Based on quarterly data collected over the last four years, the following regression equation was found to forecast the quarterly demand for the number of new copies of an economics textbook:  yˆt= 3,305-665Qtr1-1,335Qtr2+305Qtr3, where Qtr1, Qtr2, and Qtr3 are dummy variables corresponding to Quarters 1, 2, and 3.

The demand forecast for Quarter 2 of the next year is __________

Multiple Choice

1,970

2,640

3,305

3,610

To find the demand forecast for Quarter 2 of the next year, we will use the given regression equation:

\[ \hat{y_t} = 3,305 - 665Qtr1 - 1,335Qtr2 + 305Qtr3 \]

For Quarter 2:
- \( Qtr1 = 0 \)
- \( Qtr2 = 1 \)
- \( Qtr3 = 0 \)

Substituting these values into the equation:

\[ \hat{y_t} = 3,305 - 665(0) - 1,335(1) + 305(0) \]

Simplifying this:

\[ \hat{y_t} = 3,305 - 1,335 \]

\[ \hat{y_t} = 1,970 \]

So, the demand forecast for Quarter 2 of the next year is \( \boxed{1,970} \).

Would you like more details or have any questions about this problem? Here are 8 additional questions related to this topic:

1. How do dummy variables help in regression analysis?
2. What is the interpretation of the coefficient -665 for \( Qtr1 \) in the regression equation?
3. Why is it important to check the statistical significance of the regression coefficients?
4. How would you interpret a positive coefficient for \( Qtr3 \) in the context of this regression equation?
5. How can seasonal variations be accounted for in regression models?
6. What are some potential limitations of using a regression model for forecasting?
7. How would the forecast change if the regression equation included interaction terms between quarters?
8. Can this regression model be used for long-term forecasting? Why or why not?

**Tip:** Always verify the assumptions of your regression model, such as linearity, independence, homoscedasticity, and normality of residuals, to ensure the validity of your forecasts.

Learn how to forecast demand using regression analysis with a detailed example. Understand the application of dummy variables and regression equations in predicting quarterly demand. Suitable for undergraduate students and researchers.

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