When constructing a scatterplot, what does a correlation coefficient of r = -1 indicate?

A correlation coefficient of ( r = -1 ) indicates a perfect negative correlation between the two variables being analyzed. This means that as one variable increases, the other variable decreases in a perfectly linear manner. In graphical terms, if you were to construct a scatterplot based on these two variables, all the points would lie exactly along a straight line that slopes downward.

In this scenario, not only does the correlation show a consistent relationship, but it does so at the most extreme level of negative association possible. The negative sign indicates that the relationship is inversely proportional. This is distinct from perfect positive correlation, which would be represented by ( r = 1), where both variables move in the same direction.

The values of ( r ) that indicate no correlation (which is ( r = 0 )) or any measure of positive correlation do not apply in this context, as they would reflect relationships that are not aligned in a perfectly linear manner, thus distinguishing the option that refers to perfect negative correlation as the accurate interpretation of the given coefficient.