Correlation and Regression

Correlation and regression deal with the meaning and measurement of data. 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. The main property of these variables is that they are interdependent. Correlation is used to express how the variables vary from each other systematically. For example, during summer, we tend to use fans more often at home, which increases electricity consumption and a rise in electricity bills. Here, the amount on the bill is related to the season. Correlation deals with varying factors like these. 

Correlation: Types of relationship

After a drought, certain vegetables like onions, potatoes, etc., become expensive. This is due to greater demand and a drop in the product’s availability. As demand increases, so does the price. 

Correlation: Meaning and Types

Correlation is the analysis of relationships between variables. Correlation is regarded as covariation. It focuses on how a change in one variable affects the second variable. This variation could be positive, where variation in one variable reflects in a similar direction in the other variable. Or it could be negative. Sometimes, the variables have no relationship in variation; for example, a person’s ability to swim does not depend on his English language proficiency.

Correlation can be classified into the following types: 

• Positive correlation: There are gas laws in physics like Boyle’s law, Charles law, etc. When a balloon filled with air is placed under the sun, it bursts. The volume of the air inside the balloon expands with a temperature rise. This is a positive correlation.
• Negative correlation: When we apply pressure on a closed syringe, the volume of air inside reduces. Here, the variables are said to be in negative correlation.
• Zero correlation: Changing the colour of a particular balloon does not affect the variation; hence there is zero correlation.

Other types of correlation are

• Linear correlation: If the variation of one variable affects the second variable constantly and the change is represented linearly, it is called linear correlation.
• Nonlinear correlation: If the variation is not linear but random, this fluctuation leads to a nonlinear curve. This type of correlation is called nonlinear correlation.
• Simple correlation: If the relationship between only two variables is studied, it is called a simple correlation; for example, increased demand for a limited edition phone leads to a rise in price.
• Partial correlation: 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.
• Multiple correlations: In the case of rainfall, various factors lead to one single result. This is called multiple correlations.

Properties of the correlation coefficient: 

The correlation coefficient expresses 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 does not have any relationship, it is 0. Usually, perfect relationships can be observed theoretically, and the experimental values result in decimal values.

Here are some features of the correlation coefficient:

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

Regression

Regression is a statistical process to determine the relationship between the dependent variable (y) and the independent variable (x). It is a useful technique in economics, finance, and business analysis. Investment professionals use regression in money monitoring.

Types of regression

There are five types of regression:

1. Linear regression
2. Ridge regression
3. Polynomial regression
4. Lasso regression
5. Logistic regression

Conclusion

As the demand for everyday essentials increases so does the supply. Here, supply and demand are related. The change in one of the variables projects in the other. Such changes are studied systematically in correlation and regression. 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 a negative relation. If there is no significant variation, then it is called zero correlation.