Linear Regression and Its Application to Economics

Introduction1. Regression and Correlation 1.1. General Comments on Regression and Correlation 1.2. Two-Dimensional Random Variables 1.2.1. Definitions and Symbols 1.2.2. Two-Dimensional Discrete Random Variables 1.2.3. Two-Dimensional Continuous Random Variables 1.2.4. Moments of a Two-Dimensional Variable 1.2.5. Regression I 1.2.6. Regression II 1.2.7. Linear Regression 1.2.8. Correlation. Correlation Ratio and Correlation Coefficient 1.2.9. The Two-Dimensional Normal Distribution 1.3. Non-Linear Regression in R22. The Application of Regression and Correlation to Economic Research 2.1. On the Relation Between Economics and Mathematics, on Statistics and Econometrics 2.2. More Important Applications of Regression and Correlation Theory in Economic Research 2.2.1. Want Curves 2.2.2. Income Distribution Curves 2.2.3. Demand Curves 2.2.4. Cost Curves 2.2.5. Time Curves 2.2.6. Techno-Economic Curves3. Estimating Linear Regression Parameters 3.1. General Remarks About Methods of Estimating 3.2. Estimating Linear Regression Parameters by the Method of Least Squares 3.2.1. The Derivation of Formulae. Examples 3.2.2. The Technique of Computing Regression Parameters in a Small and a Large Sample. Contingency Table 3.3. Estimating Linear Regression Parameters by the Two-Point Method 3.3.1. The Derivation of Formulae 3.3.2. The Technique of Computing Regression Parameters in a Small and a Large Sample. Examples 3.3.3. The Properties of Estimates Obtained by the Two-Point Method 3.3.4. Comments on Estimating the Correlation Coefficient by the Two-Point Method4. On Testing Certain Statistical Hypotheses 4.1. Two Tests to Verify the Hypothesis that the Distribution of the General Population Ω is Normal 4.1.1. The Formulation of the Problem 4.1.2. Testing Hypothesis H by Rotating the Coordinate System (Method A) 4.1.3. Testing the Hypothesis H by Dividing the Plane into Quadrants (Method B) 4.2. Checking the Hypothesis that the Regression Lines in General Population Ω are Straight Lines 4.2.1. General Comments 4.2.2. Testing Hypothesis HL in a Small Sample by a Run Test 4.2.3. Testing Hypothesis HL in a Large Sample by Fisher's Test 4.3. An Analysis of the Significance of Regression Parameters 4.4. An Analysis of the Significance of the Correlation Coefficient5. The Transformation of Curvilinear into Linear Regression6. The Regression Line and the Trend 6.1. The Definition of Trend 6.2. Some Tests for Verifying Hypothesis Ht 6.2.1. The Run Test 6.2.2. The χ2 Test 6.2.3. Pitman's Test 6.3. The Determination of Trend ex Post and ex AnteAppendixList of SymbolsTablesBibliography