Correlation vs Regression

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To start with the discussion, we can say that both correlation and regression deal with variables and their connection with each other. In correlation, we look at the relations that the variables have between them and measure how strong it is. Whereas in regression, we see how one variable affects the other variable, a causal relationship between them.

So in a way, we can say that correlation depends on regression. As correlation measures causality and regression defines it. In this article we will see the key differences between correlation and regression:

Feature	Correlation	Regression
Meaning	It is a statistical method to determine the relationship between two variables.	It is a statistical method to determine how the independent variable is related to the dependent variable.
Use	It is used to draw a linear relationship between the variables.	It is used to draw a best fit line to predict one variable based on the other.
Variables	There are no different variables	There is independent variable and dependent variable
Indication	Correlation tells how far the variables can move together	Regression tells the impact of the effect of the change in independent variable on the dependent variable
Aim	To find a numerical value that describes the relationship between two variables	To estimate the value of random variable based on the values of the fixed variables
Mathematical equation	Uses no equation	y = a + bx
Interchangeable variables	Variables x and y can be changed	Variables x and y cannot be changed

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What is correlation?

Correlation determines the relationship between the two variables. Although, it does not bother to tell which variable affect which one and the direction of their relationship. Correlation just states the degree to which both the variables will move together.

Correlation can be positive and negative. Like when two variables move together (increase in one variable causes the increase in other variable) is called positive correlation. Example: Investment in advertising and sales

Correlation is said to be negative when the variables move in different directions (when one variable increases, the other decreases). Example: the sales of sweaters decrease in the summer season.

The various measures of correlation are:

Karl Pearson’s Product-moment correlation coefficient
Spearman’s rank correlation coefficient
Scatter diagram
Coefficient of concurrent deviations

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What is regression?

Regression is said to be the statistical method that determines the change in the dependent variable based on the change in the independent variable. It is treated as a powerful statistical tool to predict the values of variables that are yet to occur, based on the existing x – y variables and their values. Data science is an emerging technology that uses regression algorithms on a large scale.

Example: based on the past performance of the company, the sales department determine the upcoming sales target for the year.

The equation of the regression line is:

y = a + bx

Here, y is the dependent variable and x is the independent variable. a is a constant and b is the regression coefficient.

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