# What is correlation and covariance in statistics

### What is correlation and covariance in statistics

Covariance and correlation are two mathematical concepts which are commonly used in statistics. When comparing data samples from different populations, covariance is used to determine how much two random variables vary together, whereas correlation is used to determine when a change in one variable can result in a change in another.

Both covariance and correlation measure linear relationships between variables. When the correlation coefficient is positive, an increase in one variable also results in an increase in the other. When the correlation coefficient is negative, the changes in the two variables are in opposite directions. When there is no relationship, there is no change in either.
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Covariance - Covariance is for two random variables whereas Variance is for one random variable. Co-variance tells how two series are related.

The magnitude of the Co-variance does not mean anything as the magnitude is dependent upon the magnitude of the constituent entries in the series. Therefore, what matters is the sign. However the normalized covariance (also called Correlation coefficient) can be of help.

For two random variables X and Y , if Co-variance is > 0, then Y increases as X increases. And if Co-variance < 0, then Y decreases as X increases.

So there is always some sort of relationship between X and Y and hence co-variance may be positive or negative but never zero. If Co-variance = 0, then the two series are independent of each other.

Example - The calorific intake of a person and his weight has a high Correlation. But the calorific intake and his name - not correlated.