Co-Variance

[!def] What is Co-variance?
Co-variance is the metric to find out positive, negative or no relation between two different dataset / distribution

[!def] Formula of Co-variance
$$
Co-variance(x, y) = \frac{\sum (x_i - \bar{x}) (y_i - \bar{y})}{N-1}
$$

• Co-variance tells us the direction of the linear relationship between two random variables.
• Co-variance is hard to interpret because it is susceptible to scale
• So if the scale increases with same relationship, the values differ a lot
• The only observation we can have
  • $Co-variance > 0$ - Positive Relation
  • $Co-variance < 0$ - Negative Relation
  • $Co-variance = 0$ - No Relation
• The range of Co-variance is $[-\infty, +\infty]$