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:  yˆt= 2,298-335Qtr1-1,446Qtr2+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.

For a given year, the demand in Quarter 4 is on average __________.

Multiple Choice

2,601 new copies

852 new copies

1,993 new copies

2,298 new copies

To determine the average demand in Quarter 4, we need to evaluate the given regression equation for the specific case where \( Qtr1 = 0 \), \( Qtr2 = 0 \), and \( Qtr3 = 0 \). These dummy variables are zero because Quarter 4 is the reference quarter (base case), meaning no adjustment is needed for the other quarters.

The regression equation provided is:

\[ \hat{y}_t = 2,298 - 335Qtr1 - 1,446Qtr2 + 303Qtr3 + 26t \]

For Quarter 4:

\[ Qtr1 = 0 \]
\[ Qtr2 = 0 \]
\[ Qtr3 = 0 \]

Plugging these values into the equation simplifies it to:

\[ \hat{y}_t = 2,298 + 26t \]

To find the average demand in Quarter 4, we only need the constant term for \( t = 1 \) because \( t \) represents the time period starting with \( t = 1 \). However, since the question asks for the average demand, the time component \( 26t \) is not relevant as it changes each period. 

Thus, the average demand for Quarter 4 is simply the constant term:

\[ \hat{y}_t = 2,298 \]

Therefore, the correct answer is:

2,298 new copies

Would you like further details or have any questions?

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Here are 8 relative questions for expansion:
1. How are dummy variables used in regression analysis?
2. What is the significance of the constant term in a regression equation?
3. How would the demand change if \( t \) were 5 years into the data collection period?
4. What is the role of time series data in forecasting?
5. Can the coefficients of dummy variables be interpreted similarly to other coefficients in regression analysis?
6. How does seasonality affect demand forecasting?
7. What methods can be used to validate the accuracy of the regression model?
8. How would the demand forecast differ for Quarter 2?

**Tip:** In regression analysis, interpreting the coefficients of dummy variables requires understanding the reference category they compare against, which is critical for accurate predictions.

Explore how regression analysis predicts quarterly demand using a specified equation. Understand the role of dummy variables and the constant term in forecasting. Detailed solution provided for finding average demand in Quarter 4.

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