Linear Regression and Its Application to Economics

1st Edition - January 1, 1963

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• Author: Zdzisław Hellwig
• eBook ISBN: 9781483225760

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Description

Linear Regression and its Application to Economics presents the economic applications of regression theory. This book discusses the importance of linear regression for multi-dimensional variables. Organized into six chapters, this book begins with an overview of the elementary concepts and the more important definitions and theorems concerning two-dimensional and multi-dimensional random variables. This text then examines the important applications of correlation methods to economics. Other chapters consider the methods of estimating regression parameters. This book discusses as well the methods of testing some statistical hypotheses relevant for practical applications of the correlation analysis. The final chapter deals with the fact that correlation methods can be used not only in static but also in dynamic research. This book is a valuable resource for scientists in economic, agricultural, and technical colleges who deal with economic problems in their research. Graduates of economic and technical colleges employed in different branches of the national economy will also find this book useful.

• Introduction

1. 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 R2

2. 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 Curves

3. 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 Method

4. 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

4.2.2. 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 Coefficient

5. The Transformation of Curvilinear into Linear Regression

6. 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 Ante

Appendix

List of Symbols

Tables

Bibliography

Product details

• No. of pages: 250
• Language: English