Question

the radius and circumference of several objects were measured. which best describes the strength of the correlation, and what is true about the causation between the variables? radius and circumference of objects radius (in.) circumference (in.) 3 18.8 4 25.1 6 37.7 9 56.5 it is a weak positive correlation, and it is not likely causal. it is a strong positive correlation, and it is likely causal. it is a strong positive correlation, and it is not likely causal. it is a weak positive correlation, and it is likely causal.

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius.

Step2: Analyze the relationship

As the radius $r$ increases, the circumference $C$ increases proportionally since $C$ is directly - related to $r$ by a constant factor of $2\pi$. So, it is a strong positive correlation. Also, the radius of a circle causes its circumference (as per the formula), so it is a causal relationship.

Answer:

It is a strong positive correlation, and it is likely causal.