Which scatterplot description best represents no linear correlation between $x$ and $y$?

• A. Points cluster tightly around a line that slopes downward from left to right.
• B. Points form a roughly circular cloud with no clear upward or downward trend as $x$ increases.
• C. Points follow a strong curved (U-shaped) pattern as $x$ increases.
• D. Points cluster tightly around a line that slopes upward from left to right.

Answer: (B)

Verified step by step guidance

1. Understand that linear correlation measures the strength and direction of a straight-line relationship between two variables, \(x\) and \(y\).
2. Recognize that a strong positive linear correlation means points cluster tightly around a line that slopes upward from left to right, indicating \(y\) increases as \(x\) increases.
3. Recognize that a strong negative linear correlation means points cluster tightly around a line that slopes downward from left to right, indicating \(y\) decreases as \(x\) increases.
4. Identify that no linear correlation means there is no clear linear pattern; the points do not cluster around any line with a positive or negative slope.
5. Therefore, the scatterplot that best represents no linear correlation is the one where points form a roughly circular cloud with no clear upward or downward trend as \(x\) increases.