It looks like you're working on a linear regression problem involving the mileage and selling price of a vehicle model, the Cadet. The regression equation provided is:

$y = 41.53 - 0.48x$ Where:

• $y$ represents the used selling price (in thousands of dollars),
• $x$ represents the mileage (in thousands of miles).

Let's break down the tasks:

(a) Interpreting the relationship between selling price and mileage:

• The first part of the question asks whether used selling prices greater than the mean are paired with mileages above or below the mean.

Given that the slope of the regression line is negative ($-0.48$), we know that as mileage increases, the selling price tends to decrease. Therefore, used selling prices greater than the mean of selling prices would generally correspond to mileages below the mean of mileages.

(b) Change in price for each additional 1,000 miles:

• The regression equation has a slope of $-0.48$. This means that for every increase of 1,000 miles in mileage, the selling price decreases by 0.48 thousand dollars (or $480). Therefore, an increase of one thousand miles results in a decrease of 0.48 thousand dollars in the used selling price.

Key points:

• Negative slope: Indicates an inverse relationship between mileage and selling price.
• Decrease of 0.48 thousand dollars for every additional thousand miles driven.

Would you like further details on how to calculate these relationships, or would you like me to go over how the mean affects the relationship?

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Related Questions:

1. How do you calculate the mean of a dataset and interpret it in the context of regression analysis?
2. What does the slope of a regression line tell you about the relationship between variables?
3. How can you predict a used car's price based on its mileage using the regression equation?
4. How would the interpretation change if the slope of the regression line were positive?
5. What is the significance of the intercept in a regression equation like $y = 41.53 - 0.48x$?

Tip:

In regression analysis, understanding the slope's sign is key to interpreting the relationship between the independent (x) and dependent (y) variables.