What does a correlation coefficient of +1 imply?

A correlation coefficient of +1 indicates a perfect positive linear relationship between two variables. This means that as one variable increases, the other variable increases in a perfectly linear manner. For every increase in the first variable, there is a consistent and proportional increase in the second variable, demonstrating a strong and direct relationship.

In practical terms, if you were to plot these two variables on a scatterplot, all the data points would fall exactly along a straight line that slopes upwards. This absolute correlation signifies that the two variables move together in the same direction without any deviations, showcasing the strength and predictability of their relationship.

Other potential options describe scenarios that do not apply to a +1 correlation: for instance, a correlation of zero would imply no relationship at all, while a perfect negative linear relationship would be indicated by a correlation of -1, reflecting that as one variable increases, the other decreases. Moreover, the phrase "some degree of variability" does not capture the definitive and consistent relationship expressed by a +1 correlation.