Final answer:
A correlation coefficient of r=1 implies perfect positive correlation, meaning the points all fall on an upward sloping line, both (b) and (c) are correct. It indicates a strong, direct, linear relationship between two variables.
Step-by-step explanation:
When dealing with the concept of the correlation coefficient, r, a value of r=1 indicates a perfect linear relationship between two variables. In this case, this means that every increase in the independent variable (x) is matched by a proportional increase in the dependent variable (y), and vice versa, resulting in a perfect positive linear relationship. Therefore, the correct answer to the question would be (b) The points all fall on a line, which slopes up, because this scenario describes a situation where there is a perfect positive correlation. Because the points all fall perfectly on a single line, they are as clustered as they can be along that line, thus making option (e) also correct, which states both (b) and (c) are correct. It is important to note that perfect correlation implies that all the data points lie exactly on a straight line with a positive slope, indicating that as one variable increases, so does the other.
It is also important to remember that correlation does not imply causation. This simply means that while the variables change together in a perfect correlation scenario, it does not indicate that one causes the other to change. The correlation coefficient, with its value between -1 and +1, can help in understanding the strength and direction of the linear relationship. A value of +1 is a strong indicator of a direct relationship, whilst a value of -1 would indicate a strong inverse relationship.