Given a scatterplot of $\mathrm{price}$ versus $\mathrm{mileage}$ for $20$ used sedans, what type of correlation would you most likely expect to observe between $\mathrm{price}$ and $\mathrm{mileage}$?

• A. A positive correlation, where higher $\mathrm{mileage}$ is associated with higher $\mathrm{price}$
• B. No correlation between $\mathrm{mileage}$ and $\mathrm{price}$
• C. A perfect positive correlation
• D. A negative correlation, where higher $\mathrm{mileage}$ is associated with lower $\mathrm{price}$

Answer: (D)

Verified step by step guidance

1. Understand the variables involved: 'price' is the dependent variable (what we want to explain or predict), and 'mileage' is the independent variable (a factor that might influence price).
2. Recall the typical relationship between mileage and price for used cars: generally, as mileage increases, the car is considered more used or worn, which tends to decrease its price.
3. Define correlation: it measures the strength and direction of a linear relationship between two variables. A positive correlation means both variables increase together, a negative correlation means one increases while the other decreases, and no correlation means no linear relationship.
4. Based on the typical relationship, expect a negative correlation between price and mileage, meaning as mileage goes up, price tends to go down.
5. Visualize this on a scatterplot: points would trend downward from left to right, indicating a negative slope and thus a negative correlation.