Page 208 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes 14.1 Correlation Analysis

So far we have studied problems relating to one variable only. In practice, we come across a large
number of problems involving the use of two or more than two variables. If two quantities vary in
such a way that movements in one are accompanied by movements in the other, these quantities are
correlated. For example, there exists some relationship between age of husband and age of wife,
price of a commodity and amount demanded, increase in rainfall up to a point and production of
rice, an increase in the number of television licences and number of cinema admissions, etc. The
statistical tool with the help of which these relationships between two or more than two variables are
studied is called correlation. The measure of correlation, called the correlation coefficient, summarizes
in one figure the direction and degree of correlation. Thus correlation analysis refers to the techniques
used in measuring the closeness of the relationship between the variables. A very simple definition
of correlation is that given by A.M. Tuttle. He defines correlation as: “An analysis of the covariation
of two or more variables is usually called correlation”.
The problem of analysing the relation between different series can be broken down into three steps:
(1) Determining whether a relation exists and, if does, measuring it.
(2) Testing whether it is significant.
(3) Establishing the cause and effect relation, if any.
In this unit, only the first aspect will be discussed. For second aspect a reference may be made in the
unit on Tests of Significance. The third aspect in the analysis, that of establishing the cause-effect
relation, is beyond the scope of statistical analysis. An extremely high and significant correlation
between the increase in smoking and increase in lung cancer would not prove that smoking causes
lung cancer. The proof of a cause and effect relation can be developed only by means of an exhaustive
study of the operative elements themselves.
It should be noted that the detection and analysis of correlation (i.e., covariation) between two statistical
variables requires relationships of some sort which associate the observations in pairs, one of which
pair being a value of each of the two variables. In general, the pairing relationship may be of almost
any nature, such as observations at the same time or place over a period of time or different places.

The computation concerning the degree of closeness is based on the regression equation.
However, it is possible to perform correlation analysis without actually having a regression
equation.

Utility of the Studt of Correlation
The study of correlation is of immense use in practical life because of the following reasons:
1. Most of the variables show some kind of relationship. For example, there is relationship between
price and supply, income and expenditure, etc. With the help of correlation analysis, we can
measure in one figure the degree of relationship existing between the variables.
2. Once we know that two variables are closely related, we can estimate the value of one variable
given the value of another. This is done with the help of regression equations discussed in Unit 8.
3. Correlation analysis contributes to the economic behaviour, aids in locating the critically important
variables on which others depend, may reveal to the economist the connection by which
disturbances spread and suggest to him the paths through which stabilizing forces become effective.
In business, correlation analysis enables the executive to estimate costs, sales, prices and other
variables on the basis of some other series with which these costs, sales, or prices may be
functionally related. Some guesswork can be removed from decisions when the relationship
between a variable to be estimated and the one or more other variables on which it depends are
close and reasonably invariant.

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