Which of the following defines a linear correlation?

The definition of a linear correlation accurately focuses on the relationship between two variables that can exhibit either a positive or negative pattern. When there is a positive linear correlation, as one variable increases, the other variable also increases. Conversely, a negative linear correlation indicates that as one variable increases, the other variable decreases. In both cases, the relationship can be visually represented by a straight line on a scatter plot, which signifies consistency in the relationship between the two variables. This characteristic helps researchers understand and interpret how changes in one variable are related to changes in another.

The other options fall short of defining linear correlation appropriately. A relationship where variables do not affect each other describes a situation of no correlation at all, while complex interactions involving multiple variables go beyond the simple two-variable relationship that defines linear correlation. Lastly, a relationship that changes direction with each observation indicates a non-linear or unpredictable pattern, which is contrary to the consistent nature of linear correlation.