In a scatterplot, which description best represents a positive correlation between $x$ and $y$?

• A. There is no consistent upward or downward pattern; the points form a random cloud.
• B. As $x$ increases, $y$ tends to increase (an upward trend from left to right).
• C. All points fall exactly on a vertical line (the same $x$ value for all observations).
• D. As $x$ increases, $y$ tends to decrease (a downward trend from left to right).

Answer: (B)

Verified step by step guidance

1. Understand what a positive correlation means in the context of a scatterplot: it indicates that as the values of variable \(x\) increase, the values of variable \(y\) also tend to increase.
2. Visualize the scatterplot: a positive correlation will show points that generally move upward from left to right, forming an upward trend.
3. Eliminate options that do not fit this pattern: a random cloud of points shows no correlation, points on a vertical line mean no variation in \(x\), and a downward trend indicates a negative correlation.
4. Recognize that the correct description for a positive correlation is: 'As \(x\) increases, \(y\) tends to increase (an upward trend from left to right)'.
5. Summarize that positive correlation is about the direction of the relationship between \(x\) and \(y\), specifically that both variables increase together.