Which scatterplot pattern indicates a strong linear relationship?

Which scatterplot pattern indicates a strong linear relationship?

• A. Points widely scattered
• B. All points identical
• C. Points forming a circle
• D. Points tightly clustered around a straight line

Answer: (D)

The main idea is how tightly data points align to a straight line indicates the strength of a linear relationship. When the scatterplot shows a tight cluster of points hugging a straight line, changes in one variable reliably accompany changes in the other, so you can predict one variable from the other with little error and the correlation is near either +1 or -1. This is what strong linear relationship looks like. If the points are widely scattered, there isn’t a consistent linear pattern, so the linear relationship is weak or absent. If all points are identical, there’s no variation to reveal any relationship at all. A circular or curved pattern signals a nonlinear relationship, where a straight line would misrepresent the relationship. So the pattern with points tightly clustered around a straight line best indicates a strong linear relationship.

The main idea is how tightly data points align to a straight line indicates the strength of a linear relationship. When the scatterplot shows a tight cluster of points hugging a straight line, changes in one variable reliably accompany changes in the other, so you can predict one variable from the other with little error and the correlation is near either +1 or -1. This is what strong linear relationship looks like.

If the points are widely scattered, there isn’t a consistent linear pattern, so the linear relationship is weak or absent. If all points are identical, there’s no variation to reveal any relationship at all. A circular or curved pattern signals a nonlinear relationship, where a straight line would misrepresent the relationship.

So the pattern with points tightly clustered around a straight line best indicates a strong linear relationship.