Final answer:
The linear correlation coefficient, r, ranges from -1 to +1, signaling the strength and direction of a relationship between two variables, but not causation. The correlation is weakest when r is closest to 0, indicating a negligible linear relationship.
Step-by-step explanation:
The properties of the linear correlation coefficient, commonly represented by r, include its range from -1 to +1, where it indicates the strength and direction of a linear relationship between two variables. The correlation coefficient can be positive or negative, indicating the respective direction of the relationship, but it is not an indicator of causation. Therefore, options B (represents the strength of the relationship between variables) and A (range from -1 to 0, which is partially correct as the complete range is -1 to +1) from the original question are true. However, the complete correct range needs to be considered. Option C (always positive) is incorrect as r can be negative, and option D (measures causation) is also incorrect because correlation does not imply causation.
Regarding the second question, the correlation coefficient indicates the weakest relationship when it is closest to 0 (option a), meaning there is little to no linear relationship between the variables being studied. A coefficient close to -1 or +1 indicates a stronger relationship, whether negative or positive.