Page 207 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 14: Correlation Analysis Vs. Regression Analysis
Dilfraz Singh, Lovely Professional University

Unit 14: Correlation Analysis Vs. Regression Analysis Notes

CONTENTS
Objectives
Introduction
14.1 Correlation Analysis
14.2 Regression Analysis

14.3 Correlation Analysis Vs. Regression Analysis
14.4 Summary
14.5 Key-Words
14.6 Review Questions

14.7 Further Readings

Objectives

After reading this unit students will be able to:

• Describe Correlation and Regression Analysis.
• Explain Correlation Analysis Vs. Regression Analysis.
Introduction

Correlation and regression analysis are related in the sense that both deal with relationships among
variables. The correlation coefficient is a measure of linear association between two variables. Values
of the correlation coefficient are always between – 1 and + 1. A correlation coefficient of + 1 indicates
that two variables are perfectly related in a positive linear sense, a correlation coefficient of – 1 indicates
that two variables are perfectly related in a negative linear sense, and a correlation coefficient of 0
indicates that there is no linear relationship between the two variables. For simple linear regression,
the sample correlation coefficient is the square root of the coefficient of determination, with the sign
of the correlation coefficient being the same as the sign of b 1, the coefficient of x l in the estimated
regression equation.
Neither regression nor correlation analyses can be interpreted as establishing cause-and-effect
relationships. They can indicate only how or to what extent variables are associated with each other.
The correlation coefficient measures only the degree of linear association between two variables.
Any conclusions about a cause-and-effect relationship must be based on the judgment of the analyst.
When once a relationship between two variables is ascertained, it is quite likely that estimating the
value of one for some given value of other is expected. This can be done with the help of regression.
It measures the average relationship between two or more variables in terms of original units of the
data. The dictionary meaning of the term ‘Regression’ is to revert or return back. The term was used
for the first time by Sir Francis Galton in 1877. In statistics, the technique of Regression is used in all
those fields where two or more variables have the tendency to go back to the mean. While correlation
measures the direction and strength of the relationship between two or more variables, regression
involves methods by which estimates are made of the values of a variable from the knowledge of the
values of one or more other variables. Along with this, measurement of the error involved in the
estimation process are also included. This means, the regression technique can be used for the
prediction on the basis of the average relationship.

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