Correlation and Regression are the two multivariate distribution based analyses. A multivariate distribution is called multiple variables distribution. Correlation is described as the analysis that allows us to know the relationship between two variables 'x' and 'y' or the absence of it.

On the other hand, the Regression analysis predicts the value of the dependent variable based on the known value of the independent variable, assuming that there is an average mathematical relation between two or more variables.

Given Below Are The Measures of Correlation -

The correlation coefficient of Karl Pearson’s Product-moment

Scatter diagram

Coefficient of concurrent deviations

Coefficient of Spearman’s rank correlation

The term correlation is a combination of two words 'Co' (together) and the relation between two quantities. Correlation is when it is observed that a change in a unit in one variable is retaliated by an equivalent change in another variable, i.e., direct or indirect, at the time of study of two variables. Or else the variables are said to be uncorrelated when the motion in one variable does not amount to any movement in a specific direction in another variable. It is a statistical technique that represents the strength of the linkage between variable pairs.

Correlation can be either negative or positive. If the two variables move in the same direction, i.e. an increase in one variable results in the corresponding increase in another variable, and vice versa, then the variables are considered to be positively correlated. For example, Investment and profit.

On the contrary, if the two variables move in different directions so that an increase in one variable leads to a decline in another variable and vice versa, this situation is known as a negative correlation. For example, Product price and demand.

A statistical technique based on the average mathematical relationship between two or more variables is known as regression, to estimate the change in the metric dependent variable due to the change in one or more independent variables. It plays an important role in many human activities since it is a powerful and flexible tool that used to forecast past, present or future events based on past or present events. For example, The future profit of a business can be estimated on the basis of past records.

There are two variables x and y in a simple linear regression, wherein y depends on x or say that is influenced by x. Here y is called as a variable dependent, or criterion, and x is variable independent or predictor. The line of regression y on x is expressed as below:

Y = a + bx

where, a = constant,

b = regression coefficient,

The a and b are the two regression parameters in this equation.

Here’s the difference between correlation and regression analysis. To sum up, there are four key aspects that differ from those terms.

There is a relationship between the variables when it comes to correlation. In contrast, regression places emphasis on how one variable affects the other.

Correlation does not capture causality whilst it is based on regression.

The correlation between x and y is identical to that between y and x. Contrary to this, a regression of x and y, and y and x, results completely different.

Finally, one single point is a graphical representation of a correlation. Whereas one line visualizes a linear regression.

Correlation and regression are two analyzes, based on multiple variables distribution. They can be used to describe the nature of the relationship and strength between two continuous quantitative variables.

It is evident with the above discussion that there is a big difference between correlation and regression, the two mathematical concepts although these two are being studied together. Correlation is used when the researcher wishes to know whether or not the variables being studied are correlated, if yes then what the strength of their association is. Pearson's correlation coefficient is considered as the best correlation measure. A functional relationship between two variables is established in regression analysis, in order to make future projections on events.

FAQ (Frequently Asked Questions)

1. What are the different types of regression according to their functionality?

Ans. Regression is a method used to model and evaluate relationships between variables, and at times how they contribute and are linked to generating a specific result together. The different types of regression according to their functionality are as follows:

Simple Linear Regression - This is a statistical method used to summarize and study the relationships between any two continuous variables – an independent variable and a dependent one.

Multiple Linear Regression - This regression type examines the linear relationship between a dependent variable and more than one independent variable that exists.

2. What are the different types of Correlation according to their character?

Ans. The three types of relation to their character are -

Positive Correlation - If two variables are seen moving in the same direction, whereby an increase in the value of one variable results in an increase in another, and vice versa.

Negative Correlation - on the other hand, when two variables are seen moving in different directions, and in a way that any increase in one variable results in a decrease in the value of the other, and vice versa.

Zero Correlation - If any change in one variable is not dependent on the other, then Zero Correlation is said to have the variables.