Kovariancia

Kovariancia is a statistical measure that describes the extent to which two random variables change together. If two variables tend to increase or decrease together, they have a positive covariance. If one variable tends to increase as the other decreases, they have a negative covariance. If there is no consistent relationship between the variables, the covariance is close to zero.

Mathematically, the covariance between two random variables X and Y is defined as the expected value of the product of their deviations from their respective means. For a sample, it is calculated by summing the products of the differences of each observation from its mean and dividing by the number of observations minus one. A positive covariance indicates that when X is above its mean, Y is also likely to be above its mean, and vice versa. A negative covariance suggests that when X is above its mean, Y is likely to be below its mean, and vice versa.

The magnitude of the covariance is dependent on the scale of the variables. Therefore, it is often standardized to create the correlation coefficient, which ranges from -1 to +1 and provides a unitless measure of the linear relationship between two variables. Covariance is a fundamental concept in statistics and is used in various applications, including portfolio management, regression analysis, and machine learning. It is a key component in understanding the joint variability of multiple random variables.