1 Introduction. - 1. 1 Relationships. - 1. 2 Determining Relationships: A Specific Problem. - 1. 3 The Model. - 1. 4 Least Squares. - 1. 5 Another Example and a Special Case. - 1. 6 When Is Least Squares a Good Method?. - 1. 7 A pleasure of Fit for Simple Regression. - 1. 8 Mean and Variance of b0 and b1. - 1. 9 Confidence Intervals and Tests. - 1. 10 Predictions. - 2 Multiple Regression. - 2. 1 Introduction. - 2. 2 Regression Model in Matrix Notation. - 2. 3 Least Squares Estimates. - 2. 4 Examples 31 2. - 2. 6 Mean and Variance of Estimates Under G-M Conditions. - 2. 7 Estimation of ?. - 2. 8 Measures of Fit 39?2. - 2. 9 The Gauss-Markov Theorem. - 2. 10 The Centered Model. - 2. 11 Centering and Scaling. - 2. 12 *Constrained Least Squares. - 3 Tests and Confidence Regions. - 3. 1 Introduction. - 12 Linear Hypothesis. - 3. 3 *Likelihood Ratio Test. - 3. 4 *Distribution of Test Statistic. - 3. 5 Two Special Cases. - 3. 6 Examples. - 3. 7 Comparison of Repression Equations. - 3. 8 Confidence Intervals and Regions. - 4 Indicator Variables. - 4. 1 Introduction. - 4. 2 A Simple Application. - 4. 3 Polychotomous Variables. - 4. 4 Continuous and Indicator Variables. - 4. 5 Broken Line Regression. - 4. 6 Indicators as Dependent Variables. - 5 The Normality Assumption. - 5. 1 Introduction. - 5. 2 Checking for Normality. - 5. 3 Invoking Large Sample Theory. - 5. 4 *Bootstrapping. - 5. 5 *Asymptotic Theory. - 6 Unequal Variances. - 6. 1 Introduction. - 6. 2 Detecting Heteroscedasticity. - 6. 3 Variance Stabilizing Transformations. - 6. 4 Weighing. - 7 *Correlated Errors. - 7. 1 Introduction. - 7. 2 Generalized Least Squares: Case When ? Is Known. - 7. 3 Estimated Generalized Least Squares. - 7. 4 Nested Errors. - 7. 5 The Growth Curve Model. - 7. 6 Serial Correlation. - 7. 7 Spatial Correlation. - 8 Outliers and Influential Observations. - 8. 1 Introduction. - 8. 2 The Leverage. - 8. 3The Residuals. - 8. 4 Detecting Outliers and Points That Do Not Belong to the Model 157. - 8. 5 Influential Observations. - 8. 6 Examples. - 9 Transformations. - 9. 1 Introduction. - 9. 2 Some Common Transformations. - 9. 3 Deciding on the Need for Transformations. - 9. 4 Choosing Transformations. - 10 Multicollinearity. - 10. 1 Introduction. - 10. 2 Multicollinearity and Its Effects. - 10. 3 Detecting Multicollinearity. - 10. 4 Examples. - 11 Variable Selection. - 11. 1 Introduction. - 11. 2 Some Effects of Dropping Variables. - 11. 3 Variable Selection Procedures. - 11. 4 Examples. - 12 *Biased Estimation. - 12. 1 Introduction 2. - 12. 2 Principal Component. Regression. - 12. 3 Ridge Regression. - 12. 4 Shrinkage Estimator. - A Matrices. - A. 1 Addition and Multiplication. - A. 2 The Transpose of a Matrix. - A. 3 Null and Identity Matrices. - A. 4 Vectors. - A. 5 Rank of a Matrix. - A. 6 Trace of a Matrix. - A. 7 Partitioned Matrices. - A. 8 Determinants. - A. 9 Inverses. - A. 10 Characteristic Roots and Vectors. - A. 11 Idempotent Matrices. - A. 12 The Generalized Inverse. - A. 13 Quadratic Forms. - A. 14 Vector Spaces. - Problems. - B Random Variables and Random Vectors. - B. 1 Random Variables. - B. 1. 1 Independent. Random Variables. - B. 1. 2 Correlated Random Variables. - B. 1. 3 Sample Statistics. - B. 1. 4 Linear Combinations of Random Variables. - B. 2 Random Vectors. - B. 3 The Multivariate Normal Distribution. - B. 4 The Chi-Square Distributions. - B. 5 The F and t Distributions. - B. 6 Jacobian of Transformations. - B. 7 Multiple Correlation. - Problems. - C Nonlinear Least Squares. - C. 1 Gauss-Newton Type Algorithms. - C. 1. 1 The Gauss-Newton Procedure. - C. 1. 2 Step Halving. - C. 1. 3 Starting Values and Derivatives. - C. 1. 4 Marquardt Procedure. - C. 2 Some Other Algorithms. - C. 2. 1 Steepest Descent Method. - C. 2. 2 Quasi-Newton Algorithms. - C. 2. 3 The Simplex Method. - C. 2. 4 Weighting. - C. 3 Pitfalls. - C. 4 Bias Confidence Regions and Measures of Fit. - C. 5 Examples. - Problems. - Tables. - References. - Author Index. Language: English