Answer :
Final answer:
The linear correlation coefficient r = 0.523 corresponds to a Weak positive correlation, indicating a tendency for the variables to increase together but not a strong enough relationship to be considered tightly clustered around a line.
option b is correct answer.
Explanation:
In order to match the linear correlation coefficient to the scatter diagram with r = 0.523, we need to understand the range of values that the correlation coefficient can take and what they signify. The correlation coefficient, r, is a measure that tells us how strong a linear relationship exists between two variables x and y. This coefficient can have a value between -1 and +1. A positive correlation occurs when x and y tend to increase together; when r is close to +1, it indicates a strong positive correlation, and when it is closer to 0 but positive, it indicates a weak positive correlation. Conversely, a negative correlation means as x increases, y tends to decrease, and vice-versa; a value close to -1 indicates a strong negative correlation, and a value closer to 0 but negative indicates a weak negative correlation.
Given that r = 0.523 is a positive value that is more than half way between 0 and 1, but not close enough to 1 to be considered strong, the appropriate match for the scatter diagram is B. Weak positive correlation. This means that while there is a tendency for y to increase as x increases, the data points are not tightly clustered around a line, and the relationship is not very strong.
