SECTION 2.2 Summary

• The correlation $r$ measures the strength and direction of the linear association between two quantitative variables $x$ and $y$. Although you can calculate a correlation for any scatterplot, $r$ measures only straight-line relationships.
• Correlation indicates the direction of a linear relationship by its sign: $r>0$ for a positive association and $r<0$ for a negative association.
• Correlation always satisfies $-1\le r\le 1$ and indicates the strength of a relationship by how close it is to $-1$ or 1. Perfect correlation, $r=\pm 1$, occurs only when the points on a scatterplot lie exactly on a straight line.
• Correlation ignores the distinction between explanatory and response variables. The value of $r$ is not affected by changes in the unit of measurement of either variable. Correlation is not resistant, so outliers can greatly change the value of $r$.