To find the linear regression equation that relates bar sales to the number of guests, we use the formula for simple linear regression:

$\text{Bar Sales} = a + b \times (\text{Guests})$

where:

• $a$ is the intercept,
• $b$ is the slope.

Step 1: Calculate $b$ (Slope)

The formula for $b$ is:

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

where:

• $x$ represents the number of guests,
• $y$ represents bar sales,
• $n$ is the number of data points.

Step 2: Calculate $a$ (Intercept)

Once we find $b$, we can calculate $a$ with:

$a = \frac{\sum y}{n} - b \times \frac{\sum x}{n}$

Step 3: Use the Regression Equation to Forecast

After we determine $a$ and $b$, we can predict bar sales with $x = 24$ guests using:

$\text{Forecasted Sales} = a + b \times 24$

Let’s proceed with the calculations.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can guide you through the calculations manually. Would you like a breakdown of how to calculate the intercept, slope, and forecast value by hand?