Let's break down and address the questions based on the provided regression line and dataLet's break down and address the questions based on the provided regression line and

The given regression equation is: $y = 41.77 - 0.50x$ where $y$ represents the used selling price in thousands of dollars, and $x$ represents the mileage in thousands of miles.

Part (A)

The question is asking about the relationship between used selling prices that are greater than the mean of the used selling prices and their corresponding mileages.

To answer this, let's first understand the relationship between mileage and price based on the regression line. The regression line $y = 41.77 - 0.50x$ tells us that as mileage increases, the used selling price decreases, with a slope of $-0.50$.

Given this, used selling prices that are greater than the mean are likely to be paired with mileages lower than the mean mileage because higher prices tend to occur with lower mileages due to the negative relationship (as mileage increases, price decreases).

Answer: For these data, used selling prices that are greater than the mean of the used selling prices tend to be paired with mileages that are lower than the mean mileages.

Part (B)

The regression equation is: $y = 41.77 - 0.50x$ The slope of the regression line is $-0.50$. The slope tells us how much the used selling price decreases when mileage increases by 1,000 miles.

Answer: According to the regression equation, for an increase of 1,000 miles in Cadet mileage, there is a corresponding decrease of 0.50 thousand dollars (or $500) in the used selling price.

Would you like more details on this solution, or do you have any other questions?

Relative questions:

1. How do you calculate the mean mileage and mean selling price from the given data?
2. What are the implications of a negative slope in a regression line?
3. How would you interpret the intercept $41.77$ in this context?
4. How could you determine if the regression line is a good fit for the data?
5. What additional information could improve the prediction of the used selling price?

Tip:

When interpreting the slope of a regression line, remember it represents the rate of change between the two variables.