## Correlation

**Correlation:**

When for every value of a variable *X *we known a corresponding value of a second variable *Y*, i.e., the data is in the form of paired measurements, then we are interested in the relationship of these two variables. The analysis of univariate data in case of economic, social and scientific areas becomes insufficient. So, in some situations, say production price, height of father and son, marks obtained in two subjects, height of husbands and their wives, a series of expenses on advertisement and sales. If change in one variable is accompanied (or appears to be accompanied) a change in other variable and vice-versa, then the two variables are said to be correlated and this relationship is known as correlation or covariation.

**Correlation Analysis:**

The methods that are employed to determine if there exists any relationship between two variables and to express this relationship numerically comes under correlation analysis. Correlation analysis was developed by Francis Galton and Karl Pearson. Here we should consider only a logical relationship. Nature of the Relationship or Factors Responsible for Relationship:

**1. Direct Relationship :** One variable may be the cause of the other. As to which is the cause and which the effect is to be judged from the circumstances.

**2. Common Cause :** Correlation may be due to any other common cause. That is both variables may be the result of a common cause. For example, the heights of parents and their offspring are related due to their blood relation.

**3. Mutual Reaction:** It is not necesary that a series will affect the other.The two series may affect each other. Then it is not possible to differentiate between cause and effect.

**4. Useless or Nonsense or Spurious Correlation :** It might sometimes happen that between two variables a relationship may be observed when none of such relationship exists in the universe. Such a correlation is known as Spurious correlation. For example, the relationship between the number of tourists and production of sugar in India.

This means, the presence of correlation between two variables X and Y does not necessarily imply the existence of direct causation, though causation will always result in correlation. Spurious correlation practically has no meaning and we may consider that the observed correlation is due to chance.

**Utility and Importance of Correlation Analysis:**

Correlation analysis is a very important technique in statistics. It is useful in physical and social sciences and business and economics. The correlation analysis is useful in the following cases :

**1**. To have more reliable forecasting.

**2**. To study economic activities.

**3**. To estimate the variable values on the basis of an other variable values.

**4**. To make analysis, drawing conclusions etc. in the research or statistical investigations.

In economics, we study the relationship between price and demand, price and supply, income and expenditure, etc. According to Neiswanger, Correlation analysis contributes to the understanding of economic behavior, aids in locating the critically important variables on which others depend . may reveal to the economist the connections by which disturbances spread and suggest to him the paths through which stabilizing force may become effective. To a businessman correlation analysis helps to estimate costs , sales, prices and other related variables. Correlation analysis is the basis of the concept of regression and ratio of variation.

According to tippet, The effects of the correlation is to reduce the range of uncertainty of our prediction.

**Types of Correlation:**

On the basis of direction correlation:

**1**. Positive correlation and

**2**. Negative correlation.

When the increase (or decrease) in one variable results in a corresponding increase (or decrease) in the other (i.e., the two variables tend to move together in the same direction), the correlation is said to be positive or direct correlation. For example, demand and price. When the increase (or decrease) in one variable results in a corresponding decrease (or increase) in the other (i.e., the two variable tend to move together in opposite direction) , the correlation said to be negative or indirect correlation. For example: supply and price.

On the basis of ratio of change:

**1**. Linear correlation

**2**. Non-linear correlation.

If the ratio of change between the two variables is uniform i.e., when the amount of movement in one variable bears a constant ratio to the amount of change in the order, the correlation is said to be linear otherwise it is called non- linear or curvilinear. On the basis of the number of variables:

**1**. Simple correlation

**2**. Multiple correlation and

**3**. partial correlation.