Tutorial Introductions

Linear Regression by James V Stone.

Preface

Chapter 1 What is Linear Regression? 

1.1 Introduction 

1.2 The Equation of a Line  

1.3 The Best Fitting Line 

1.4 Regression and Causation  

1.5 Regression: A Summary 

2 Finding the Best Fitting Line  

2.1 Introduction 

2.2 Exhaustive Search  

2.3 Onwards and Downwards  

2.4 The Normal Equations 

2.5 Numerical Example 

3 How Good is the Best Fitting Line? 

3.1 Introduction 

3.2 Variance and Standard Deviation  

3.3 Covariance and Correlation 

3.4 Partitioning the Variance 

3.5 The Coefficient of Determination 

3.6 Numerical Example 

4 Statistical Significance: Means 

4.1 Introduction 

4.2 The Distribution of Means  

4.3 Degrees of Freedom 

4.4 Estimating Variance  

4.5 The p-Value 

4.6 The Null Hypothesis  

4.7 The z-Test 

4.8 The t-Test 

4.9 Numerical Example 

5 Statistical Significance: Regression 

5.1 Introduction 

5.2 Statistical Significance  

5.3 Statistical Significance: Slope 

5.4 Statistical Significance: Intercept

5.5 Significance Versus Importance 

5.6 Assessing the Overall Fit 

5.7 Numerical Example 

6 Maximum Likelihood Estimation 

6.1 Introduction 

6.2 The Likelihood Function  

6.3 Likelihood and Least Squares Estimation 

7 Multivariate Regression 

7.1 Introduction 

7.2 The Best Fitting Plane 

7.3 Vector--Matrix Formulation  

7.4 Finding the Best Fitting Plane 

7.5 Statistical Significance 

7.6 How Many Regressors? 

7.7 Numerical Example 

8 Weighted Linear Regression 

8.1 Introduction 

8.2 Weighted Sum of Squared Errors 

8.3 Vector--Matrix Formulation 

8.4 Statistical Significance

8.5 Numerical Example

9 Nonlinear Regression 

9.1 Introduction 

9.2 Polynomial Regression 

9.3 Nonlinear Regression 

9.4 Numerical Example 

10 Bayesian Regression: A Summary  

10.1 Introduction 

10.2 Bayes' Theorem 

Appendices  

  A Glossary  

  B Mathematical Symbols  

  C A Vector and Matrix Tutorial  

  D Setting Means to Zero 

  E Key Equations 

Index