CORRELATION

Introduction:

Correlation is an important topic in Statistics. In NCERT Book Class 11 Statistics Chapter 7 Correlation deals with meaning and measurements of correlation. It includes techniques for measuring correlation like Karl Pearson’s Coefficient of Correlation and Spearman’s Rank Correlation. Correlation is simply the relationship and association among two or more variables. It is the quantitative way to find how the measurements are related to each other. The main property of these variables is that they are interdependent. Correlation is used to express how the variables vary with each other systematically. For example, during summer, we tend to use fans more often at home and this would, in turn, increase the electricity consumption and would lead to a rise in electricity bills. Here that price is related to the climate. Correlation deals with varying factors like these. 

Correlation: Types of relationship

After a drought the price of certain vegetables like onion, potato etc. rise. This is due to the demand for the products and the reduced availability of the products. As demand increases, so does the price.On a random day when we see somedoes not affect house, this type of relationship cannot be established. It can be attributed to pure coincidence. And for the third type in a particular season, seasonal fruits would be available in bulk and hence the price of those would be lower. As the production increases, the price decreases. These are the three types of relationships that we can see in our everyday lives.

Correlation: Meaning and Types

Correlation is the analysis of relationships between variables. Correlation is regarded as covariation. That implies that when there is a change in one variable how the second variable is affected is its focus. It doesn’t relate to finding a casual relationship. This variation could be either in a positive way where one variation is reflected in a similar direction in the other variable. Or, it could be in the reverse negative way. Sometimes, the variables have no relationship in variation, for example, a person is learning swimming and his proficiency in English is not at all a factor influencing his learning.

So Correlation can be classified into the following types: 

• Positive Correlation
• Negative correlation
• Zero Correlation

There are gas laws in Physics like Boyle’s law, Charles law etc. When a balloon filled with air is placed outside in the sun, it bursts. The volume of the air expands with temperature. This is a positive correlation. Whereas, when we apply pressure on a syringe that is closed its volume of air inside reduces. Here the variables are said to be in negative correlation. When we change the colour of a particular balloon in the first stage this colour has no effect on the variation, hence there is zero correlation.

Other types of correlation are 

• Linear and nonlinear correlation 
• Simple, partial and multiple correlations

If the variation of one variable affects the second variable constantly and the change can be represented linearly, it is called linear correlation.

If the variation is not linear and is random then this fluctuation leads to a nonlinear curve. This type of correlation is called nonlinear correlation.

If the relationship is studied between only two variables, it is called a simple correlation. For example when demand increases for a phone of limited edition, its price increases. 

In cases of rainfall, various factors lead to one single result. This is called multiple correlations.

In making simple relationships in the gas equation, we assume some variables to be constant to deduce the laws. Those types of relationships are partial correlations.

Correlation Calculator:

Some of the techniques for measuring correlation are:

• Scatter Diagram

The nature of the relationship can be expressed visually without mentioning its values using a scatter plot. It is the simplest approach to finding the relationship between two variables.

• Karl Pearson’s Coefficient of Correlation

The numerical measurements of two variables can be expressed in between -1 and +1 values. A linear relationship is where one is perfectly correlated with another variable. Perfect positive and negative correlations are represented by straight-line graphs. 

• Spearman’s rank correlation

Based on certain special and common properties we could rank the variables in order and can establish the relationship when the values cannot be accurately measured. 

Properties of the Correlation coefficient: 

The correlation coefficient is used to express the variation between two factors on a scale from +1 to -1. If a system is perfectly correlated positively this coefficient will have a value of +1. If it is correlated negatively. And if it doesn’t have any relationship it is 0. Usually, the perfect relationships can be observed theoretically and the experimental values result in decimal values.

1. The correlation coefficient is unitless. It is simply a number that lies within a certain limit. 
2. Inverse relationships are negatively correlated.
3. Positive relationships show changes in a similar direction.
4. The value of the coefficient always lies between +1 and -1. Values outside of this range show errors in measurement.
5. A correlation coefficient of 0 implies that there is no relationship among the variables.
6. High values of coefficient suggest linear relationships and low value suggests weak relationships among variables.

Uses of coefficient of correlation:

1. To test the validity of results in any experiment.
2. To find the reliability of experimental results.
3. To give the relationship between factors in any expressions. 
4. Predict the behaviour of variables in a measurement

Conclusion: 

In regular everyday instances, we can see many factors changing concerningsome doesriables. For example, the demand for everyday essentials increases and to make the needs met, the supply also increases. So here the supply and demand are related. The change in one of the variables projects in another variable. These kinds of changes are studied systematically in correlation. If the variation in any variable is affected by a similar directional change in another variable it is called a positive variable. If it is in the opposite direction, it is termed a negative relation. If there is no significant variation then it is called zero correlation.