# What is Correlation?

Correlation is a statistical tool that measures the quantitative relationship between different variables. It studies the degree and intensity of the connection between the two variables. The relationship between two variables is studied with the help of a statistical tool i.e. ‘Correlation’.

## Types of Correlation

Based on the nature of the relationship between the two variables, correlation can be broadly classified into the following three categories:

• Positive and Negative Correlation
• Linear and Curvilinear Correlation
• Simple and Multiple Correlation

### Positive correlation

A positive correlation between two variables exists when both of them move in the same direction. In other words, if with the increase in one variable, the other also increases, and with the decrease in one variable the opposite also decreases
then, the 2 variables are said to be positively correlated. For example, in summers as the temperature rises, the demand for soft drinks rises. Thus, the demand for soft drinks and temperatures are positively correlated.

### Negative correlation

Two variables are said to be negatively correlated if the two variables move in the opposite direction. In other words, when one variable increases and the other variable falls, the two variables are said to be negatively correlated. For example, in winters as the temperature falls, the demand for room heaters increases. Thus, the demand for room heaters and temperature is negatively correlated.

### Linear correlation

If the ratio for change between the two variables is constant or fixed, then the 2 variables are said to be linearly correlated.

### Curvilinear correlation (Non-linear)

As against, linear correlation, if the ratio of change between the two variables is not constant, then the two variables are said to be curvilinearly correlated.

### Simple correlation

The study of the relationship between only two variables is known as a simple correlation. For example, the relationship between price and demand.

### Multiple correlations

The study of relationships among three or more than three variables simultaneously is called multiple correlations. For example, the study of the relationship between price, demand, tastes, and income of the consumers.

## Degrees of Correlation

The degree or the extent of correlation between two variables is described by the value of the correlation coefficients. The degrees of correlation are:

• Perfect Correlation
• Zero Correlation
• Limited Degree of Correlation

### Perfect correlation

The perfect correlation exists when two variables change in exactly equal proportion. It is often further classified into two categories.

• Perfect Positive Correlation
• Perfect Negative Correlation

Perfect positive correlation: When the proportional change in two variables is within the same direction, then it is called a perfect positive correlation. For a perfect positive correlation between two variables, the value of the correlation coefficient is equal to +1.

Perfect negative correlation: There exists a perfect negative correlation between two variables if the proportional change in the two variables is in the opposite direction. The value of the correlation coefficient for a perfect negative correlation is – 1.

### Zero correlation

If there is no relation between two variables, i.e. change in one variable has no effect on the change in the other, then the variable lacks correlation. The value of the correlation coefficient for zero correlation equals zero.

Note: A zero correlation between any two variables does not mean that there is no relationship at all between them. In fact, it should be interpreted that the 2 variables are not linearly related. However, it may be possible that the two variables may be nonlinearly related to each other.

### Limited degree of correlation

Between the extremes of perfect correlation and zero correlation, there exists a limited degree of correlation. This implies that although the two variables are related, an increase (or decrease) in one variable is not accompanied by an equal proportionate increase (or decrease) in the other variable. In this case, the value of the correlation coefficient lies between zero and one.

### Measures of Dispersion in Statistics

Dispersion measures the extent to which the different items tend to disperse away from the central tendency. In other words, while central tendency indicates a representative value, the measures of dispersion indicate the divergence of the values of different items from the central value.

### Measures of central tendency

Central tendency refers to a central value that represents the whole statistical series. The central value is sometimes simply referred to as average. The following are the objectives of measures of central tendency.

### Why do we Need to Study Economics?

By studying economics, we can understand how an economy solves these central problems. We can thus say that economics is the study of the mechanisms used by an economy

### Statistics in Plural Sense

In the plural sense, statistics refers to the systematic collection of numerical facts. It indicates information in terms of numbers or numerical data such as employment statistics and population statistics.

### Statistics in Singular Sense

In the singular sense, statistics refers to the science of studying statistical methods. It indicates the techniques or methods of collecting, organizing, presenting, analyzing, and interpreting data.

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