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In the image, you're working on a homework problem that involves identifying explanatory and response variables for various scenarios, creating scatterplots, and discussing the association between the variables.

The task asks you to:

1. **Determine the explanatory and response variables** in each pair of variables provided.
2. **Explain the relationship** between the variables, such as positive or negative association.
3. **Describe the scatterplot** that would result (the form, direction, and strength of the association).

The four scenarios provided are:
- **a)** Cell phone data plans for a person who wants a large file size: file size, cost.
- **b)** Lightning strikes by a person watching a lightning storm: distance from lightning, time delay of the thunder.
- **c)** A streetlight that you are approaching: apparent brightness, distance from it.
- **d)** Cars catalogued at a dealership: weight of car, age of owner.

Let's go through **scenario a)** for an example:
- **Explanatory variable:** File size
- **Response variable:** Cost
- **Reason:** The cost of a data plan is likely dependent on the file size you want to download, so file size (independent variable) influences cost (dependent variable).
- **Scatterplot Association:** Likely positive (as file size increases, cost increases).

Would you like me to continue with the other scenarios, or provide more detailed steps?

Here are some related questions:
1. What are explanatory and response variables in statistics?
2. How do you determine the direction of a scatterplot association?
3. What is the difference between a strong and weak association in scatterplots?
4. How can you visually identify positive and negative associations in scatterplots?
5. Can you explain the concept of correlation strength and its impact on a scatterplot?

**Tip:** Always ensure that the explanatory variable is the one that causes or predicts changes in the response variable.

Suppose you were to collect data for each pair of variables listed below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength.
a) Cell phone data plans for a person who wants a large file size: file size, cost
b) Lightning strikes by a person watching a lightning storm: distance from lightning, time delay of the thunder
c) A streetlight that you are approaching: its apparent brightness, your distance from it
d) Cars being catalogued at a dealership: weight of car, age of owner

Understand how to identify explanatory and response variables, form scatterplots, and describe associations. This problem involves key statistics concepts and is suitable for students in Grades 9-11.

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