Standard deviation line

In statistics, the standard deviation line (or SD line) marks points on a scatter plot that are an equal number of standard deviations away from the average in each dimension. For example, in a 2-dimensional scatter diagram with variables ${\displaystyle x}$ and ${\displaystyle y}$, points that are 1 standard deviation away from the mean of ${\displaystyle x}$ and also 1 standard deviation away from the mean of ${\displaystyle y}$ are on the SD line.^[1] The SD line is a useful visual tool since points in a scatter diagram tend to cluster around it,^[1] more or less tightly depending on their correlation.

Plot of the standard deviation line (SD line), dashed, and the regression line, solid, for a scatter diagram of 20 points.