To find the slope of the least squares regression line, we can use the following formula:

$\text{Slope} = b = \frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2}$

Where:

• $n$ is the number of data points,
• $x$ and $y$ are the mileage (in thousands) and the used selling price (in thousands of dollars), respectively,
• $xy$ is the product of each $x$ and $y$.

Step 1: Summing the Data

We need to compute the following sums:

• $\sum x$ (the sum of all mileages),
• $\sum y$ (the sum of all used selling prices),
• $\sum xy$ (the sum of all products $xy$),
• $\sum x^2$ (the sum of the squares of each $x$).

Step 2: Calculate the slope $b$

Using the values obtained, we will plug them into the formula to compute the slope.

Let's perform the calculations.

Given Data:

Let's calculate the required sums and the slope.The slope of the least squares regression line for the given data is approximately $-2.82$, rounded to two decimal places.

This negative slope indicates that as the mileage of the vehicle increases, the selling price tends to decrease.

Do you want more details or have any questions?

Here are 5 related questions to explore:

1. How can we interpret the slope of the regression line in practical terms?
2. What does it mean if the slope of the regression line is positive?
3. How would you calculate the intercept of the regression line?
4. How does the magnitude of the slope affect the steepness of the regression line?
5. Can the regression line be used to predict future values? If so, how reliable are those predictions?

Tip: The slope of the regression line represents the average change in the dependent variable (price) for each one-unit change in the independent variable (mileage).