05477nam 2200685Ia 450 991083009050332120170810195603.01-282-30736-397866123073620-470-31676-40-470-31742-6(CKB)1000000000687550(EBL)468906(OCoLC)264621182(SSID)ssj0000342784(PQKBManifestationID)11247811(PQKBTitleCode)TC0000342784(PQKBWorkID)10286098(PQKB)10013860(MiAaPQ)EBC468906(PPN)159487889(EXLCZ)99100000000068755019871005d1988 uy 0engur|n|---|||||txtccrSensitivity analysis in linear regression[electronic resource] /Samprit Chatterjee, Ali S. HadiNew York Wileyc19881 online resource (341 p.)Wiley series in probability and mathematical statistics. Applied probability and statisticsDescription based upon print version of record.0-471-82216-7 Includes bibliography and index.Sensitivity Analysis in Linear Regression; PREFACE; Contents; 1. INTRODUCTION; 1.1. Introduction; 1.2. Notations; 1.3. Standard Estimation Results in Least Squares; 1.4. Assumptions; 1.5. Iterative Regression Process; 1.6. Organization of the Book; 2. PREDICTION MATRIX; 2.1.Introduction; 2.2. Roles of P and (I -P) in Linear Regression; 2.3. Properties of the Prediction Matrix; 2.3.1. General Properties; 2.3.2. Omitting (Adding) Variables; 2.3.3. Omitting (Adding) an Observation; 2.3.4. Conditions for Large Values of pii; 2.3.5. Omitting Multiple Rows of X; 2.3.6. Eigenvalues of P and (I- P)2.3.7. Distribution of pü2.4. Examples; 3. ROLE OF VARIABLES IN A REGRESSION EQUATION; 3.1. Introduction; 3.2. Effects of Underfitting; 3.3. Effects of Overfining; 3.4. Interpreting Successive Fining; 3.5. Computing Implications for Successive Fitting; 3.6. Introduction of One Additional Regressor; 3.7. Comparing Models: Comparison Criteria; 3.8. Diagnostic Plots for the Effects of Variables; 3.8.1. Added Variable (Partial Regression) Plots; 3.8.2. Residual Versus Predictor Plots; 3.8.3. Component-Plus-Residual (Partial Residual) Plots; 3.8.4. Augmented Partial Residual Plots3.9. Effects of an Additional Regressor4. EFFECTS OF AN OBSERVATION ON A REGRESSION EQUATION; 4.1. Introduction; 4.2. Omission Approach; 4.2.1. Measures Based on Residuals; 4.2.1.1. Testing for a Single Outlier; 4.2.1.2. Graphical Methods; 4.2.2. Outliers, High-leverage, and Influential Points; 4.2.3. Measures Based on Remoteness of Points in X-Y Space; 4.2.3.1. Diagonal Elements of P; 4.2.3.2. Mahalanobis Distance; 4.2.3.3. Weighted Squared Standardized Distance; 4.2.3.4. Diagonal Elements of Pz; 4.2.4. Influence Curve; 4.2.4.1. Definition of the Influence Curve4.2.4.2. Influence Curves for β and σ24.2.4.3. Approximating the Influence Curve; 4.2.5. Measures Based on the Influence Curve; 4.2.5.1. Cook's Distance; 4.2.5.2. Welsch-Kuh's Distance; 4.2.5.3. Welsch's Distance; 4.2.5.4. Modified Cooks Distance; 4.2.6. Measures Based on the Volume of Confidence Ellipsoids; 4.2.6.1. Andrews-Pregibon Statistic; 4.2.6.2. Variance Ratio; 4.2.6.3. Cook-Weisberg Statistic; 4.2.7. Measures Based on the Likelihood Function; 4.2.8. Measures Based on a Subset of the Regression Coefficients; 4.2.8.1. Influence on a Single Regression Coefficient4.2.8.2. Ilnfluence on Linear Functions of β4.2.9. Measures based on the Eigensmcture of X; 4.2.9.1. Condition Number and Collinearity Indices; 4.2.9.2. Collinearity-Influential Points; 4.2.9.3. Effects of an Observation on the Condition Number; 4.2.9.4. Diagnosing Collinearhy-Influential Observations; 4.3. Differentiation Approach; 4.4. Summary and Concluding Remarks; 5. ASSESSING THE EFFECTS OF MULTIPLE OBSERVATIONS; 5.1. Introduction; 5.2. Measures Based on Residuals; 5.3. Measures Based on the Influence Curve; 5.3.1. Sample lnfluence Curve; 5.3.2. Empirical Influence Curve5.3.3. Generalized Cook's DistanceTreats linear regression diagnostics as a tool for application of linear regression models to real-life data. Presentation makes extensive use of examples to illustrate theory. Assesses the effect of measurement errors on the estimated coefficients, which is not accounted for in a standard least squares estimate but is important where regression coefficients are used to apportion effects due to different variables. Also assesses qualitatively and numerically the robustness of the regression fit.Wiley series in probability and mathematical statistics.Applied probability and statistics.Regression analysisPerturbation (Mathematics)Mathematical optimizationRegression analysis.Perturbation (Mathematics)Mathematical optimization.519.5519.536Chatterjee Samprit1938-14454Hadi Ali S21014MiAaPQMiAaPQMiAaPQBOOK9910830090503321Sensitivity analysis in linear regression1142811UNINA