Regression Analysis

Introduction

The dictionary meaning of the word 'regression' is the act of returning or going back. The word 'regression' was first used by the Sir Francis Galton (1822-1910). In the year 1877 while studying the relationship between the height of fathers and send. This word was introduced by him in the paper 'regression towards mediocrity in hereditary stature'. His study of height of about one 1000 fathers and some revealed a very intrusting relationship, i.e. the tall fathers tend to have tall sons & short fathers tends to have short sons. But the average height of the sons of a group of tall fathers is less than that of the fathers than that of the fathers. The line describing the tendency to regress or going back was termed by Galton a regression line.' The term is still used to describe that the line drawn for a group of points to show the present trend , but it is no longer necessarily carries the original implication of ''stepping back'' that Galton the term estimating line instead of regression line as the expression estimating line is more clarification in character.

Let us analyze some definitions of the term regression.

''The Regression is the measurement of the average relationship between two or more variables in terms of the original units of the data.''

"The term regression analysis refers to the methods or techniques by which the estimates are made of the values of a variable from knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation process."

''One of the most frequently used methods in economics and business research. To determine the relation between two or more variables that are related casually is regression analysis.''

''The Regression analysis attempts to establish the 'nature of the relationship' between variables-that is, to study the functional relationship between the variables and thereby provide a mechanism for prediction or forecasting.''

It is clear from the above definitions that regression analysis is a statistical device with the help of which we are in a position to estimate or predict the unknown values of one variable from the known values of another variable. The variable which is used to predict the variable of interest is known as the independent variable of the explanatory variable and the variable we are trying to predict is known as the dependent variable or explained variable. The independent variable is represented by X and the dependent variable by Y. The analysis used is known as the simple liner regression analysis-simple because there is only one predictor or independent variable and liner because of the supposed liner relationship between the dependent and the independent variables. The term liner means that an equation of a straight line of the form Y = α = box, where a & b are constants is used to describe the average relationship that exists between the two variables.

It must be noted that the term 'dependent' and 'independent' refer to the mathematical or functional meaning of dependence-they do not imply that there is necessarily any cause and effect relationship between the variables. What it meant is simply that the estimates of values of the dependent variable Y may be obtained for a given value of the independent variable X from a mathematical function involving X and Y. In that way, the values of Y are dependent upon the values of X. The X variable may or may not be the product from figures on advertising expenditures, sales is normally taken as the dependent variable. However, there may or may not be causal connection between these two factors as that changes in advertising expenditures cause changes in sales. In fact, in certain cases the cause-effect relation may be just opposite of what appears to be the obvious one.