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Linear Regression
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Linear Regression
A Mathematical Introduction



July 2018 | 240 pages | SAGE Publications, Inc

Damodar N. Gujarati’s Linear Regression: A Mathematical Introduction presents linear regression theory in a rigorous, but approachable manner that is accessible to students in all social sciences. This concise title goes step-by-step through the intricacies, and theory and practice of regression analysis. The technical discussion is provided in a clear style that doesn’t overwhelm the reader with abstract mathematics. End-of-chapter exercises test mastery of the content and advanced discussion of some of the topics is offered in the appendices.

 
Chapter 1: The Linear Regression Model (LRM)
1.1 Introduction: Meaning of Linear regression  
1.2 estimation of the Linear regression Model: An Algebraic Approach  
1.3 Goodness of fit of a Regression Model: The Coefficient of Determination (R2)  
1.4 R2 for regression through the Origin  
1.5 An Example: The determination of Wages in the US  
1.6 To Sum up  
 
Chapter 2: The Classical Linear Regression Model (CLRM)
2.1 Assumptions of CLRM  
2.2 The Sampling of Probability distribution of the OLS estimators  
2.3 Properties of OLS estimators: The Gauss-Markov Theorem  
2.4 Estimating Linear Functions of the OLS Paramters  
2.5 Large Sample Properties of OLS Estimators  
2.6 Summary  
 
Chapter 3: The classical normal linear regression model: The method of maximum likelihood
3.1 Introduction  
3.2 The Mechanics of ML  
3.3 Likelihood function of the k-variable regression model  
3.4 Properties of the maximum likelihood model  
3.5 Summary  
 
Chapter 4: Linear regression model: Distribution Theory and Hypothesis testing
4.1 Types of Hypothesis  
4.2 Procedure for Hypothesis Testing  
4.3 The determination of Hourly wages in the US  
4.4 Testing hypothesis about individual regression coefficients  
4.5 Testing the hypothesis that the regressors collectively have no influence on the regressand  
4.6 Testing the incremental contribution of a regressor(s)  
4.7 Confidence interval for the error variance  
4.8 Large sample tests of hypotheses  
4.9 Summary and conclusions  
 
Chapter 5: Extensions of the Classical Linear regression model: generalized least squares (GLS)
5.1 estimation of regression parameters with a non-scalar covariance matrix  
5.2 Estimated Generalized least squares  
5.3 Heteroscedasticity and Weighted least squares (WLS)  
5.4 White's Heteroscedacity-consistent Standard Errors  
5.5 Autocorrelation  
5.6 Summary and conclusions  
 
Chapter 6: Extensions of the Classical linear regression model: the case of stochastic or endogenous regressors
6.1 A regressor and the error term are independently distributed  
6.2 A regressor and the error term are contemporaneously uncorrelated  
6.3 A regressor and the error term are neither independently distributed nor are contemporaneously uncorrelated  
6.4 The case of k regressors  
6.5 What is the solution? The Method of Instrumental Variables (IV)  
6.6 Hypothesis testing unde IV Estimation  
6.7 Practical Problems in the application of IV Regression Method  
6.8 Regression involving more than one endogenous regressor  
6.9 An Illustrative Example: Earnings and Educational Attainment of US youth  
6.10 IV regression with more than one endogenous regressor  
6.11 Summary and conclusions  
 
Chapter 7: Selected Topics in Linear Regression
7.1 The Nature of Multicollinearity  
7.2 Specification Errors  
7.3 Functional forms of regression models  
7.4 Qualitative or Dummy regressors  
7.5 Consequences of non-normal error term  

“This is a nifty volume that complements the series of ‘Little Green Books’ nicely. It offers a blend of the abstract and the concrete, presenting both ‘the math’ and the ‘how-to’ that will be of use to both experienced and novice users.”

 
Wendy L. Martinek
Binghamton University

“Damodar Gujariti brings his world-class expertise as an econometrician to bear on explicating the fundamentals of the math behind regression analysis, the most widely-used social science research tool around. His presentation shows clarity, understanding and range, always with good applied illustrations.”

Michael S. Lewis-Beck
University of Iowa

“This text is a useful monograph on linear models theory. The writing is clear and derivations insightful.”

Jay Verkuilen
CUNY Graduate Center
Key features

KEY FEATURES: 

  • This book offers with unique brevity a discussion of the basics of regression analysis. 
  • Discussion of the method of Maximum Likelihood (ML), a topic which does not receive much attention in other texts, is covered.
  • Succinct discussion of distribution theory offers discussion of estimation and hypothesis—topics that are the foundation of statistical inference.
  • Two large data based examples of regression analysis, allowing with practical problems that are illustrated with the data, show how regression theory is applied in practice. 
 

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