Pearson’s Correlation Coefficient

What is Pearson’s Correlation Coefficient

Building upon the work from French scientist Francis Galton, Pearson developed the Pearson’s correlation coefficient (r):

r = \frac{1}{n - 1} \sum (z_{x_{i}}) (z y_{i})

Pearson’s correlation coefficient tells us the strength of linear association between two quantitative variables (and direction!)

Notice that it can only indicates linear relationship, its possible that exists other relationship with r very small

If $r > 0$ then the correlation is positive
If $r < 0$ then the correlation is negative

If $r$ is around 0.5 then we would say it is moderate.
If $r$ is less than 0.3 then we would say it is weak
If $r$ is greater than 0.7 then we say it is strong

Properties

r has no units
r measures the strength of a linear relationship
r is between -1 and 1
The closer r is to 0 -> weaker relationship
The further r is from 0 -> stronger relationship
r=0 -> no linear relationship
changing scale of either variable doesn’t affect r value