Korrelasjonssummen

Korrelasjonssummen, often translated as correlation sum or scatter sum, is a statistical measure used to quantify the linear relationship between two variables. It is closely related to the Pearson correlation coefficient, but it is not normalized. The correlation sum is calculated by multiplying the sum of the products of the deviations of each variable from its mean by the number of data points. Specifically, if X and Y are two variables with data points $(x_i, y_i)$ for $i = 1, \dots, n$, their means are $\bar{x}$ and $\bar{y}$, then the correlation sum is given by $\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})$. A positive correlation sum indicates that as one variable increases, the other tends to increase as well. A negative correlation sum suggests that as one variable increases, the other tends to decrease. A correlation sum close to zero implies a weak or no linear relationship between the two variables. Unlike the Pearson correlation coefficient, which ranges from -1 to +1, the correlation sum can take on any real value. Its magnitude depends on the scale and variability of the data. Therefore, while it indicates the direction and strength of the linear association, it does not provide a standardized measure of the relationship independent of the data's units.