Sales of Volkswagens have grown steadily at auto dealerships in Nevada during the past 5 years​ (see table​ below).
                                                    
Year
Sales
1
455
2
495
3
520
4
563
5
595
 
Part 2
​a) Forecasted sales for year 6 using the trend projection​ (linear regression) method are enter your response here sales ​(round your response to one decimal​ place).

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.

Sales of Volkswagens have grown steadily at auto dealerships in Nevada during the past 5 years. Forecasted sales for year 6 using the trend projection (linear regression) method.

Learn how to forecast sales for year 6 using linear regression with a trend projection method. This problem focuses on calculating the best-fit line for sales growth over 5 years and projecting future sales. Suitable for students in Grades 10-12 with knowledge of statistics and linear regression.

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