![](http://devskrol.com/wp-content/uploads/2020/07/corr.png)
Correlation Coefficient is a statistical measure of the strength of the relationship between the relative movements of two variables.
We know that the equation of Sum of Squared Errors is as below.
![Image for post](https://miro.medium.com/max/459/1*JMg-ypeUeX8d5mZxlvCjRg.png)
![Image for post](https://miro.medium.com/max/416/1*szgQ7c6ZHxYG0oTLQAqU5w.png)
If there is a perfect Linear Regression exists between 2 variables x & y, then the line of regression runs through all the points and so there will be no error.
![Image for post](https://miro.medium.com/max/824/1*_0ynH0a4H3I5Dg-u4ae_rg.png)
This is the maximum value of r² which is 1.
The maximum SSE occurs only when there is no correlation. i.e minimum correlation.
![Image for post](https://miro.medium.com/max/385/1*h69U7-h_5Gmw1gW-sU7y1g.png)
This means that r² is 0 which is the minimum value of r².
If the gradient (i.e. Slope) of line of regression is -ve, then Sxy <0. So r² < 0.
If it is +ve, then Sxy > 0. So r > 0.
Hence -1≤ r ≤+1