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Tanima Dutta, Lovely Professional University Unit 9: Regression Analysis

Unit 9: Regression Analysis Notes

CONTENTS
Objectives

Introduction
9.1 Two Lines of Regression

9.1.1 Line of Regression of Y on X
9.1.2 Line of Regression of X on Y
9.1.3 Correlation Coefficient and the two Regression Coefficients

9.1.4 Regression Coefficient in a Bivariate Frequency Distribution
9.2 Least Square Methods
9.2.1 Fitting of Linear Trend

9.2.2 Fitting of Parabolic Trend
9.2.3 Fitting of Exponential Trend
9.3 Summary

9.4 Keywords
9.5 Review Questions

9.6 Further Readings
Objectives

After studying this unit, you will be able to:
Define the term regression equation
State the relevance of regression equation in statistics

Discuss two lines of regression
Analyze correlation coefficient and the two regression coefficients
Explain various methods of least square and mention its merits and demerits

Introduction

If the coefficient of correlation calculated for bivariate data (X , Y ), i = 1,2, ...... n, is reasonably
i i
high and a cause and effect type of relation is also believed to be existing between them, the next
logical step is to obtain a functional relation between these variables. This functional relation is
known as regression equation in statistics. Since the coefficient of correlation is measure of the
degree of linear association of the variables, we shall discuss only linear regression equation.
This does not, however, imply the non-existence of non-linear regression equations.
The regression equations are useful for predicting the value of dependent variable for given
value of the independent variable. As pointed out earlier, the nature of a regression equation is
different from the nature of a mathematical equation, e.g., if Y = 10 + 2X is a mathematical

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