What is the difference between correlation and regression

In this tutorial, we shall learn the key differences between correlation and regression. Correlation and regression are used quite often for statistical analysis.

What is the difference between correlation and regression?

In this tutorial, we will learn the differences between correlation and regression. But first, let's define correlation and regression in simple terms.

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Correlation –

Correlation is a measure that determines whether two variables are related or not. It's a statistical method for expressing the strength of a relationship between two variables.

Positive and negative correlations exist. When two variables move in the same direction, that is, when an increase in one variable causes a commensurate increase in the other variable and vice versa, the variables are said to be positively linked. For example, consider the quantity and price of a product. A negative correlation occurs when the two variables move in opposite ways so that an increase in one variable causes a drop in the other, and vice versa. For example, consider the price and demand for a product.

The correlation measures are as follows:
• Karl Pearson’s Product-moment correlation coefficient
• Scatter diagram
• Spearman’s rank correlation coefficient


Regression –

The numerical relationship between an independent variable and the dependent variable is described by regression. Based on the average mathematical relationship between two or more variables, it is a statistical technique for estimating the change in the metric dependent variable owing to a change in one or more independent variables.

It is a powerful and adaptable instrument that is used to forecast past, present or future occurrences based on past or present events, and it plays an important part in many human activities. For example, a company's future profit can be anticipated based on historical data.

There are two variables in a simple linear regression, x, and y, where y is dependent on x or influenced by x. The dependent or criterion variable is y, while the independent or predictor variable is x. The y on x regression line is written as follows:

y = a + bx

where a is the constant and b is the regression coefficient
The two regression parameters in this equation are a and b.


Now, the major difference between correlation and regression are as follows –

1. The linear link between two variables is represented by correlation. Regression, on the other hand, is used to find the optimal line and estimate one variable based on another.
2. There is no distinction between dependent and independent variables in correlation, therefore the correlation between x and y is the same as the correlation between y and x. The regression of y on x, on the other hand, is not the same as x on y.
3. The degree of the link between variables is indicated by correlation. Regression, on the other hand, measures the effect of a unit change in the independent variable on the dependent variable.
4. Finding a numerical value that expresses the link between variables is the goal of correlation. In contrast to regression, which aims to predict the values of a random variable based on the values of a fixed variable.

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