Correlation VS Covariance: The easy way

Hello everyone. This is my second post in Machine Learning series, where I am trying to explain the concepts of machine learning in Layman terms. We will discuss one popular Machine learning interview question “what is the difference between correlation and covariance?” We will try to find the easiest answer of the question.

While both correlation and covariance measures the relationship and dependency between two variables they differ in some aspects. For that we will first understand how covariance measures then will see the correlation.

How Covariance measures the relationship between two variables?-

Covariance indicates the direction of the linear relationship between two variables. (-∞ to +∞). It does not indicates any strength of them.

How Correlation measures the relationship between two variables?-

Correlation measures both direction and strength of linear relationship between variables (-1 to +1).

Mathematical formulae for Correlation coefficient:-

where E(x) is the mean of variable x and E(y) is the mean of variable y.

From the above equation we can say that the correlation is a function of covariance.

Now the answer to our question here are the some points:

1. Covariance is effected by the change in scale while correlation not. Covariance is used when the variables are on similar scales and the correlation is used when the scales of the variable differs.
2. Covariance having units but correlation is unitless.
3. Correlation is normalized form of Covariance.

Thanks for reading. :)
And, Clap if this was a good read. Enjoy!