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Unit 8: Correlation Analysis

The knowledge of this type of relationship is useful for predicting the value of one variable Notes
given the value of the other. It also helps in understanding and analysis of various economic and
business problems. It should be noted here that statistical relations are different from the exact
mathematical relations. Given a statistical relation Y = a + bX, between two variables X and Y,
we can only get a value of Y that we expect on the average for a given value of X. The study of
relationship between two or more variables can be divided into two broad categories:
1. To determine whether there exists some sort of association between the variables. If so,
what is the degree of association or the magnitude of correlation between the two.
2. To determine the most suitable form of the relationship between the variables given that
they are correlated.
The first category relates to the study of ‘Correlation’ which will be discussed in this unit and the
second relates to the study of ‘Regression’, to be discussed in next unit.

8.1 Correlation

Various experts have defined correlation in their own words and their definitions, broadly
speaking, imply that correlation is the degree of association between two or more variables.

8.1.1 Definitions of Correlation

Some important definitions of correlation are given below:

“If two or more quantities vary in sympathy so that movements in one tend to be accompanied
by corresponding movements in other(s) then they are said to be correlated.”
— L.R. Connor

“Correlation is an analysis of covariation between two or more variables.”
– A.M. Tuttle
“When the relationship is of a quantitative nature, the appropriate statistical tool for discovering
and measuring the relationship and expressing it in a brief formula is known as correlation .”
— Croxton and Cowden
“Correlation analysis attempts to determine the ‘degree of relationship’ between variables“.
— Ya Lun Chou
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.

8.1.2 Scope of Correlation Analysis

If there is a correlation between two variables, it may be due to any of the following situations:

1. One of the variable may be affecting the other: A correlation coefficient calculated from
the data on quantity demanded and corresponding price of tea would only reveal that the
degree of association between them is very high. It will not give us any idea about
whether price is affecting demand of tea or vice-versa. In order to know this, we need to
have some additional information apart from the study of correlation. For example, if on
the basis of some additional information, we say that the price of tea affects its demand,
then price will be the cause and quantity will be the effect. The causal variable is also
termed as independent variable while the other variable is termed as dependent variable.

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