Covariance

Link: Mean, variance and standard deviation

What is covariance? §

Covariance measures variables in pair. It can tell us the relationship of the variable and how much it change together.

A simple example §

Instead of picking mRNAs from 5 cells in Gene X, we pick them from 5 cells in Gene X and Gene Y. The result could be, high mRNAs number in X can also have high number in Y, which is, there’s a positive trend where the values for X and Y increase together.

Three types of relationships §

1. Positive trend
2. Negative trend
3. No relationship and no trend

Covariance and correlation §

Covariance is needed for Correlation. Unlike covariance, correlation is not sensitive to the scale of the data.

How to calculate covariance §

$$\frac{\sum (x-\overline{x})(y-\overline{y})}{n-1}$$

A positive covariance: positive trends, and vice versa.

Understand and interpret the covariance value §

We can only sure of its trend by positive/negative. It’s hard to inteprete its high/low value because it all depends. Besides, covariance values are sensitive to the scale of the data.

Due to this reason, covariance itself is not so useful, but its other results (correlation or PCA) would be more interesting and useful.