When studying the relationship between two or more variables, it is important to know the difference between correlation and regression. In this Correlation vs. Regression tutorial, you will learn the similarities and differences between these two.

## Correlation

When a change in one variable is followed by a change in another variable, whether direct or indirect, this is known as correlation. If a change in one variable does not affect the other, the variables are said to be "uncorrelated." In a nutshell, it is a tool for determining the relationship between two variables.

Suppose there are two variables, ‘X' and 'Y'. If an increase in X results in an increase in Y value (and vice versa), they are positively correlated. If an increase in X results in a decrease in Y value (and vice versa), it is negatively correlated.

The above data is from World Happiness Report 2021. Here, if you observe, you can see that perception of corruption and happiness score have a negative correlation of -0.4. This means when perception of corruption increases, the happiness score decreases, and vice versa.

## Regression

Regression is a parameter used to explain the relationship between two variables. It's more of a dependent feature, in which one variable's actions influence the outcome of the other. To put it another way, regression aids in determining how variables interact.

The regression-based analysis aids in determining the status of a relationship between two variables, say x and y. This makes future projections more relatable by estimating events and structures.

Suppose there are two variables, x, and y in linear regression, wherein y depends on x. Here y is called a dependent variable, and x is an independent variable. The line of regression y on x is expressed as below:

Y = a + bx

where,

a = constant

b = regression coefficient

The above graph is taken from the Iris flower dataset.

From the above plot, you can conclude that–

- Species Setosa has smaller petal lengths and widths.
- Versicolor Species lies in the middle of the other two species in terms of petal length and width.
- Species Virginica has the largest of petal lengths and widths.

## Correlation vs. Regression

You will now understand the main difference between correlation and regression with the help of this table.

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## Summary

Regression is the most effective method for constructing a robust model, an equation, or predicting a response. The correlation is the best option if you want a quick response over a summary to determine the strength of a relationship.

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If you have any doubts or questions, please mention them in this tutorial’s comments section, and we'll have our experts answer them for you at the earliest!