To forecast the demand using simple linear regression, we first need to calculate the linear regression equation in the form:

$y = mx + b$

where:

• $y$ is the number of cups sold (dependent variable).
• $x$ is the price (independent variable).
• $m$ is the slope of the regression line.
• $b$ is the y-intercept.

Step 1: Organize the Data

Given dataTo forecast the demand using simple linear regression, we first need to calculate the linear regression equation in the form:

$y = mx + b$

where:

• $y$ is the number of cups sold (dependent variable).
• $x$ is the price (independent variable).
• $m$ is the slope of the regression line.
• $b$ is the y-intercept.

Step 1: Organize the Data

Given

Price ($x$)	Number Sold ($y$)
2.70	765
3.40	510
2.00	975
4.10	245
3.10	320
4.00	490

Step 2: Calculate the slope (m) and intercept (b)

We use the following formulas for the slope and intercept: $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$ $b = \frac{\sum y - m(\sum x)}{n}$ Where:

• $n$ is the number of data points.
• $\sum xy$ is the sum of the product of corresponding $x$ and $y$ values.
• $\sum x$ is the sum of the $x$ values.
• $\sum y$ is the sum of the $y$ values.
• $\sum x^2$ is the sum of the squares of the $x$ values.

Step 3: Apply Regression Equation to Predict Demand

Once we have the regression equation $y = mx + b$, we can substitute $x = 1.80$ (the price) into the equation to forecast the demand.

Let me calculate the values for you:The forecasted demand for mocha latte coffees, given a price of $1.80 per cup, is approximately 961.9 cups (rounded to one decimal place).

Would you like a detailed explanation of the calculations, or do you have any questions?

Here are 5 related questions that expand on this topic:

1. How would changing the price to $5.00 affect the forecasted demand?
2. What is the significance of the slope in a linear regression model?
3. How can we measure the accuracy of this linear regression forecast?
4. What would happen to the forecast if we included more historical data points?
5. How can other factors (besides price) be included in the demand model?

Tip: Linear regression is best suited when there is a linear relationship between the variables. Always visualize your data to confirm this before applying it.