### CORRELATION MEANING | NEGATIVE CORRELATION | POSITIVE CORRELATION | PEARSON CORRELATION | CORRELATION COEFFICIENT | NUMERICAL AND STATISCAL METHODS

**CORRELATION
**

## WHAT IS CORRELATION ?

Correlation is the relationship that exists between two or more variables.

Two variables are said to be correlated if a change in one variable affects a change in the other variable.

Such a data connecting two variables is called bivariate data.

Thus, correlation statistical analysis which measures and analyses the degree or extent to which two variables fluctuate with reference to each other.

Few examples of such a relationship are as follows:

1. Relationship between heights and weights.

2. Relationship between price and demand of commodity.

3. Relationship between rainfall and yield of crops

4. Relationship between age of husband and age of wife.

**TYPES OF CORRELATIONS**

Correlation is classified into four types :

1. Positive and negative correlations

2. Simple and multiple correlations

3. Partial and total correlations

4. Linear and nonlinear correlations

**1) Positive and Negative correlations :**

Depending on the variation in the variables, correlation may be positive or negative

**Positive Correlation :-**

If both the variables vary in the same direction, the correlation is said to be positive.

In other words, if the value of one variable increases the value of the other variable also increases, or, if value of one variable decreases, the value of the other variable decreases,

e.g.

The correlation between heights and weights of group of persons is a positive correlation.

**Negative Correlation :-**

If both the variables vary in the opposite direction, correlation is said to be negative. In other words, if the value of one variable increases, the value of the other variable decreases, or, if the value of one variable decreases, the value of the other variable increases,

e.g.

The correlation between the price and demand of a commodity is a negative correlation.

**2) Simple and Multiple Correlations :**

Depending upon the study of the number of variables, correlation may multiple be simple or simple Correlation.

**Simple Correlation :-**

When only two variables are studied, the relationship is termed as simple correlation, e.g.

The quantity of money and price level

**Multiple Correlation :-**

When more than two variables are studied, the relationship is described as multiple correlation.

e.g.

Relationship of price, demand, and supply of a commodity.

**3) Partial and Total Correlations :**

Multiple correlation may be either partial or total.

**Partial Correlation :-**

When more than two variables are studied excluding some other variables, the relationship is termed as partial correlation.

**Total Correlation :-**

When more than two variables are studied without excluding any variables, the relationship is termed total correlation.

**4) Linear and Nonlinear Correlations :**

Depending upon the ratio of change between two variables, the correlation may be Linear or nonlinear.

**Linear Correlation :-**

If the ratio of change between two variables is constant, the correlation is said to be linear.

If such variables are plotted on a graph paper, a straight line is obtained.

e.g.

**Nonlinear Correlation :-**

If the ratio of change between two variables is not constant, the correlation is said to nonlinear.

The graph of a nonlinear or curvilinear relationship will be a curve.

e.g.

**NOTES**

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