näytekovarianssista

Sample covariance, or näytekovarianssi in Finnish, is a statistical measure that quantifies the degree to which two random variables change together in a sample. It is calculated from a set of paired observations. A positive sample covariance indicates that as one variable increases, the other tends to increase as well. Conversely, a negative sample covariance suggests that as one variable increases, the other tends to decrease. A sample covariance close to zero implies a weak linear relationship between the two variables.

The formula for sample covariance between two variables X and Y, based on n paired observations (x_i, y_i), is given by:

Cov(X, Y) = Σ[(x_i - x̄)(y_i - ȳ)] / (n - 1)

where x̄ and ȳ are the sample means of X and Y, respectively, and n is the number of observations. The denominator (n - 1) is used for sample covariance to provide an unbiased estimate of the population covariance.

Unlike correlation, which is a standardized measure and ranges between -1 and +1, the sample covariance is not standardized and its magnitude depends on the units of the variables. Therefore, interpreting the absolute value of sample covariance can be difficult without considering the scale of the data. Sample covariance is a fundamental concept in statistics, used in various analyses including regression, portfolio management, and understanding relationships within datasets.