.
3 Examining and Transforming Regression Data.
Univariate Displays.
Transformations for Symmetry.
Transformations for Linearity.
Transforming Nonconstant Variation.
Interpreting Results When Variables Are Transformed.
4 Unusual Data: Outliers, Leverage, and Influence.
Measuring Leverage: Hat Values.
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.
5 Nonnormality and Nonconstant Error Variance.
Detecting and Correcting Nonnormality.
Detecting and Dealing With Nonconstant Error Variance.
Robust Coefficient Standard Errors.
Bootstrapping.
Weighted Least Squares.
*Robust Standard Errors and Weighted Least Squares: Details.
6 Nonlinearity.
Component-Plus-Residual Plots.
Marginal Model Plots.
Testing for Nonlinearity.
Modeling Nonlinear Relationships With Regression Splines.
*Transforming Explanatory Variables Analytically.
7 Collinearity.
Collinearity and Variance Inflation.
Visualizing Collinearity.
Generalized Variance Inflation.
Dealing With Collinearity.
*Collinearity: Some Details.
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.
9 Concluding Remarks.
Complementary Reading.
References.
Index.
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 at https://tinyurl.com/RegDiag.
