**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.