# correlation coefficient definition

Correlation coefficient is a quantity that measures the strength of the association (or dependence) between two variables (x and y). For example if we are interested to know whether there is a relationship between the heights of fathers and son, a correlation coefficient can be calculated.

There are different correlation coefficients :

• Pearson r : linear dependence
• Kendall tau : rank-based correlation coefficient
• Spearman rho : rank-base correlation coefficient

Pearson correlation is the most used one.

correlation formula is described here.

# Negative and positive correlation

The value of correlation coefficient can be negative or positive and it is comprised between -1 and 1 (see the plots below).   • -1 means strong negative correlation : In this case y decreases when x increases (left panel figure)
• 0 means that there is no relationship between the two variables (x and y) (middle panel figure)
• 1 means strong positive correlation : In this case y increases when y increases (right panel figure)