$$Which of the following scatterplots shows the weakest positive linear association between two variables?$$

• A. $$A scatterplot where the points are widely scattered but generally trend upward from left to right.$$
• B. $$A scatterplot where the points form a tight cluster along a line sloping downward from left to right.$$
• C. $$A scatterplot where the points are randomly scattered with no apparent trend.$$
• D. $$A scatterplot where the points form a tight cluster along a line sloping upward from left to right.$$

Answer: (A)

Verified step by step guidance

1. Step 1: Understand what a positive linear association means. It indicates that as one variable increases, the other variable tends to increase as well, which is visually represented by points trending upward from left to right in a scatterplot.
2. Step 2: Recognize that the strength of a linear association depends on how closely the points cluster around a straight line. A tight cluster indicates a strong association, while widely scattered points indicate a weaker association.
3. Step 3: Identify that a scatterplot with points widely scattered but generally trending upward shows a positive linear association, but it is weaker because the points are not tightly clustered.
4. Step 4: Compare this to other options: a tight cluster along a line sloping upward shows a strong positive association; a tight cluster sloping downward shows a strong negative association; and random scatter with no trend shows no linear association.
5. Step 5: Conclude that the scatterplot with points widely scattered but generally trending upward represents the weakest positive linear association among the options.