Question

the radius and circumference of several objects were measured.

radius and circumference of objects

radius (in)	circumference (in)
4	25.1
6	37.7
9	56.5

which best describes the strength of the correlation, and what is true about the causation between the variables?

• it is a weak positive correlation, and it is not likely causal.
• it is a weak positive correlation, and it is likely causal.
• it is a strong positive correlation, and it is not likely causal.
• it is a strong positive correlation, and it is likely causal.

Explanation:

Step1: Analyze correlation trend

As radius increases, circumference increases. Calculate the ratio of circumference to radius for each pair:
$\frac{18.8}{3} \approx 6.27$, $\frac{25.1}{4} \approx 6.28$, $\frac{37.7}{6} \approx 6.28$, $\frac{56.5}{9} \approx 6.28$
These values are very close to $2\pi \approx 6.28$, showing an almost perfect linear relationship.

Step2: Evaluate causation

Circumference $C = 2\pi r$ by definition, so a larger radius directly causes a larger circumference.

Answer:

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