Table of Contents

# Correlation

Correlation is a statistical tool used to study the relationship between two or more variables. Two variables are said to be correlated if the change in one variable there will change in other variable. On the other hand if the change in one variable does not bring any change in other variable then we say that the two variables are not correlated to each other.

## Types of Correlation

There are four types of correlation –

1. Simple, Partial and Multiple correlation

2. Positive and Negative correlation

3. Perfect and Imperfect correlation

4. Linear and Non-linear correlation

## Simple, Partial and Multiple correlation

Simple correlation is the relationship between any two variables. Partial correlation is the study of relationship between any two out of three or more variables ignoring the effect of other variables. For example, let us suppose that we have three variables X_{1} = marks of Maths, X_{2} = marks of Science, and X_{3} = marks of English. So if we study the relationship between X_{1} and X_{2} ignoring the effect of X_{3}, then it is partial correlation.

Multiple correlation is the study of simultaneous relationship between one or group of other variables. For example, if we study X_{1}, X_{2}, X_{3} simultaneously then correlation between X_{1} and (X_{2}, X_{3}) is multiple correlation. Multiple correlation is not commonly used.

## Positive and Negative correlation

Two variables are said to be positively correlated when the both the variables under study move in the same direction, i.e., if one variable increase, the other variable should also increase and one variable decreases the other variable should also decrease. Variables are said to be negatively correlated if increase in one variable leads to decrease in other variable and vice versa. That is the variables move in opposite direction. For positive correlation, the graph will be an upward curve whereas in case of negative correlation the graph will be downward curve.

## Perfect and Imperfect correlation

When both the variables changes at a constant rate irrespective of the change in direction then it is called perfect correlation. When the variables changes at different ratio then it is called imperfect correlation. The values of perfect correlation is 1 or -1 and the values of imperfect correlation lies in between -1 and 1.

## Linear and Non-linear correlation

Linear correlation is a correlation when the graph of the correlated data is a straight line. That is the variables are perfectly correlated. The linear correlation can be either positive or negative when the graph of straight line is either upward or downward in direction. On the other hand the non-linear or curvy-linear correlation is a correlation when the graph of the variables gives a curve of any direction. Like perfect correlation, non-linear correlation can be either be positive or negative in nature depending upon the upward and downward direction of the curve.

## Methods of measurement of correlation

Following are the three important methods of measuring the correlation between the variables –

1. Scatter Diagram Method

2. Karl Pearson’s Coefficient Method

3. Spearman’s Rank Coefficient Method

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