# A Beginner Guide to Pearson Correlation Coefficient – Machine Learning Tutorial

By | December 6, 2020

Pearson correlation coefficient aims to measure the strength of the relationship between two variables. In this tutorial, we will introduce it for machine learning beginners.

## Pearson Correlation Coefficient

There are two types of pearson correlation coefficient: pearson correlation coefficient in population and pearson correlation coefficient in sample.

As to population, population correlation coefficient is defined as:

Here $$cov(X, y)$$ is the covariance of X and Y,$$\sigma_X$$ and $$\sigma_Y$$ are the standard deviation of X and Y.

As to sample, sample correlation coefficient is defined as:

Here $$n$$ is the total number of a sample, $$\overline{X}$$ and $$\overline{Y}$$ are the mean of X and Y.

## The value of pearson correlation coefficient

The value of pearson correlation coefficient is in [-1, 1]

• -1: negative correlation
• 0: no correlation
• 1: positive correlation

Moreover, it can be viewed as:

• .00-.19: very weak
• .20-.39: weak
• .40-.59: moderate
• .60-.79: strong
• .80-1.0: very strong

Here is an picture to show the correlation.