Which of the following relationships would most likely have the weakest correlation?

• A. A person's shoe size and their intelligence quotient ($\mathrm{IQ}$)
• B. The amount of rainfall and the water level in a river
• C. The number of hours studied and exam scores
• D. The outside temperature and the number of ice creams sold

Answer: (A)

Verified step by step guidance

1. Understand what correlation measures: it quantifies the strength and direction of a linear relationship between two variables, ranging from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear correlation.
2. Analyze each pair of variables to assess the expected relationship: for example, the number of hours studied and exam scores are likely positively correlated because more study time generally leads to higher scores.
3. Consider the nature of the variables in each pair: some pairs, like outside temperature and ice cream sales, tend to have a positive correlation because warmer weather often increases ice cream consumption.
4. Evaluate pairs where the relationship is less direct or logical: for instance, a person's shoe size and their IQ are unlikely to have any meaningful linear relationship, suggesting a correlation close to zero.
5. Conclude that the pair with the weakest correlation is the one where the variables are least likely to influence each other or have any systematic association, which in this case is shoe size and IQ.