# Covariance and Correlation

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269 Co-Variance: Covariance is a measure of the directional relationship between two or more variables. Covariance measures how the mean values of two variables move together. If stock A’s return moves higher whenever stock B’s return moves higher and the same relationship is found when each stock’s return decreases, then these stocks are said to have a positive covariance.

We can say, Covariance is a measure indicating the extent to which two random variables change in tandem. Specifically, covariance measures the degree to which two variables are linearly associated.
A large covariance can mean a strong relationship between variables.  Values of covariance Lie between -∞ and +∞. The sign of the covariance therefore shows the tendency of  linear relationship between two variables.

However, we can’t compare variances over data sets with different scales (like pounds and inches). A weak covariance in one data set may be a strong one in a different data set with different scales. Properties of Covariance:

1. The covariance is a general representation of the same concept as the variance. That is, the variance measures how a random variable moves with itself, and the covariance measures how one random variable moves with another random variable.
2. The Covariance of a variable with itself is equal to variance of the variable.

Correlation: Correlation (co-relation) refers to the degree of relationship (or dependency) between two variables. The Linear correlation also known as Pearson Correlation refers to straight-line relationships between two variables.

In practice, the covariance is difficult to interpret. This is mostly because it can take on extremely large values, ranging from negative to positive infinity, and just like the variance, these values are expressed in terms of square units.

Whereas, Correlation coefficient varies between -1 and +1. If Correlation Coefficient is equal +1 then variables have perfect positive correlation and if Correlation Coefficient is equal -1 then variables have perfect negative correlation. If Correlation Coefficient is equal to 0 then there is no linear relationship between two variables. Below is the formula to calculate the Correlation: 