Page 210 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes degree of correlation itself. The high degree of correlation indicates only the mathematical result. We
should reach a conclusion based on logical reasoning and intelligent investigation on significantly
related matters. It should also be noted that errors in correlation analysis include not only reading
causation into spurious correlation but also interpreting spuriously a perfectly valid association.
14.2 Regression Analysis

Meaning and Definition

The term regression was for the first time used by Sir Francis Galton in 1877 while studying the
relationship between the height of fathers and sons. He carried out a study on height of one thousand
fathers and sons and revealed that tall fathers tend to have tall sons and short fathers short sons, but
the average height of the sons of a group of tall fathers is less than that of the fathers and the average
height of the sons of a group of short fathers is greater than that of the fathers. This line describing
the tendency to regress or going back was called as a regression line by Galton. The term is still used
to describe that line drawn for a group of points to represent the trend present, however, today it
does not necessarily have the original implication of stepping back (for which Galton had used this
term). In modern times term ‘estimating line’ is coming to be used instead of ‘regression line’. On
examining a few definitions, the term regression as used in statistics can be clearly described.
(1) As described by Morris Hamburg, “The term regression analysis refers to the methods by which
estimates are made of the values of a variable from a knowledge of values of one or more other
variables and to the measurement of the errors involved in this estimation process.”
(2) According to Taro Yamane, “One of the most frequently used techniques in economics and
business research, to find, relation between two or more variables that are related casually, is
regression analysis.”
On the basis of the above definitions, it has become very clear that regression analysis is done for estimating
or predicting the unknown value of one variable from the known value of the other variable. The variable
which is used to predict the variable of interest is called the independent variable or explanatory variable
and the variable we are trying to predict is called the dependent or explained variable.

In the words of Ya Lum Chou, “Regression analysis attempts to establish the nature
of the relationship between variables, that is, to study the functional relationship
between the variable and thereby provide a mechanism for prediction or forecasting.”

14.3 Correlation Analysis Vs. Regression Analysis

Most of the times, the correlation and regression analysis are confused with one another, probably
because of the fact that both of them study about the relationship between two variables. By studying
the points of differentiation, this would become clear:
(1) Correlation coefficient measures the degree of covariability between X and Y. The regression
analysis, on the other hand, studies the nature of relationship between X and Y so that one may
be predicted on the basis of the other.
(2) Correlation only ascertains the degree of relationship between two variables and it not be made
clear that one variable is the cause and the other is the effect. But in regression analysis, one
variable is taken as dependent while other as independent so that the cause and effect relationship
can be studied.
(3) In correlation r = r but regression coefficients b is never equal to b .
xy yx xy yx
b ≠ b .
xy yx
(4) Correlation may be found to exist between two variables by chance with no practical relevance.
But in regression the results are never by chance.

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