Questions: Suppose there is a strong positive correlation between v and w. Which of the following must be true? A. When v increases, w tends to decrease. B. When v increases, w tends to increase. C. An increase in v causes w to decrease. D. An increase in v causes w to increase.

Solution Steps

To determine the correct statement about the relationship between \( v \) and \( w \) given a strong positive correlation, we need to understand the implications of correlation. A strong positive correlation indicates that as one variable increases, the other variable tends to increase as well. This does not imply causation, only a tendency or association.

A strong positive correlation between two variables, \( v \) and \( w \), implies that as one variable increases, the other variable tends to increase as well. This relationship is characterized by a correlation coefficient close to +1.

Given the options:

• A: When \( v \) increases, \( w \) tends to decrease.
• B: When \( v \) increases, \( w \) tends to increase.
• C: An increase in \( v \) causes \( w \) to decrease.
• D: An increase in \( v \) causes \( w \) to increase.

Options A and C suggest a negative relationship, which contradicts the given strong positive correlation. Options C and D imply causation, which is not necessarily true with correlation alone.

The correct interpretation of a strong positive correlation is that when \( v \) increases, \( w \) tends to increase. This aligns with option B.

Final Answer