5.2.A—Interpret the correlation for a linear relationship

Interpret the correlation for a linear relationship.

• The correlation coefficient, r, summarizes the strength and direction of the linear association between two quantitative variables. The correlation coefficient r is unit-free and always between −1 and 1, inclusive. A negative correlation coefficient v alue indicates a negative association, and a positive correlation coefficient value indicates a positive association.
• The strength of the linear association is determined by how close the correlation coefficient is to −1 or 1. A value of r =0 indicates that there is no linear association. A value of r =- 1 or r =1 indicates that there is a perfect linear association.
• A correlation coefficient close to −1 or 1 does not necessarily mean that a linear model is appropriate.
• A perceived or real relationship between two variables does not mean that changes in one variable cause changes in the other. That is, correlation does not necessarily imply causation.