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Linear Regression
A Mathematical Introduction

- Damodar N. Gujarati - West Point, New York, USA

**Volume:**177

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.

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 |

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 |

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 |

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 |

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 |

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 |

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.”

**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.”

**University of Iowa**

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

**CUNY Graduate Center**

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