Page 182 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics Dilfraz Singh, Lovely Professional University

Notes Unit 12 : Linear Regression Analysis :

Introduction and Lines of Regression

CONTENTS
Objectives
Introduction
12.1 Introduction to Linear Regression Analysis
12.2 Line of Regression
12.3 Summary
12.4 Key-Words

12.5 Review Questions
12.6 Further Readings

Objectives

After reading this unit students will be able to :
• Introduce Linear Regression Analysis
• Discuss Line of Regression.
Introduction

In the previous unit we discussed correlation analysis, which seeks to determine the degree of linear
relationship or correlation between two variables in a bivariate distribution. The coefficient of
correlation indicates whether the variables are linearly related and if so, how strong the relationship
is. In scatter diagram method of determining correlation, we observed that if r = ± 1, then all the
points lie exactly on a straight line showing a linear relationship between the two variables. Also for
high positive or negative value of correlation coefficient, we observed that the point in a scatter
diagram lie near about a straight line. In case r = 0, the scatter of points is considerable and the linear
trend disappears. Such observations give rise to questions : what is the straight line in the scatter
diagram, how can this line be obtained and finally what is the usefulness of this line. Statistical
methods used to answer such questions are the subject matter of regression analysis. The regression analysis
is concerned with the formulation and determination of algebraic expressions for the relationship between the
two variables. We use the general form ‘regression lines’ for these algebraic expressions. These regression lines
or the exact algebraic forms of the relationship are then used for predicting the value of one variable from that of
the other. Here, the variable whose value is to be predicted is called dependent or explained variable and
the variable used for prediction is called independent or explanatory variable.

Galton termed the line describing the average relationship between the two variables as the
line of regression.

The word regression, which means reversion, was first introduced by Sir Francis Galton in the study
of heredity. His study on the heights of fathers and sons revealed an interested relationship. He showed that
the heights of sons tended or reverted towards the average rather than two extreme values, i.e., tall fathers tend

176 LOVELY PROFESSIONAL UNIVERSITY