In the context of scatterplots, correlation occurs when which of the following is true about two variables?

• A. The points in the scatterplot show a consistent upward or downward trend, indicating an association between the variables.
• B. The data points form a perfectly horizontal line, showing no change in one variable as the other changes.
• C. Both variables are measured in the same units.
• D. The two variables have the same mean value.

Answer: (A)

Verified step by step guidance

1. Understand that correlation measures the strength and direction of a linear relationship between two variables.
2. Recognize that in a scatterplot, a positive correlation is shown by points forming a consistent upward trend, while a negative correlation is shown by a consistent downward trend.
3. Note that if the points form a perfectly horizontal line, it means there is no change in one variable as the other changes, indicating no correlation.
4. Realize that correlation does not depend on the units of measurement or the means of the variables, but rather on how the variables change together.
5. Conclude that correlation occurs when the points in the scatterplot show a consistent upward or downward trend, indicating an association between the variables.