Based on quarterly data collected over the last five years, the following regression equation was found to forecast the quarterly demand for the number of new copies of a business statistics textbook:  yˆ= 2,298 − 6,635Qtr1 − 1,446Qtr2 + 303Qtr3 + 26t, where Qtr1, Qtr2, and Qtr3 are dummy variables corresponding to Quarters 1, 2, and 3, and t = time period starting with t = 1.

The demand forecast for the second quarter of the next year is __________ .

Multiple Choice

2,922

3,199

1,424

2,181

To forecast the demand for the second quarter of the next year using the given regression equation \( \hat{y} = 2,298 - 6,635 \text{Qtr1} - 1,446 \text{Qtr2} + 303 \text{Qtr3} + 26t \), we need to determine the values of the dummy variables and the time period \( t \).

For the second quarter of the next year:
- \( \text{Qtr1} = 0 \) (since it is not the first quarter)
- \( \text{Qtr2} = 1 \) (since it is the second quarter)
- \( \text{Qtr3} = 0 \) (since it is not the third quarter)

To find the value of \( t \):
- The data was collected over the last five years, which is 5 years * 4 quarters/year = 20 quarters.
- The next year will be the 21st to 24th quarters.
- For the second quarter of the next year, \( t = 22 \).

Plugging these values into the regression equation:

\[
\hat{y} = 2,298 - 6,635(0) - 1,446(1) + 303(0) + 26(22)
\]

Simplify the equation:

\[
\hat{y} = 2,298 - 1,446 + 26 \cdot 22
\]

Calculate the term involving \( t \):

\[
26 \cdot 22 = 572
\]

Combine all terms:

\[
\hat{y} = 2,298 - 1,446 + 572
\]

\[
\hat{y} = 1,424
\]

So, the demand forecast for the second quarter of the next year is:

\[
\boxed{1,424}
\]

Do you have any questions or would you like more details?

Here are 8 relative questions expanding on the information:

1. What are dummy variables and how are they used in regression analysis?
2. How do you interpret the coefficients of dummy variables in a regression equation?
3. What is the significance of the time variable \( t \) in the regression equation?
4. How would the forecast change if it were for a different quarter of the next year?
5. What methods are used to collect quarterly data for such regression analysis?
6. How can the accuracy of this regression model be evaluated?
7. What are some potential limitations of using this regression model for forecasting?
8. How does seasonality affect the demand forecast in time series analysis?

**Tip:** When interpreting regression coefficients, it's crucial to consider the context and the units of the variables to understand their real-world implications accurately.

Explore how to forecast demand using a regression equation based on quarterly data collected over the last five years. This example focuses on business statistics, dummy variables, and time series analysis. Learn how to apply regression analysis to predict future demand with step-by-step calculations.

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