To calculate the slope of the least-squares best-fit regression line, we use the formula for the slope $m$ in simple linear regression:

$m = \frac{n \sum{(x_i y_i)} - \sum{x_i} \sum{y_i}}{n \sum{(x_i^2)} - (\sum{x_i})^2}$

Where:

• $x_i$ represents the advertising budget
• $y_i$ represents the sales
• $n$ is the number of observations (in this case, $n = 10$)

We will now compute this step by step.

Step 1: Calculate the necessary sums:

• $\sum{x_i}$: Sum of advertising budgets
• $\sum{y_i}$: Sum of sales
• $\sum{(x_i^2)}$: Sum of squares of advertising budgets
• $\sum{(x_i y_i)}$: Sum of the product of advertising budgets and sales

Let’s calculate these values.The necessary sums are:

• $\sum{x_i} = 1,300,000$
• $\sum{y_i} = 7,927,000$
• $\sum{x_i^2} = 172,600,000,000$
• $\sum{x_i y_i} = 1,052,820,000,000$

Step 2: Substitute these values into the slope formula:

$m = \frac{n \sum{(x_i y_i)} - \sum{x_i} \sum{y_i}}{n \sum{(x_i^2)} - (\sum{x_i})^2}$

Now, let's compute the slope $m$.The slope of the least-squares best-fit regression line is $6.2$, rounded to the nearest hundredth.

Would you like more details or have any further questions? Here are five related questions that build on this concept:

1. How do we interpret the slope in this context?
2. What is the equation of the least-squares regression line?
3. How can we use this model to predict sales for a specific advertising budget?
4. What is the y-intercept of the least-squares regression line?
5. How do we compute the coefficient of determination (R²) for this regression?

Tip: The slope of a regression line represents the change in the dependent variable (sales) for every unit increase in the independent variable (advertising budget).