CORRELATION & CO-EFFICIENT
Till the previous chapter we have been mainly concerned with univariate data. In this chapter we study bivariate and multivariate populations. According to Ya-lun Chou, “There are two related but distinct aspects of the study of association between variables. Correlation analysis and regression analysis. Correlation analysis has the objective of determining the degree or strength of the relationship between variables. 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 of prediction, or forecasting.”
In our daily lives we notice that the bigger the house the higher are its upkeep charges, the higher rate of interest the greater is the amount of saving, the rise in prices bring about a decrease in demand and the devaluation of country’s currency makes export cheaper or import dearer. The above example clearly shows that there exists some kind of relationship between the two variables. Croxton and Cowden rightly said, “when relationship between two variables is of quantitative nature the appropriate statistical tool for measuring and expressing it in formula is known as correlation. Thus correlation is a statistical device which helps in analyzing the relationship and also the covariation of two or more variables. According to Simpson and Kafta “correlation analysis deals with the association between two or more variables.” If two variables vary in such a way that movements in one are accompanied by movements in the other, then these quantities are said to be correlated.
Importance of Correlation
A car owner knows that there is a definite relationship between petrol consumed and distance travelled. Thus on the basis of this relationship the car owner can predict the value of one on the basis of other. Similarly if he finds that there is some distortions of relationship, he can set it right.
Correlation helps in the following ways
1. It helps to predict event and the events in which there is time gap i.e. it helps in planning
2. It helps in controlling events.
Types of Correlation
Correlation can be classified under the following heads
1. Positive and negative correlation
2. Simple multiple and partial correlation
3. Linear and non-linear correlation
Positive and Negative Correlation
Two variables are said to be positively correlated when both the variables move in the same direction. The correlation is said to be positive (directly related) when the increase in the value of one variable is accompanied by an increase in the value of the other variable and vice versa.
Two variables are said to be negatively correlated when both the variables move in the opposite direction. The correlation is said to be negative (inversely related) when the increase in the value of one variable is accompanied by a decrease in the value of the other variable and vice versa.
Simple, Multiple and Partial Correlation
Correlation is said to be simple when only two variables are studied. In multiple correlation three or more variables are studied simultaneously. In partial correlation though more than two variables are recognised, but only two are considered to be influencing each other; and the effect of other influencing variables are kept constant.
Linear and Non-linear Correlation
If the amount of change in one variable tends to bear a constant ratio to the amount of change in the other variable, then the correlation is said to be linear. The correlation is said to be non-linear if the amount of change in one variable does not bear a constant ratio to the amount of change in the other related variable.
Measurement of Correlation
The correlation can be measured by any of the following methods
1. Scatter Diagram
2. Karl Pearson’s coefficient of correlation
3. Rank correlation coefficient