To forecast the sales for year 6 using the trend projection (linear regression) method, we first need to calculate the equation of the best-fit line (linear regression line). The linear regression equation is typically written as:

$\hat{y} = a + bx$

Where:

• $\hat{y}$ is the forecasted sales,
• $a$ is the intercept,
• $b$ is the slope of the line,
• $x$ is the year.

The formula for the slope $b$ is:

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

The formula for the intercept $a$ is:

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

Steps:

1. Use the given data to compute the sums:
   • Sum of the years $\sum x$
   • Sum of the sales $\sum y$
   • Sum of the product of the years and sales $\sum xy$
   • Sum of the square of the years $\sum x^2$
2. Plug these values into the formulas for $a$ and $b$.
3. Use the linear regression equation to forecast sales for year 6 by substituting $x = 6$.

Let me compute that for you.The forecasted sales for year 6 using the trend projection (linear regression) method are 630.0 units.

Would you like more details on how this was calculated or have any other questions?

Here are 5 related questions to explore further:

1. How do you interpret the slope in a linear regression model?
2. What happens if you have more than 5 years of sales data? How does it affect the forecast?
3. Can this method be used for non-linear trends in sales growth?
4. What is the significance of the intercept in the sales forecast?
5. How does a high variation in past sales impact the accuracy of a trend projection?

Tip: In linear regression, the slope $b$ indicates the average change in sales per year.