We know that Pearson correlation coefficient (r) ranges from -1 to +1. And a zero Pearson correlation coefficient means there exists no **linear** relationship between the variables.

Here the word **linear** is crucial. Why? Let's find this out using an example where Pearson Correlation Coefficient = 0.

Consider a case where Y=X^{2}.

**X** -3 -2 -1 +1 +2 +3

**Y** +9 +4 +1 +1 +4 +9

If we calculate the Pearson Correlation Coefficient for this dataset, it will be 0.

But we know that Y is dependent on X because Y=X^{2}.

This relationship is non-linear. You can see from the above graph that the relation created a curve. Pearson Correlation Coefficient is unable to capture this non-linear association.

Linear relations produce straight lines such as the ones shown below:

**What to do when the relationship is non-linear?**

- Use other correlation measures such as Spearman's rank correlation coefficient or Kendall's rank correlation coefficient to capture the non-linear association.
- In some cases, transformation such as log transformation of variables might be useful. For more on this, you can read this blog.