Pearson’s R and Coefficient of Determination

Correlation coefficients are the measure of strength of linear relationship between two variables.

Pearson’s R is the most popular correlation coefficient. The value of Pearson’s R always ranges between -1 to 1, with 1 being perfect positive relationship, and -1 being perfect negative relationship. A value of 0 means that the two variables are just aren’t correlated.

Given a random pair of variables X and Y, the formula for pearson’s R is below. This formula is good for population, but a formula can be derived for sample as well based on this.

Problem with Pearson’s R: Pearson’s correlation is unable to tell difference between target variable and predictor. You get same result while trying to find how A correlates to B, vs when trying to find how B correlates to A. So, you need to be aware of your target variable and predictor.

Relation with R² — Coefficient of Determination:

Coefficient of Determination is just the square of pearson’s correlation coefficient R. This is done as it is easier to explain linear regression in terms of R² than R. As R ranges from -1 to 1, R² would range from 0 to 1 — clearly explaining relationship with 0 being not related and 1 being perfectly related.