In this problem, you are asked to determine the explanatory and response variables for a scatterplot involving college freshmen's shoe size and grade point average (GPA).

Explanation:

The explanatory variable (independent variable) typically influences or helps to predict the response variable (dependent variable).

Evaluating the choices:

• Option A suggests either variable could be explanatory or response, which is not accurate since shoe size and GPA likely have no causal relationship.
• Option B suggests shoe size as explanatory and GPA as the response. This implies that shoe size could predict GPA, which is not a reasonable assumption.
• Option C suggests GPA as explanatory and shoe size as the response, implying GPA predicts shoe size, which is also unlikely.
• Option D (correct answer) states that it’s not possible to assign explanatory or response variables because the variables are unrelated (no logical or predictive relationship between shoe size and GPA).

This option fits best, as there's no inherent cause-and-effect or predictive relationship expected between shoe size and GPA.

Would you like further details or have specific questions?

Here are 5 related questions:

1. How do you determine which variable is explanatory and which is the response?
2. Can correlation exist without causation? Explain with examples.
3. What factors affect the strength of correlation between two variables?
4. Why is it important to distinguish between explanatory and response variables?
5. How can you visually interpret correlation using scatterplots?

Tip: Always question whether there is a logical basis for correlation before assigning variable roles.