Page 193 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 13: Coefficient of Simple Regression Method
Pavitar Parkash Singh, Lovely Professional University

Unit 13: Coefficient of Simple Regression Method Notes

CONTENTS
Objectives
Introduction
13.1 Regression Equations
13.2 Coefficient of Simple Regression Method
13.3 Summary
13.4 Key-Words
13.5 Review Questions
13.6 Further Readings

Objectives

After reading this unit students will be able to:
• Explain Regression Equations
• Discuss the coefficients of Simple Regression Method.

Introduction

After having established the fact that two variables are closely related, we may be interested in
estimating (predicting) the value of one variable given the value of another. For example, if we know
that advertising and sales are correlated, we may find out the expected amount of sales for a given
advertising expenditure or the required amount of expenditure for attaining a given amount of sales.
Similarly, if we know that the yield of rice and rainfall are closely related, we may find out the
amount of rain required to achieve a certain production figure. The statistical tool with the help of which
we are in a position to estimate (or predict) the unknown values of one variable from known values of another
variable is called regression. With the help of regression analysis,* we are in a position to find out the
average probable change in one variable given a certain amount of change in another.
Regression analysis is a branch of statistical theory that is widely used in almost all the scientific
disciplines. In economics it is the basic technique for measuring or estimating the relationship among
economic variables that constitute the essence of economic theory and economic life. For example, if
we know that two variables, price (X) and demand (Y), are closely related, we can find out the most
probable value of X for a given value of Y or the most probable value of Y for a given value of X.
Similarly, if we know that the amount of tax and the rise in the price of commodity are closely
related, we can find out the expected price for a certain amount of tax levy. Thus we find that the
study of regression is of considerable help to the economists and businessmen.
13.1 Regression Equations

Regression equations are algebraic expressions of the regression lines. Since there are two regression
lines, there are two regression equations–the regression of X on Y is used to describe the variation in
the values of X for given changes in Y and the regression equation of Y on X is used to describe the
variation in the values of Y for given changes in X.
Regression Equation of Y on X

The regression equation of Y on X is expressed as follows:
Y = a + bX
c

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