Linear regression : a mathematical introduction /: a mathematical introduction. (2018)

• Record Type: Book
• Further Information: Note: Damodar N. Gujarati.
• Authors: Gujarati, Damodar N
• Contents: List of Figures; Series Editor’s Introduction; Preface; About the Author; Acknowledgments; Chapter 1: The Linear Regression Model (LRM); 1.1 Introduction; 1.2 Meaning of “Linear” in Linear Regression; 1.3 Estimation of the LRM: An Algebraic Approach; 1.4 Goodness of Fit of a Regression Model: The Coefficient of Determination (R2); 1.5 R2 for Regression Through the Origin; 1.6 An Example: The Determination of the Hourly Wages in the United States; 1.7 Summary; Exercises; Appendix 1A: Derivation of the Normal Equations; Chapter 2: The Classical Linear Regression Model (CLRM); 2.1 Assumptions of the CLRM; 2.2 The Sampling or Probability Distributions of the OLS Estimators; 2.3 Properties of OLS Estimators: The Gauss–Markov Theorem; 2.4 Estimating Linear Functions of the OLS Parameters; 2.5 Large-Sample Properties of OLS Estimators; 2.6 Summary; Exercises; Chapter 3: The Classical Normal Linear Regression Model: The Method of Maximum Likelihood (ML); 3.1 Introduction; 3.2 The Mechanics of ML; 3.3 The Likelihood Function of the k-Variable Regression Model; 3.4 Properties of the ML Method; 3.5 Summary; Exercises; Appendix 3A: Asymptotic Efficiency of the ML Estimators of the LRM; Chapter 4: Linear Regression Model: Distribution Theory and Hypothesis Testing; 4.1 Introduction; 4.2 Types of Hypotheses; 4.3 Procedure for Hypothesis Testing; 4.4 The Determination of Hourly Wages in the United States; 4.5 Testing Hypotheses About an Individual Regression Coefficient; 4.6 Testing the Hypothesis That All the Regressors Collectively Have No Influence on the Regressand; 4.7 Testing the Incremental Contribution of a Regressor; 4.8 Confidence Interval for the Error Variance s 2; 4.9 Large-Sample Tests of Hypotheses<br /> 4.10 Summary; Exercises; Appendix 4A: Constrained Least Squares: OLS Estimation Under Linear Restrictions; Chapter 5: Generalized Least Squares (GLS): Extensions of the Classical Linear Regression Model; 5.1 Introduction; 5.2 Estimation of B With a Nonscalar Covariance Matrix; 5.3 Estimated Generalized Least Squares; 5.4 Heteroscedasticity and Weighted Least Squares; 5.5 White’s Heteroscedasticity-Consistent Standard Errors; 5.6 Autocorrelation; 5.7 Summary; Exercises; Appendix 5A: ML Estimation of GLS; Chapter 6: Extensions of the Classical Linear Regression Model: The Case of Stochastic or Endogenous Regressors; 6.1 Introduction; 6.2 X and u Are Distributed Independently; 6.3 X and u Are Contemporaneously Uncorrelated; 6.4 X and u Are Neither Independently Distributed Nor Contemporaneously Uncorrelated; 6.5 The Case of k Regressors; 6.6 What Is the Solution? The Method of Instrumental Variables (IVs); 6.7 Hypothesis Testing Under IV Estimation; 6.8 Practical Problems in the Application of the IV Method; 6.9 Regression Involving More Than One Endogenous Regressor; 6.10 An Illustrative Example: Earnings and Educational Attainment of Youth in the United States; 6.11 Regression Involving More Than One Endogenous Regressor; 6.12 Summary; Appendix 6A: Properties of OLS When Random X and u Are Independently Distributed; Appendix 6B: Properties of OLS Estimators When Random X and u Are Contemporaneously Uncorrelated; Chapter 7: Selected Topics in Linear Regression; 7.1 Introduction; 7.2 The Nature of Multicollinearity; 7.3 Model Specification Errors; 7.4 Qualitative or Dummy Regressors; 7.5 Nonnormal Error Term; 7.6 Summary; Exercises; Appendix 7A: Ridge Regression: A Solution to Perfect Collinearity; Appendix 7B: Specification Errors; Appendix A: Basics of Matrix Algebra; A.1 Definitions; A.2 Types of Matrices; A.3 Matrix Operations; A.4 Matrix Transposition; A.5 Matrix Inversion; A.6 Determinants; A.7 Rank of a Matrix; A.8 Finding the Inverse of a Square Matrix; A.9 Trace of a Square Matrix; A.10 Quadratic Forms and Definite Matrices; A.11 Eigenvalues and Eigenvectors; A.12 Vector and Matrix Differentiation; Appendix B: Essentials of Large-Sample Theory; B.1 Some Inequalities; B.2 Types of Convergence; B.3 The Order of Magnitude of a Sequence; B.4 The Order of Magnitude of a Stochastic Sequence; Appendix C: Small- and Large-Sample Properties of Estimators; C.1 Small-Sample Properties of Estimators; C.2 Large-Sample Properties of Estimators; Appendix D: Some Important Probability Distributions; D.1 The Normal Distribution and the Z Test; D.2 The Gamma Distribution; D.3 The Chi-Square (? 2) Distribution and the ? 2 Test; D.4 Student’s t Distribution; D.5 Fisher’s F Distribution; D.6 Relationships Among Probability Distributions; D.7 Uniform Distributions; D.8 Some Special Features of the Normal Distribution; Index;
• Publisher Details: Thousand Oaks : SAGE Publications, Inc
• Publication Date: 2018
• Extent: 1 online resource (272 pages)
• Subjects: 519.536; Regression analysis; Matrices; Sampling (Statistics)
• Languages: English
• ISBNs: 9781544336558; 1544336551
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.