Which of the following best describes the scatterplot of a car's value compared to the age of the car?

• A. There is a negative association; as the age of the car increases, its value tends to decrease.
• B. There is no association; the value of the car is unrelated to its age.
• C. The scatterplot shows a perfect linear relationship with a positive slope $m>0$.
• D. There is a positive association; as the age of the car increases, its value tends to increase.

Answer: (A)

Verified step by step guidance

1. Understand what a scatterplot represents: it is a graphical display of two quantitative variables, where each point corresponds to one observation with coordinates (x, y). In this case, the variables are the age of the car (x-axis) and the value of the car (y-axis).
2. Recall the meaning of association in a scatterplot: a positive association means that as one variable increases, the other also increases; a negative association means that as one variable increases, the other decreases; no association means there is no clear pattern or relationship between the variables.
3. Consider the real-world relationship between a car's age and its value: typically, as a car gets older, its value tends to decrease due to depreciation, wear and tear, and obsolescence.
4. Translate this understanding into the scatterplot context: points would generally trend downward from left to right, indicating a negative association between age and value.
5. Evaluate the answer choices based on this reasoning: the best description is that there is a negative association; as the age of the car increases, its value tends to decrease.