The question asks about the best interpretation of a slope of 0.031 in the context of a scatterplot showing the relationship between average income (in dollars) and rent for a 2-bedroom apartment.

The slope of 0.031 indicates how much the rent increases for each additional dollar of average income. The correct interpretation should relate to how rent changes as income changes.

Let's evaluate the answer choices:

• A) "On average, each $1 increase in average income was associated with a $0.031 increase in average rent."
  This is a correct interpretation of the slope. The slope of 0.031 means that for every dollar increase in income, rent increases by $0.031.

• B) "On average, each $0.031 increase in average income was associated with 1 point increase in average rent."
  This is incorrect. It incorrectly flips the relationship between rent and income. It implies that a small increase in income causes a large increase in rent, which doesn't match the slope of 0.031.

• C) "We would predict a city whose average income was $0 to have an average rent of $0.031."
  This is incorrect because the intercept of the regression line, not the slope, would give the rent when income is zero. The slope describes the change, not the starting value.

• D) "We would predict a city whose average income was $0 to have an average rent of $0."
  This is also incorrect, as it misinterprets the role of the slope and ignores the intercept, which would likely not be zero.

Conclusion:

The best interpretation is A.

Would you like more details or have any questions? Here are 5 questions you might explore:

1. How is the slope of a regression line calculated?
2. What does the intercept in a linear regression represent?
3. How do you interpret the goodness of fit (R²) in a regression model?
4. Can the slope of a regression line be negative? What does that mean?
5. How can outliers affect the slope of a regression line?

Tip: In a regression, the slope represents the rate of change between two variables, indicating how much the dependent variable changes for each unit increase in the independent variable.