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Linear Regression
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Linear Regression
A Mathematical Introduction



July 2018 | 240 pages | SAGE Publications, Inc

Regression analysis is one of the most widely and intensively used techniques of quantitative research in the social and behavioral sciences, economics, and the health sciences. It is used in any area of research where one is interested in studying the relationship between a variable of interest, called the response variable, and a set of predictor variables.

Damodar N. Gujarati presents linear regression theory in a rigorous but approachable manner, so that it is accessible to beginning graduate students in the social sciences. The technical discussion is provided in a clear and accessible style, with advanced discussion of some of the topics offered in the appendices to the various chapters. This book is a concise exploration of the subject, and includes end-of-chapter exercises to test mastery of the chapter content.

 
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  

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ISBN: 9781544336572
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